HMH Into Math Texas, Grade 1

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

The program materials include multiple scope and sequence resources that clearly outline the Texas Essential Knowledge and Skills (TEKS), English Language Proficiency Standards (ELPS), and concepts taught throughout the course. The materials include yearlong scope and sequence documents located within the Program Overview and Implementation Guide.


The scope and sequence charts show how each module and lesson aligns with the TEKS and ELPS and identify the concepts taught throughout the instructional year. Additional program materials support this alignment through correlations with the TEKS and ELPS, and the “Correlations by Lesson” documents break down concepts taught by module. The scope and sequence documents in the “Discover” tab, found under the program dropdown, outline the TEKS, ELPS, and lesson concepts that support instructional planning and pacing.

Evaluation for 1.1b
Materials include suggested pacing (pacing guide/calendar) to support effective implementation for various instructional calendars (e.g., varying numbers of instructional days - 165, 180, 210).

The materials include “Scope and Sequence with Yearly Pacing” guidance for 165-day and 210-day instructional calendars. This resource “moves step by step through each module and shows how each module covers the instructional sequence and standards, and then lists each Module Review and Module Test.” These options support effective implementation while remaining aligned with the TEKS, ELPS, and course concepts.

The materials provide guidance on extending the 165-day pacing calendar to 180 days by adding “one extra day to each lesson where a Readiness Standard is first taught.” Educators can use the extra day to provide targeted reinforcement, practice, or challenges based on formative assessments, quick checks, and observations.

Evaluation for 1.1c
Materials include an explanation for the rationale of unit order as well as how concepts to be learned connect throughout the course.

The Teacher’s Guide includes a “Module Order Rationale” that explains the intentional sequence of units and lessons throughout the course. The “Teacher Background” section of each unit explains the lesson order and describes how concepts build across modules to support mathematical understanding.

For example, the “Module Order Rationale” describes that “modules 8 through 10 apply the skills developed in modules 6 and 7 as students explain strategies for adding and subtracting, generate and solve problems, and then determine the values of collections of coins.”

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

The materials guide educators on internalizing each unit and lesson through comprehensive planning supports, structured instructional routines, and embedded educator guidance throughout the materials. The Teacher’s Guide reviews the standards, outlines what students will learn in each module, explains the module flow, identifies the TEKS and ELPS, and includes background information to support instructional preparation and lesson internalization.

The materials include resources that help educators understand the sequence of learning within each module and prepare for daily instruction. The “Before You Teach” sections outline the mathematical understanding needed for each lesson and explain what students will learn. Tools such as the “Editable Lesson Plan,” pacing guidance, module flow charts, and explanations on lesson sequencing support educator preparation.

The “Step Through a Module” section of the Implementation Guide supports educators as they internalize module and lesson components, while the “Teacher Background” sections include mathematical rationale, examples, summaries, and explanations of the importance of concepts to deepen educator understanding before instruction. The materials also include the “Module Internalization Tool” and “Lesson Internalization Tool,” which provide guiding questions such as “What concepts, strategies, or procedures will students learn?” and “What do the lesson and language objectives expect from students?” Educators may use these tools individually or collaboratively for notetaking or discussion guides as they prepare for and internalize upcoming modules and lessons.

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

The materials include resources and guidance documents for instructional leaders to support educators in implementing the program as designed. The materials provide resources such as “Professional Learning” and the “Coaching Guide,” which include instructional support, implementation guidance, pacing recommendations, and professional learning resources to assist leaders in supporting effective program use.

The materials include tools that support classroom observations, reflection, and coaching conversations. For example, the “Look-Fors and Reflection Guide” provides classroom observation indicators, implementation expectations, reflection questions, and suggested discussion topics to help instructional leaders monitor instruction and support educator planning.

The materials include look-for checklists designed for the first 30 days of instruction, along with reflection tools and guiding questions that support classroom visits, targeted feedback, and ongoing instructional implementation conversations with educators.

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

The Teacher’s Guide includes comprehensive module overviews that provide background knowledge and academic vocabulary necessary to teach the module’s concepts effectively. The “Module Planning” sections include guidance on the mathematical focus, instructional progression, and vocabulary connected to the learning goals. For example, module 4, “Solve Problems with Sets Within 20,” includes guidance on prior learning and future learning connections that support educator understanding of how concepts connect across learning.

The module planning sections support educators in understanding key mathematical language. For example, the planning section for module 4, “Explore Numbers to 10,” directs educators to use the “Words to Learn (WTL)” routine and the module’s vocabulary cards to help students master review vocabulary and new vocabulary terms. The materials identify vocabulary connected to specific lessons, including join, sets, difference, minus, separate, and subtract.

The Teacher’s Guide includes a glossary of academic vocabulary and mathematical definitions so educators can effectively facilitate mathematical discussions and instruction. The materials state that “the Glossary aims to provide teachers with specific mathematical definitions to support their understanding of the mathematics in their lessons.”

Evaluation for 1.2b
Materials contain supports for families in both Spanish and English for each unit with suggestions on supporting the progress of their student.

The materials include a “Family Letter” in English and Spanish for each module. This letter provides an overview of the module, academic vocabulary, and a home activity to support learning. For example, one home activity in module 20 suggests that caregivers “discuss with your child something they might want, but do not need for breakfast.”

Evaluation for 1.3a
Materials include comprehensive, structured, detailed lesson plans that include daily objectives, questions, tasks, materials, and instructional assessments required to meet the content and language standards of the lesson (aligned with the TEKS and the ELPS).

The materials include comprehensive, structured, detailed lesson plans with daily objectives, questions, tasks, materials, and instructional assessments required to meet the lesson’s content and language standards, aligned with the TEKS and ELPS. For example, in lesson 10.1, the “Manipulatives and Materials” section of “Before You Teach” lists “25 Foam Two-Color Counters,1 Coin Set, Coins (Printable).”

Each module also includes a planning guide. For example, the module 12 planning guide includes lesson 12.2, “Represent Subtraction Word Problems to 20.” The plan identifies four tasks to facilitate mastery of the content objective. These tasks include questions for educators to ask and instructional routines, such as the “Collect and Display” routine designed to help students discuss their thinking.

The materials include tasks and assessments aligned to the lesson objectives. The assessments provided for each module include a “Prerequisite Check,” “Quick Check,” and “Module Test.”

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

The Teacher’s Guide includes guidance and recommendations for the timing of each lesson component. For example, the “What’s in Each Lesson” section of module 17 recommends about 45 minutes of Essential Sessions and 15-plus minutes of “Differentiation and Practice” opportunities. Each part of lesson 17.1 includes suggested time frames, such as one minute for the “Learning Goal,” eight minutes for “Spark Your Learning,” 14 minutes for task 1, and 14 minutes for task 2.

The Teacher’s Guide includes overviews that identify the materials needed to deliver the lesson effectively. For example, the module 12 guide for lesson 12.3, “Choose an Operation to Represent Word Problems to 20,” includes a “Manipulatives & Materials” section. That section lists “20 Foam Two-Color Counters” and “20 Linking Cubes” per student and “20 Foam Two-Color Counters” and “20 Linking Cubes” per group. The lesson overview also identifies the instructional components used throughout the lesson.

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

The materials include guidance on the effective use of lesson materials for extended practice. For example, the “Differentiation and Practice” sections provide multiple opportunities for continued learning beyond the Essential Sessions. These sections identify resources such as “Practice on Your Own,” “Practice Plus” homework, and independent practice activities to reinforce lesson concepts.

The materials include guidance on effectively using “Differentiation and Practice” activities to support students at varying levels of performance. For example, the module 12 guide for lesson 12.3, “Choose an Operation to Represent Word Problems to 20,” includes a “Differentiation and Practice” section that guides educators on using data to differentiate instruction and practice. The materials provide focused reteach opportunities for students who are “Almost There” and challenge activities for students who need extension.

The materials guide educators on how to effectively use the adaptive digital platform. For example, the “Differentiation and Practice” sections identify resources such as “Personalized Practice in Waggle” and the “Program Activity Report.” These materials guide educators on selecting practice activities based on student performance levels and using adaptive digital resources to reinforce and extend learning.

Evaluation for 2.1a
Materials include a variety of instructional assessments at the unit and lesson level (including diagnostic, formative, and summative) that vary in types of tasks and questions.

The materials include summative assessments that vary in types of tasks and questions. For example, the module 10, form A test includes questions requiring students to identify the total value of a collection of coins, determine equivalent coin values, and solve real-world word problems involving money. Students respond to prompts such as “What is the total value of the coins?” “How many pennies have the same value as a nickel?” and “Max made 5 groups of pennies. He put 2 pennies in each group. What is the total value of the coins?” These varied task types allow students to demonstrate understanding through computation, reasoning, and application of mathematical concepts.

The materials include lesson-level formative assessments that vary in types of tasks and questions. For example, the module 10 “Planning Guide” for lesson 1 includes a “Quick Check” that assesses mastery of the learning goal. Students demonstrate understanding by identifying pennies, nickels, dimes, and quarters by value and writing the value using the cent symbol (¢). These formative assessment opportunities allow students to demonstrate understanding through identification, classification, and written-response tasks throughout instruction.

The materials include unit-level summative assessments that vary in types of tasks and questions. For example, the module 10, form A test includes multiple-choice, matching, and short-answer questions that require students to identify coin values, count collections of coins, compare equivalent values, solve real-world money situations, and represent amounts using the cent symbol. These varied assessment formats provide students with multiple opportunities to demonstrate mastery of module content.

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

The materials include the definition and intended purpose of the program’s instructional assessments. In the Implementation Guide, the “Step Through a Module” section provides the “what,” “why,” and “how” for assessment components. The “Quick Check and Learning Goal” page defines the assessments as tools that provide formative assessment data at the end of the whole-class session. The materials explain that the “Quick Check” provides information about how well students understood the lesson content. At the same time, the “Learning Goal” allows students to communicate their confidence in meeting the learning objective.

Beyond providing program-level assessment guidance, the materials define individual assessment types and explain their intended use. In the Implementation Guide, the “Step Through a Module” section defines the “Prerequisite Check” as an assessment that determines whether students have mastered a module’s prerequisite concepts. The materials explain that the assessment provides insight into students’ mastery of prerequisite skills for upcoming learning. Additionally, the guidance explains that educators administer the assessment at the beginning of each module and use the results to identify students’ readiness and determine appropriate instructional support before new learning begins.

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

The materials guide educators on ensuring consistent and accurate administration of instructional assessments. In the Implementation Guide, the “Step Through a Module” section provides administration guidance for the “Quick Check and Learning Goal.” The materials specify that educators administer the assessment at the end of the whole-class session and indicate an estimated administration time of 5–10 minutes. The guidance explains how students complete the “Quick Check” and directs educators to assess the language objective and have students respond to the “Learning Goal.” This guidance supports consistent administration of formative assessments across classrooms.

In addition to formative assessment guidance, the materials guide educators on summative assessments. In the Implementation Guide, the “Step Through a Module” section explains that educators administer the “Module Test” at the end of each module and indicates an estimated administration time of 45 minutes. The materials direct educators to assign either the digital or printable assessment, review and grade student responses, and use the results to identify areas requiring reinforcement. This guidance supports consistent and accurate administration of summative assessments throughout the program.

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

The formative assessments are aligned to the TEKS and to course and lesson objectives. For example, the “Practice on Your Own” guide in module 14, lesson 3, identifies the TEKS assessed for each item, the corresponding Depth of Knowledge (DOK) level, and the task to which each item aligns. The guide shows that items 1A–1B assess TEKS 1.1.D and 1.5.F and align to tasks 1 and 2. Items 2A–2C assess TEKS 1.5.G and align to tasks 3 and 4. The rubric for item 2D further aligns with task 3 and evaluates students’ understanding of the lesson objective. This alignment demonstrates that the assessment measures student understanding of both the TEKS and the lesson objectives.

In addition to formative assessment alignment, the summative assessments align to the TEKS and to the module’s course and objectives. For example, the module 16 test answer key identifies the TEKS assessed by each item and the lesson in which the content was taught. Item 1 assesses TEKS 1.7.A and aligns to lesson 16.1. Item 9 also assesses TEKS 1.7.A and aligns to lesson 16.3. The answer key identifies the standard measured by each assessment item and connects the assessment to module instruction. This alignment demonstrates that the assessment measures student understanding of the standards and learning objectives addressed throughout the module.

The materials include diagnostic assessments designed to evaluate students’ readiness for upcoming learning. For example, the “Prerequisite Check” reviews previously taught concepts and skills needed for the module and provides data-driven support resources to address identified learning needs. Additionally, the diagnostic benchmark assessments include answer keys with a TEKS correlation table that aligns each assessment item to the corresponding TEKS and specific lessons. This provides evidence of alignment among the assessments, course standards, and instructional content.

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

The instructional assessments include TEKS-aligned items that evaluate varying levels of complexity. For example, the “Depth of Knowledge Leveled Questions” in module 14, lesson 3 provide assessment opportunities at level 1, “Recall”; level 2, “Basic Application of Skills and Concepts”; and level 3, “Strategic Thinking and Complex Reasoning.” Students identify the missing number in an equation, explain their reasoning, and justify their solution using evidence. This progression demonstrates increasing cognitive complexity while remaining aligned to the lesson’s TEKS and learning objectives.

The instructional assessments include a variety of TEKS-aligned item types. For example, the form A test in module 12 includes multiple-choice, equation-completion, and numeric-response items aligned to TEKS 1.5.D and 1.5.E. Students solve comparison problems, determine missing values to create equivalent expressions, and select number sentences that represent mathematical situations. These varied TEKS-aligned item types provide multiple opportunities for students to demonstrate mathematical understanding and mastery of the standards.

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

The materials provide scoring information to ensure accurate scoring of instructional assessments. For example, the module 4 assessment includes scoring criteria that identify responses at each score level and provide guidance for assigning scores. The assessment includes a rubric for item 6 that describes student responses earning zero, one, or two points. This scoring guidance supports consistent and accurate evaluation of student work.

Throughout the modules, the materials include guidance for interpreting student performance on instructional assessments. For example, the module 4 review and accompanying data-driven support resources identify specific skills, TEKS correlations, and recommended reteach activities based on student results. Educators use this information to analyze assessment outcomes; identify strengths, misconceptions, and learning gaps; and determine targeted instructional supports. This guidance helps educators interpret student performance and respond with next steps for instruction.

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 materials provide guidance for the use of included tasks and activities to respond to student trends in performance on assessments. For example, the module 18 data-driven support resource accompanying the module review assessment directs educators to use the assessment results to identify specific content areas where students need additional support and to select corresponding reteach activities. This resource connects students who have difficulty telling time to the hour and half-hour to targeted reteach activities aligned with TEKS 1.7.E. This guidance helps educators use assessment data to plan tasks that address misconceptions and learning gaps.

The materials provide guidance for responding to student performance trends through the “Differentiation and Practice” section. Educators are directed to review student data from the “Program Activity Report” to determine each student’s level of mastery and identify students who may benefit from targeted instructional support. Based on results, educators select included activities such as educator-led small-group instruction, collaborative groups, independent practice, homework, and adaptive digital practice. This guidance helps educators use assessment data to assign appropriate tasks and activities that address identified learning needs.

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

The materials include tools for educators to track student progress and growth. For example, the online “Program Activity Report” provides data on individual student and class performance. Educators can analyze student performance, monitor progress over time, compare scores across assessments, and create student groups based on performance levels and domains. The report also includes data such as participation, self-evaluation, and TEKS proficiency to help educators determine students’ mastery of lesson objectives. This tool supports ongoing progress monitoring and instructional decision-making.

Beyond educator-facing progress-monitoring tools, the materials include tools for students to track their own progress and growth. For example, the “Learning Tracker” provides students with opportunities to set goals, monitor their assessment performance, and reflect on their growth throughout the year. Students respond to reflection questions at the beginning, middle, and end of the year and record scores from module assessments to assess progress toward their goals. The tracker prompts students to evaluate improvements, identify areas for continued growth, and monitor performance across modules. This tool supports student self-monitoring, goal setting, and ownership of academic progress.

Evaluation for 3.1a
Materials include teacher guidance for differentiated instruction, activities, and paired (scaffolded) lessons for students who have not yet reached proficiency on grade-level content and skills.

The materials include guidance for differentiated instruction, activities, and paired (scaffolded) lessons for students who have not yet reached proficiency on content and skills. For example, the “Differentiation and Practice” section of module 6, lesson 1 directs educators to use the “Program Activity Report” to review student data and determine each student’s mastery of the Essential Session. Based on the data, educators identify students who would benefit from small-group instruction and assign differentiated learning pathways, including the educator-led “Almost There: Count On to Add” mini-lesson for students who need additional support.

The materials include paired (scaffolded) lessons and intervention activities for students who have not yet reached proficiency on grade-level content and skills. For example, the educator-led small-group lesson “Almost There: Represent Related Facts” provides step-by-step instructional support through guided questioning and the use of counters and linking cubes to help students model equations before writing related facts independently. The materials also include intervention activities that provide structured practice through explicit directions and hands-on modeling. For example, students use cubes to demonstrate that addends can be added in any order and that the sum is the same regardless of the order. This gives students scaffolded support as they develop an understanding of grade-level concepts.

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

The materials include pre-teaching and embedded supports for unfamiliar vocabulary. For example, in module 15, lesson 5, educators are directed to use the “Words to Learn” routine to introduce and discuss the term triangular prism before students engage in the task. The guidance supports students as they connect the term to the three-dimensional figure, discuss its attributes, and use the academic language during mathematical conversations. These supports help students develop an understanding of unfamiliar mathematical vocabulary before applying it within the lesson.

The materials include embedded supports for unfamiliar references and academic language in text. For example, in module 15, lesson 5, the “Teaching Strategy: ELPS” guidance helps students distinguish between the everyday and mathematical meanings of the word face. Educators guide students to use pictures, foam geometric solids, and surrounding text to determine meaning, noting that in daily life, face refers to the front of a person’s head, but in the academic register of mathematics, it refers to a flat surface of a three-dimensional solid. These supports help students interpret unfamiliar references and understand academic language during instruction.

Evaluation for 3.1c
Materials include teacher guidance for differentiated instruction, enrichment, and extension activities for students who have demonstrated proficiency in grade-level content and skill.

The materials include guidance for differentiated instruction, enrichment, and extension activities for students who have demonstrated proficiency in grade-level content and skills. For example, the “Differentiation and Practice” section directs educators to use the “Program Activity Report” to determine student mastery. It also recommends “Ready for More” small-group instruction for students who have demonstrated proficiency. In module 17, lesson 5, the “Ready for More: Measure in Inches and Centimeters” activity guides students to measure objects using both inches and centimeters, compare measurements, explain differences in results, and determine which objects are longer. This educator-guided activity extends learning beyond the lesson objective and provides an additional challenge for proficient students.

The materials include enrichment and extension activities that promote deeper mathematical thinking for students who have demonstrated proficiency in grade-level content and skills. For example, in module 11, lesson 5, the “Ready for More: Skip Count by Tens” activity guides students to identify patterns on a 1–120 chart, skip-count by 10s, explain how skip-counting supports efficient counting, and participate in a hand-counting game using groups of 10. Students also explain how many sets of 10 they counted and justify their reasoning. These opportunities encourage students to analyze number patterns, make mathematical connections, and apply grade-level skills in a more challenging context.

Evaluation for 3.2a
Materials include explicit (direct) prompts and guidance to support the teacher in modeling and explaining the concept(s) to be learned.

The materials include prompts throughout module tasks that support educators in modeling and explaining the concepts students will learn. For example, module 6, lesson 3, task 1 includes direct questioning prompts such as “How many empty spaces are in the ten frame?” “What numbers do you need to add?” and “How many counters should you move to the ten frame?” The materials continue with prompts that guide students through the make-a-10 strategy and support educators in helping students connect concrete models to equations and explain their mathematical thinking while developing an understanding of addition within 20.

The materials include guidance to support educators in modeling and explaining concepts. For example, module 13, lesson 3, task 2 directs educators to use the “Process Standard: Use a Problem-Solving Model” routine to help students connect concrete models and equations that represent related facts. The Teacher’s Guide instructs educators to have students analyze the related facts, plan a strategy, solve the problem, justify their process, and evaluate the reasonableness of their answers. Through this structured sequence and accompanying discussion prompts, educators support students in explaining mathematical relationships and communicating their reasoning.

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

The materials include guidance and recommendations for effective lesson delivery and facilitation using a variety of instructional approaches. For example, module 15 includes Mathematical Language Routines (MLRs) such as “Stronger and Clearer Each Time,” “Three Reads,” “Collect and Display,” “Compare and Connect,” and “Discussion Supports.” The materials also recommend using “Peer Coach Videos” and identifying opportunities to reinforce academic vocabulary throughout the module. These supports provide guidance for facilitating discussion, collaboration, language development, and mathematical reasoning through varied instructional approaches.

The materials include guidance and recommendations for lesson facilitation through modeling, mathematical discourse, and collaborative learning. For example, in module 8, lesson 3, task 1, students use counters or linking cubes to model a problem, create pictorial representations, and participate in the “Critique, Correct, and Clarify” routine. Educators facilitate discussion through questioning, comparing solution strategies, and clarifying mathematical vocabulary. These supports provide multiple approaches for lesson delivery while promoting conceptual understanding and mathematical communication.

Evaluation for 3.2c
Materials support multiple types of practice (e.g., guided, independent, collaborative) and include guidance for teachers and recommended structures (e.g., whole group, small group, individual) to support effective implementation.

The materials support multiple types of practice. For example, the “What Does this Lesson Look Like in My Classroom?” section in module 9, lesson 1 directs educators to use the “Program Activity Report” to differentiate instruction. It also provides opportunities for students to engage in educator-led small-group activities, independent practice, and collaborative groups. The materials recommend 1–3 rotations per lesson and include additional practice opportunities through homework, extension, and personalized adaptive practice through the HMH Waggle. These varied practice opportunities support student learning through differentiated instruction, independent application, collaboration, and targeted intervention or enrichment.


The materials guide educators on recommended instructional structures to support effective implementation. For example, the “On Track: Identify Fourth” section in module 16, lesson 2 provides a small-group activities lesson with listed materials, educator directions, discussion prompts, and possible student responses. Educators guide students through identifying equal and unequal shares, determining whether shapes represent halves, fourths, or unequal shares, and discussing their reasoning through targeted questions. This supports effective small-group instruction and mathematical discourse.

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

The materials include guidance on providing linguistic accommodations for various levels of language proficiency as defined by the ELPS. For example, the “Emergent Bilinguals: Supporting All Language Learners” section in module 5, lesson 1 directs educators to “use sentence frames and sentence starters to support children’s oral explanations” and to “use the ‘Supporting All Language Learners’ chart to provide language scaffolding for all proficiency levels.” The chart provides differentiated supports for pre-production/beginning, intermediate, and high intermediate/advanced students through sentence frames, sentence starters, and word banks that support oral explanations, such as how to find the number of fruits Lucas puts in the basket.

The materials engage students in increasing their use of academic language across language proficiency levels. For example, the “Emergent Bilinguals: Supporting All Language Learners” section in module 19, lesson 6 provides differentiated language supports that progress from repeating modeled phrases such as “Apples have more” and “Bananas have less” to asking and answering questions using sentence frames and ultimately explaining reasoning using sentence starters. Pre-production/beginning students identify categories and use comparative language; intermediate students ask and answer questions about a graph; and high intermediate/advanced students explain which category has the most and justify their thinking using details from the graph. This progression supports students in using increasingly sophisticated academic language to communicate mathematical reasoning.

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

The materials include implementation guidance to support educators in effectively using the materials in state-approved bilingual/ESL programs. For example, the “Language Growth for All Learners” section explains how the materials support language development through “Observable, Measurable Language Objectives within Each Lesson,” alignment to the TEKS, and “Teaching Strategies that Support Mathematical Communication.” The materials also include resources such as “Words to Learn Routine and Vocabulary Cards,” “Easy-to-Use Mathematical Language Routines,” “Formative Language Assessment,” and “Language Development Resource Guide.” These resources provide educators with guidance and tools for implementing language supports throughout instruction.

The materials include embedded implementation guidance for effective use in state-approved bilingual/ESL programs. For example, the “Emergent Bilinguals: Supporting All Language Learners” section in module 13, lesson 1, directs educators to “use the ‘Supporting All Language Learners’ chart to let children choose the language scaffolding that they need.” The materials provide specific guidance for pre-production/beginning, intermediate, and high intermediate/advanced students through differentiated language supports, sentence starters, and discussion prompts. Educators are guided in scaffolding mathematical discussions and oral explanations based on students’ language proficiency levels, supporting the effective implementation of bilingual/ESL instructional practices.

Evaluation for 3.3c
Materials include embedded guidance for teachers to support emergent bilingual students in developing academic vocabulary, increasing comprehension, building background knowledge, and making cross-linguistic connections through oral and written discourse.

The materials include embedded guidance to support emergent bilingual students in developing academic vocabulary, increasing comprehension, and making cross-linguistic connections through oral and written discourse. For example, in module 16, lesson 4, task 2, the ELPS “Teaching Strategy” directs educators to help students examine the word quarter and use the surrounding context to determine its mathematical meaning. Students discuss that quarter can have multiple meanings and use the terms quarter and fourth as they explain their thinking with partners. Through discussion and contextual analysis of vocabulary, students strengthen comprehension, develop academic language, and make connections between language and mathematical concepts.

The materials include embedded guidance to support emergent bilingual students in increasing comprehension through oral and written discourse. For example, in module 4, lesson 1, the “Three Reads” routine guides students through multiple readings of a problem to build understanding of the context, quantities, and question being asked. Students discuss the problem, identify important numbers, explain what the quantities represent, and consider possible strategies before solving. Through repeated readings, educator questioning, and collaborative discussion, students develop comprehension and communicate mathematical thinking.

Beyond supporting comprehension, the materials include embedded guidance to support emergent bilingual students in developing academic vocabulary and building background knowledge through oral and written discourse. For example, in module 8, lesson 1, task 3, students explain the meaning of mathematical symbols, describe solution strategies, and communicate reasoning using mathematical vocabulary. Additionally, the emergent bilingual support in the “Quick Check” provides sentence frames such as “My addends are ___ and ___” and “I count on from ___ to get the sum ___.” This supports students in organizing and expressing mathematical thinking by using complete sentences and precise academic language. Students build conceptual understanding while developing the vocabulary and language structures to communicate mathematical ideas through oral and written discourse.

Evaluation for 3.3d
If designed for dual language immersion (DLI) programs, materials include resources that outline opportunities to address metalinguistic transfer from English to the partner language.

This guidance is not applicable because the program is not designed for dual language immersion (DLI) programs.

Evaluation for 4.1a
Practice opportunities over the course of a lesson and/or unit (including instructional assessments) require students to demonstrate depth of understanding aligned to the TEKS.

The materials include instructional assessments that require students to demonstrate depth of understanding aligned to the TEKS. For example, in the module 1 test form A, students identify equivalent representations of numbers, interpret place-value models, compose and decompose numbers, and solve addition situations using concrete models and equations. Students also analyze base 10 representations, identify missing quantities, and apply their understanding of place value to solve real-world problems. These assessment tasks require students to apply conceptual understanding through multiple representations and problem-solving rather than rely on a single procedure.

Further opportunities to demonstrate depth of understanding occur in module 15. For example, the “How Does the Module Support the Conceptual and Procedural Emphasis of the TEKS?” section of the educator guide explains that students classify, sort, and describe regular and irregular two-dimensional shapes; distinguish between defining and non-defining attributes; create two-dimensional figures; and identify three-dimensional solids. Students apply their conceptual understanding of shape attributes through classification, description, creation, and identification tasks aligned to TEKS 1.6A–1.6F. The “How Are the Process Standards (PS) Connected to the Content in This Module?” section explains that students use precise mathematical language, share ideas about two-dimensional shapes and three-dimensional solids, and apply problem-solving processes while creating and composing figures. Through these opportunities, students demonstrate understanding of geometric concepts while engaging in the mathematical practices described in the process standards.

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

The materials include questions and tasks that progressively increase in rigor and complexity, leading to grade-level proficiency in the TEKS. For example, in module 14, lesson 7, students solve increasingly complex unknown-number situations by representing problems with models and equations, selecting appropriate strategies, and explaining their reasoning. Students move beyond simply finding unknown values to justifying solutions, comparing strategies, and applying the relationships between addition and subtraction to solve problems. This progression requires students to deepen their mathematical reasoning while demonstrating grade-level proficiency aligned to the TEKS.

Further opportunities for increasing rigor and complexity occur in module 16 as students develop an understanding of equal shares. In lesson 2, “Equal Shares,” students begin by identifying figures that show equal fourths and distinguishing figures that do not represent equal parts. The task then progresses to explaining what makes parts equal or unequal and creating representations of fourths. Finally, students draw shapes partitioned into four equal parts. This progression moves students from identifying equal and unequal parts to creating representations of fourths, supporting grade-level proficiency in understanding equal shares and fourths.

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

The materials demonstrate coherence across lessons and units by explicitly connecting prior learning to new mathematical concepts. For example, in module 2, lesson 1, task 2, “Connect to Prior Learning,” students consider whether it matters if they compare the hundreds, tens, or ones first when determining which number is greater. Students draw on previously learned place-value concepts to compare 105 and 114, explain their reasoning, and justify their comparisons. By connecting prior understanding of hundreds, tens, and ones to new learning about comparing and ordering numbers, the materials reinforce important place-value relationships and support a coherent progression of mathematical understanding across lessons and units.

Further opportunities to connect mathematical concepts across lessons and units occur in module 14, lesson 7. The “Connect to Prior Learning” prompt asks students, “How can you check that your answer makes sense?” The accompanying guidance directs educators to facilitate a “Turn and Talk,” listen to students’ explanations, and invite students with different responses to share their thinking with the class. Through these discussions, students connect previously learned relationships between addition and subtraction to new problem situations, reinforcing mathematical relationships and supporting coherence across lessons and units.

Evaluation for 4.2b
Materials demonstrate coherence across units by connecting the content and language learned in previous courses/grade levels and what will be learned in future courses/grade levels to the content to be learned in the current course/grade level.

The materials demonstrate coherence across grade levels by connecting content and mathematical language learned in previous grade levels to current instruction while preparing students for future learning. For example, the materials in module 6, “What Will Students Learn in this Module?” identify prior learning by reminding educators that students have represented addition within 10 using objects, drawings, and number sentences, solved addition and subtraction word problems, and used doubles facts to make 10 and add within 20. The module builds on this foundation as students apply addition and subtraction strategies, solve unknown-quantity problems, and explain their mathematical thinking using mathematical language. The “Future Connections” section notes that students will later apply efficient addition and subtraction strategies, explain relationships between operations, and solve increasingly complex problem situations. These explicit connections support coherence by linking prior content and mathematical language to current learning while preparing students for future grade-level expectations.

The materials demonstrate coherence across grade levels by maintaining consistent mathematical language that supports learning across grade levels. For example, the “Teacher’s Glossary” provides educators with mathematical definitions to support instruction, while students develop the same concepts through vocabulary cards and the “Words to Learn” routine using grade-appropriate language. As students progress across grade levels, the materials introduce mathematical vocabulary that is reinforced, expanded, and maintained. These language supports promote coherence by connecting mathematical language from previous grade levels to current instruction and preparing students for future learning.

Evaluation for 4.2c
Materials demonstrate coherence at the lesson level by connecting students' prior knowledge of concepts and procedures from the current and prior grade level(s) to new mathematical knowledge and skills..

The materials demonstrate coherence at the lesson level by connecting students’ prior knowledge of counting concepts and procedures to new mathematical knowledge and skills. In module 6, lesson 1, “Spark Your Learning,” students revisit counting on from eight to solve addition situations before learning a more efficient counting-on strategy. During “Spark Discussions” and “Spark Your Learning: Turn and Talk” activities, students explain how counting on helps them find unknown sums and compare the efficiency of different strategies. These activities intentionally build on previously learned counting procedures to develop new addition strategies and deepen conceptual understanding.

Additional opportunities to connect students’ prior knowledge of concepts and procedures to new mathematical knowledge and skills occur in module 8, lesson 1, “Explain Strategies to Solve Addition Problems.” Students build on previously learned addition concepts and strategies by using words, objects, pictorial models, and number sentences to explain how strategies such as counting on, doubles, making a 10, and decomposing help solve addition problems within 20. By extending familiar addition procedures to include mathematical justification and communication, the lesson intentionally develops students’ conceptual understanding while strengthening their mathematical reasoning and ability to explain solution strategies.

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

“Practice Plus” activities provide spaced retrieval opportunities with previously learned skills across units. In module 9, “Generate and Solve Problem Situations,” students develop skills including counting forward and writing and solving a mathematical story problem. In module 11, “Practice Plus: Recite Numbers Forward to 120,” they revisit mathematical reasoning to strengthen long-term retention, applying previously learned problem-solving skills.

The “Train Your Memory” section extends spaced retrieval opportunities across lessons and units. In module 11, lesson 1, students revisit the addition fact 5 + 7 by writing and solving a story problem before completing missing-addend and subtraction equations. These opportunities require students to retrieve and apply previously learned addition and subtraction skills while reinforcing current learning and promoting long-term retention.

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

The materials provide interleaved practice opportunities with previously learned skills and concepts across units. For example, in module 4, lesson 3, “Practice Plus: Compare Sets to Solve Problems,” students solve comparison problems while drawing on previously learned place-value understanding, counting, addition, and subtraction fluency. Rather than practicing a single procedure repeatedly, students engage with multiple mathematical ideas within the same activity, reinforcing flexible use of previously learned skills and concepts across units.

Building on this approach, the materials continue interleaved practice across lessons and units by presenting varied problem types within a single lesson. In module 14, lesson 3, “Practice Plus: Determine the Unknown Change in Addition Problems,” students solve unknown-change problems by drawing models, writing number sentences, identifying equivalent equations, and solving missing-addend problems. The “Train Your Memory” section revisits the unknown-change model from lesson 12.3 before students complete addition fluency tasks. By requiring students to shift among representations, problem-solving strategies, equation writing, and fluency within one practice set, the materials provide interleaved practice that reinforces previously learned skills and concepts across lessons and units.

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

The materials provide regular opportunities for students to interpret, analyze, and evaluate mathematical models and representations throughout the lesson tasks. For example, in module 12, lesson 1, task 1, students use counters or cubes to model an addition situation and write a matching number sentence. They also respond to the prompt “What numbers are added in this story?” Students analyze their mathematical model to identify the quantities represented and connect the model to the addition story problem.

In module 19, lesson 1, students interpret, analyze, and evaluate mathematical models and representations using picture graphs and tally charts. Students interpret a T-chart showing “T-Shirts Worn at the Fair,” analyze the tally data to compare categories, and explain which color shirt was worn most often. Students further evaluate survey data by defending conclusions about which object classmates chose most often, using evidence from the representation.

In module 7, lesson 3, task 2, students interpret, analyze, and evaluate mathematical models and representations while using addition to solve a subtraction problem. Students analyze a model of six red and four yellow counters to determine the missing addend in the equation 6 + __ = 10. They interpret the representation to solve 10 − 6 = __, justify how they used addition to solve the subtraction problem, and evaluate the process by explaining when this strategy can be used to subtract.

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

Questions and tasks throughout the modules require students to create models to represent mathematical situations. For example, in module 11, lesson 3, task 2, students choose tools to select a representation such as cubes, counters, or a number chart to skip-count by twos for 12 blankets. Students then respond to “Show Another Way” by writing a number sentence that matches their skip counting and explain how they know their answer is reasonable. These tasks require students to create mathematical models to represent the situation and communicate their reasoning.

Additional opportunities occur in module 9, lesson 3, task 3, where students create models to represent an addition situation involving books checked out from a library. Students identify the number sentence that matches the situation, draw a pictorial model to solve the problem, and use their model to determine the total number of books. Students then respond to the “Argue” prompt by using details from their model to justify their reasoning.

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

Throughout the materials, questions and tasks provide opportunities for students to apply their conceptual understanding to new problem situations and contexts. For example, in module 13, lesson 2, task 1, students respond to the “Analyze Relationships” problem by determining how many pears remain after several groups are removed. Students explain which operation to use, model each step with counters, and respond to the prompt “Explain which operation you will use to solve the problem.” These tasks require students to apply their understanding of addition and subtraction relationships in a new mathematical context.

In module 13, lesson 2, task 1, students apply their conceptual understanding of addition and subtraction relationships to a new problem situation involving pears. Students determine the number of pears that Max starts with before using counters or drawings to represent the situation and explain which operation will solve the problem. In the “Practice On Your Own” section, students transfer this understanding to a new situation involving muffins by determining how many muffins remain after some are given away. In this way, they apply the same mathematical relationships in a different context while explaining their reasoning.

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

Each lesson includes tasks designed to build the automaticity that students need to complete grade-level tasks through repeated practice. In “Fluency Practice: Part-Part-Whole Model, Part 1,” students repeatedly decompose the whole number seven into two parts by drawing dots to represent different combinations and completing corresponding addition number sentences. This repeated practice strengthens automatic recall of part-part-whole relationships and supports efficient retrieval of addition facts needed for grade-level mathematics.

The materials include tasks designed to build the fluency that students need to complete grade-level tasks through repeated practice. Under “All Resources,” educators can assign “Fluency Practice: Subtracting Zero” during the independent practice portion of the lesson. In this activity, students repeatedly practice subtracting zero from a number and subtracting the same subtrahend from the minuend so that the difference is zero. These repeated fluency tasks strengthen accurate, efficient, and flexible computation needed to complete grade-level mathematics.

Evaluation for 5.2b
Materials provide opportunities for students to practice the application of efficient, flexible, and accurate mathematical procedures within the lesson and/or throughout a unit.

Tasks provide opportunities for students to practice applying efficient mathematical procedures within the lesson. In “Practice on Your Own,” students solve subtraction problems by using the count-on strategy, complete subtraction number sentences, and explain how counting on connects to subtraction. They repeatedly apply an efficient subtraction strategy while producing accurate solutions. These opportunities reinforce efficient mathematical procedures needed to solve grade-level tasks.

Tasks provide opportunities for students to practice applying flexible mathematical procedures within the lesson. In lesson 7.5, task 1, students use 10-frames to model subtraction while explaining their problem-solving approach. Through the “Compare and Connect” and “Turn and Talk” routines, students discuss the different methods they used to solve the problem and explain how decomposing to subtract is similar to other strategies, such as making a 10 and counting back. These opportunities develop flexible mathematical procedures by encouraging students to compare, explain, and connect multiple subtraction strategies.

Tasks provide opportunities for students to practice applying accurate mathematical procedures through additional independent practice. In “Practice Plus: Determine the Unknown Start in Addition Problems,” students solve unknown-start addition situations by modeling, writing number sentences, determining unknown starting amounts, and selecting the correct equations in multiple contexts. These repeated opportunities reinforce accurate mathematical procedures by requiring students to correctly model situations, record equations, and determine unknown quantities while applying addition strategies.

Evaluation for 5.2c
Materials provide opportunities for students to evaluate procedures, processes, and solutions for efficiency, flexibility, and accuracy within the lesson and throughout a unit.

Tasks provide students with opportunities to evaluate procedures, processes, and solutions for efficiency, flexibility, and accuracy. For example, in module 9, lesson 2, task 1, students solve a subtraction word problem using multiple representations, including base 10 blocks, an open number line, and the subtraction algorithm. During the “Turn and Talk,” students evaluate the efficiency and accuracy of these procedures by discussing “Which strategy was most helpful?” and “Did you get the same answer using each strategy?” In task 2, students solve another subtraction problem and respond to the “Show Another Way” prompt by demonstrating a different method, providing an opportunity to evaluate the flexibility of multiple solution strategies.

The materials provide opportunities for students to evaluate procedures, processes, and solutions for efficiency, flexibility, and accuracy throughout the unit. For example, in module 12, students evaluate mathematical representations and solution strategies across multiple lessons. In lesson 12.2, task 2, students respond to the “Evaluate Process” prompt by determining whether their picture matches their number sentence and explaining what they could change to make their model clearer. This provides an opportunity to evaluate the effectiveness of their mathematical representation and reflect on improvements to their solution process. In lesson 12.3, “Choose an Operation to Represent Word Problems to 20,” students solve a subtraction problem using counters and a matching number sentence before discussing how their counters, words, and number sentence all represented the same story. This requires them to evaluate the flexibility of multiple mathematical representations. Later in the lesson, students evaluate the accuracy of mathematical solutions by explaining why an incorrect number sentence does not match the problem and justifying why their own number sentence correctly represents and solves the situation.

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

The Teacher’s Guide contains embedded supports for educators to guide students toward increasingly efficient approaches. For example, module 7, lesson 4 includes prompts, questioning, and modeling that support students in using decomposition and making 10 as efficient subtraction strategies. These embedded supports guide educators in developing students’ conceptual understanding before transitioning students from concrete representations to increasingly efficient mental strategies for solving subtraction problems.

The “Teacher Background” section of module 7 provides additional embedded supports. The text explains the progression of content and strategies through the “What Is the Rationale for the Order of the Lessons in This Module?” section. The guidance explains how students progress from counting back to subtract to counting on to subtract, adding to subtract, using 10 to subtract, and decomposing numbers to subtract. These embedded supports help educators build students’ conceptual understanding through a purposeful instructional sequence before guiding students toward increasingly efficient subtraction strategies and problem-solving approaches.

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

In module 5, the section in “Teacher Background” called “How Does the Module Support the Conceptual and Procedural Emphasis of the TEKS?” explicitly states how the module addresses the conceptual and procedural emphasis of the TEKS. The guidance explains that students first develop a conceptual understanding of composing 10 by understanding why combinations that make 10 are more efficient than counting. Students then build procedural proficiency by composing 10 using concrete objects, multiple addends, and number sentences. This guidance supports educators in developing conceptual understanding before procedural proficiency.

Module 17 also includes a section that explicitly states how the materials address the conceptual and procedural emphasis of the TEKS. The guidance explains that students first develop a conceptual understanding of measuring length by understanding why different tools and units are appropriate for measuring different objects. Students then build procedural proficiency by using nonstandard units to measure length, creating a nonstandard measuring tool, and measuring length using inches and centimeters. This guidance supports educators in developing conceptual understanding before procedural proficiency.

Evaluation for 5.3b
Questions and tasks include the use of concrete models and manipulatives, pictorial representations (figures/drawings), and abstract representations, as required by the TEKS.

Questions and tasks provide students with opportunities to use concrete models and abstract representations. For example, in module 4, lesson 1, task 1, students use objects to model two sets of fish toys, identify the number in each set, write an addition number sentence, and determine the total number of fish toys. These activities require students to represent mathematical thinking using concrete manipulatives and abstract numerical representations.

In module 16, lesson 4, task 1, students draw a two-dimensional figure, partition the figure into fourths, color one fourth, and show another way to represent fourths. These activities require students to represent mathematical thinking using pictorial representations while demonstrating their understanding of equal parts.

In module 8, lesson 2, task 1, students use objects to model a subtraction situation, represent the problem using 10 frames, and write a number sentence to match their model. Together, these examples demonstrate that the materials consistently provide opportunities for students to use concrete models, pictorial representations, and abstract representations across modules and lessons, as required by the TEKS.

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.

The materials include supports for students in connecting concrete and representational models to abstract mathematical concepts, as required by the TEKS. For example, in module 4, lesson 3, task 2, students model and draw two sets of berries, compare the sets, determine who has fewer berries, and complete statements describing the comparison. These activities support students in connecting concrete models and representational models to abstract mathematical concepts through mathematical language.

Tasks provide opportunities for students to create concrete and representational models in relation to abstract mathematical concepts. For example, in module 4, lesson 3, task 3, students use circles to represent and compare quantities and demonstrate another way to solve the problem using linking cubes. These activities support students in creating concrete and representational models that connect to abstract mathematical concepts.

The digital student experience extends these opportunities by providing interactive activities that reinforce mathematical understanding through multiple representations. For example, Waggle “Representing Numbers” activities reinforce TEKS 1.2A and 1.2C by guiding students from visual representations of quantities to symbolic representations of numbers through interactive videos and adaptive learning games. Together, these examples demonstrate that the materials support students in connecting, creating, and defining and explaining concrete and representational models in relation to abstract mathematical concepts, as required by the TEKS.

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

The materials provide opportunities for students to develop academic mathematical language through structured language development strategies. In module 15, the vocabulary cards introduce geometric terms such as cube, face, edge, vertex, rectangular prism, and two-dimensional shape using a consistent instructional routine in which students hear each term, learn its meaning, discuss it, and apply it in mathematical contexts. Educator guidance reinforces vocabulary through the “Define It,” “Discuss It,” and “Use It” sections. This supports students as they develop and use academic mathematical language in context.

In module 10, lesson 1, the Teacher’s Guide provides opportunities for students to develop academic mathematical language through manipulatives and structured language routines. Educators use the “Words to Learn” routine to introduce vocabulary such as cent, penny, nickel, value, and ¢ while students examine and compare real coins and communicate their ideas with a partner. Students then participate in the “Stronger and Clearer Each Time” routine, discussing their reasoning, asking questions, and refining their mathematical explanations.

In module 11, lesson 6, the Teacher’s Guide provides opportunities for students to develop academic mathematical language through visual models and embedded language development strategies. Students use visual models and concrete representations to identify number relationships while explaining their mathematical thinking. Educator guidance incorporates purposeful questioning and emergent bilingual supports that encourage students to communicate and justify their reasoning using precise mathematical language throughout the lesson.

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

The materials include embedded educator guidance to scaffold and support students’ development and use of academic mathematical vocabulary in context. In module 15, lesson 5, the Teacher’s Guide supports educators in developing students’ understanding of geometric vocabulary through the “Turn and Talk” routine. Guidance on the ELPS helps students distinguish the mathematical meaning of face, while Universal Design for Learning (UDL) supports provide sentence stems that scaffold students as they describe the attributes of rectangular prisms and cubes using precise mathematical language.

The Language Development Resource Guide includes embedded instructional guidance that helps educators intentionally build students’ academic mathematical vocabulary through the “Words to Learn” routine. The resource explains the purpose of the routine, identifies appropriate points for implementation during instruction, and provides a structured sequence for introducing, discussing, and applying new mathematical vocabulary. This consistent guidance supports educators as students develop and use academic mathematical language across lessons.

In module 18, lesson 1, the Teacher’s Guide embeds educator prompts, “Spark Discussions” activities, and emergent bilingual supports that scaffold students’ use of academic mathematical vocabulary during instruction. Students describe analog and digital clocks using terms such as hour hand and minute hand while responding to guided questions that encourage them to communicate mathematical ideas using precise vocabulary.

Evaluation for 5.4c
Materials include embedded teacher guidance to support the application of appropriate mathematical language to include vocabulary, syntax, and discourse to include guidance to support mathematical conversations that provide opportunities for students to hear, refine, and use math language with peers and develop their math language toolkit over time as well as guide teachers to support student responses using exemplar responses to questions and tasks.

The materials include embedded guidance to support the application of appropriate mathematical language through vocabulary, syntax, and mathematical discourse. In module 14, lesson 3, the “Three Reads” routine helps students make sense of the problem before solving it. The routine gives educators guiding questions and possible student responses. The “Stronger and Clearer Each Time” routine helps students justify their reasoning, explain the meaning of the equal sign, and communicate mathematical thinking using precise vocabulary and complete mathematical explanations.

In module 16, lesson 1, the Teacher’s Guide embeds educator guidance that promotes mathematical discourse through the “Critique, Correct, and Clarify” routine. Students discuss whether diagrams represent halves, critique and correct one another’s thinking, and refine their responses after collaborative discussions. These structured opportunities encourage students to hear, refine, and use mathematical language with peers while strengthening their mathematical language toolkit over time.

In module 4, lesson 2, the Teacher’s Guide provides embedded guidance that supports student responses through exemplar answers to questions and tasks during the “Spark Discussions” activity. The guide provides educators with sequential questioning, anticipated student responses, and modeling prompts that demonstrate how students can represent, explain, and justify subtraction situations using drawings and concrete models. These embedded supports help educators facilitate mathematical discussions while reinforcing students’ use of appropriate mathematical language to communicate their reasoning.

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

The materials embed the TEKS process standards within grade-level mathematical tasks that require students to select strategies, explain their reasoning, and communicate mathematical ideas. For example, in module 11, lesson 2, “Practice on Your Own,” task 2, students complete a “PS Choose Tools” activity in which they select a mathematical tool to count backward from 86. They explain why the tool supports their thinking, record the backward counting sequence, defend their solution by checking their work, and discuss their reasoning during a “Turn and Talk.” This task integrates the TEKS process standards as students apply mathematical thinking while solving grade-level content.

The Student Edition further reinforces the TEKS process standards by embedding process standard expectations within independent practice activities. For example, “Practice on Your Own” in module 10, lesson 4, prompts students to use representations, analyze, and choose tools while solving mathematical tasks. Embedding these process standards directly into student activities demonstrates that the materials intentionally integrate them throughout daily instruction rather than presenting them as isolated skills.

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

The materials include a description of how the TEKS process standards are incorporated and connected throughout the course. In the Implementation Guide, the “Mathematical Connections” section explains how mathematical topics (MT) intentionally build across modules while integrating the mathematical process standards (MP) to strengthen problem-solving, reasoning, communication, and coherence. For example, students develop place-value understanding in module 1 before applying that knowledge to comparing numbers and combining tens and ones in modules 2 and 3. Later, students apply problem-solving models across modules 4, 8, 9, 12, and 13 and connect mathematical ideas through multiple representations, justification, and communication in modules 13 and 14. This guidance demonstrates how the process standards are intentionally connected across the grade 1 course.

The materials include a description of how the TEKS process standards are incorporated throughout the course. In the Implementation Guide, “Step Through a Module: Lesson Planning” explains that the Texas process standards guide every lesson and identify where students use mathematical processes to demonstrate understanding. The guide describes how the Teacher’s Guide reinforces mathematical communication and reasoning, incorporates reflection questions in every lesson, and provides opportunities for students to explain their thinking using multiple representations. It further explains that the process standards icon identifies where students apply mathematical processes throughout instruction.

The materials describe how the course incorporates and connects the TEKS process standards throughout the course through the recurring “Process Skills Anchor Chart.” Each module includes the same anchor chart, which instructs students to “use this chart to help you apply the Process Standards when solving problems.” The chart provides guiding questions aligned to each process standard, such as “What is the problem about?” “How does this math help someone?” and “Why does my solution make sense?” These recurring supports reinforce the consistent application of the TEKS process standards across all modules throughout the grade 1 course.

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

The materials describe how TEKS process standards are incorporated and connected throughout the unit. In the “Teacher Background” for module 1, the section “How are the Process Standards (PS) Connected to the Content in This Module?” describes how students progressively develop and apply the process standards across the module. The materials explain that “throughout module 1, children learn the steps of the problem-solving model (PS 1.B), and then they use all the steps together in the final lesson to solve a problem related to representing a number as a model, a picture, and in expanded and standard form.” The overview identifies where students select tools, communicate mathematical ideas, use representations, and apply precise mathematical language across multiple lessons.

Another example appears in the “Teacher Background” for module 10 in the section “How are the Process Standards (PS) Connected to the Content in This Module?” The materials explain that “throughout module 10, children learn the steps of the problem-solving model (PS 1.B), then they use all the steps together in lesson 10 to solve a problem related to finding the value of a collection of coins.” The overview identifies how specific lessons incorporate additional process standards, including communicating mathematical ideas (PS 1.D), using representations (PS 1.E), using precise mathematical language (PS 1.G), and selecting tools (PS 1.C). This demonstrates how the process standards are intentionally incorporated and connected throughout the module.

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

The materials include an overview of the TEKS process standards incorporated into each lesson. For example, the “Before You Teach” pages for lesson 1, “Represent Addition Word Problems to 20,” identify the TEKS process standards at the beginning of the lesson, including 1.1.B, 1.1.C, and 1.1.D. The lesson overview provides mathematical standards taught in the lesson, the learning objective, and the language objective. This demonstrates how the process standards are connected to the lesson objectives and instructional activities.

The process standards are embedded throughout the lesson tasks. For example, in module 14, lesson 1, task 1, students are guided through the complete “PS: Use a Problem-Solving Model” by prompts that direct them to analyze, plan, solve, justify, and evaluate reasonableness while solving an addition word problem. By identifying the applicable process standards within the task, the lesson provides educators with an overview of where students engage with the TEKS process standards during instruction.

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

The materials provide opportunities for students to think mathematically, persevere through solving problems, and make sense of mathematics. For example, in module 7, lesson 3, task 2, students solve the problem “Trina writes 10 postcards. 6 are in the mail. The rest are on her desk. How many postcards are on her desk? Use addition to subtract 10 − 6.” Students then work through the problem-solving model by responding to these prompts: “Analyze: If I have 6, how many more to make 10?”; “Plan: Use the addition fact to help subtract”; “Solve: How many postcards are on Trina’s desk?”; “Justify: Explain how you used addition to solve the subtraction problem”; and “Evaluate Process: How do you know when to use this process to subtract?” These opportunities encourage students to reason about the relationship between addition and subtraction, persist as they solve problems, and reflect on their mathematical thinking.

The materials provide opportunities for students to persevere through solving problems and making sense of mathematics through structured mathematical discussions. In module 10, lesson 3, the “Spark Discussions” routine directs educators to have students “brainstorm possible strategies and engage in independent think time before solving the problem.” As students solve the problem, educator guidance encourages monitoring responses, addressing common errors through purposeful questioning, and encouraging students who use correct strategies to share their thinking. Students explain their reasoning and refine their understanding through mathematical discussions, supporting perseverance and deeper mathematical sense-making.

Further opportunities for students to think mathematically, persevere through solving problems, and make sense of mathematics occur in module 14, lesson 5. The “Spark Your Learning” routine supports students as they analyze a mathematical situation before instruction and determine an unknown quantity using counters and drawings. As students complete the lesson tasks, they explain how they determined the unknown quantity, compare multiple representations, justify their reasoning, and respond to prompts such as “How do you know?” and “How are the representations alike?” Students represent their solutions in more than one way and respond to questions such as “Can you show another way?” and “Why does your strategy work?” These opportunities promote mathematical reasoning while encouraging students to persist through problem-solving and make meaningful connections among mathematical representations.

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

The materials support students in understanding that there can be multiple ways to represent and solve problems and complete tasks. For example, in module 1, lesson 4, task 1, students use base 10 blocks, drawings, and number sentences to compose 54 in multiple ways. Students respond to prompts such as “How can you compose 54 in more than one way as hundreds, tens, and ones?”; “Draw to compose 54 a different way”; and “Show Another Way: How else can you compose 54 using objects or pictures?” These opportunities help students recognize that they can represent the same number in multiple valid ways and with multiple strategies.

The materials support students in explaining that there can be multiple ways to represent and solve problems and complete tasks. During the “Spark Your Learning” routine in module 14, lesson 5, students analyze an unknown addition problem using manipulatives, drawings, and equations before discussing their reasoning with classmates. Students compare different representations of the unknown quantity, explain how each model matches the equation, and justify why different strategies lead to the same solution. These discussions help students explain how different representations communicate the same mathematical relationship.

The materials encourage students to justify that there can be multiple ways to represent and solve problems and complete tasks. For example, the guidance for module 10, lesson 4, task 2, directs educators to have students “Show Another Way” to demonstrate the same total value and recognize that the problem can be solved using multiple approaches. Students then participate in the “Compare and Connect” routine to compare how they used tools to represent the total value in another way and discuss their thinking with a partner. This reinforces that different representations and strategies can be justified when they produce the same mathematical result.

Evaluation for 6.1c
Materials are designed to require students to make sense of mathematics through multiple opportunities for students to do, write about, and discuss math with peers and teachers.

The materials are designed to require students to make sense of mathematics through multiple opportunities to do math with peers and educators. For example, in module 8, lesson 1, task 3, students solve an addition problem by explaining a strategy they can use, modeling the problem with objects, writing a matching number sentence, explaining what the symbols in the number sentence mean, and writing why the strategy they selected was the best strategy for finding the answer. Students then respond to the “Review Spark Your Learning” prompt by explaining which addition strategy they would use to solve a similar problem. These opportunities engage students in actively solving mathematical problems while making sense of mathematics with peers and educators.

Beyond solving problems, the materials require students to make sense of mathematics by writing about math with peers and educators. For example, in module 1, lesson 4, task 1, students compose 54 in more than one way using hundreds, tens, and ones by using base 10 blocks. They draw different representations, write matching number sentences, and complete the “Show Another Way” prompt to represent the number using a different combination of hundreds, tens, and ones. Students record multiple representations and matching number sentences before participating in a “Turn and Talk” to explain how they know they can compose 54 using more tens than ones or more ones than tens. These opportunities require students to organize and communicate their mathematical thinking through written representations as they make sense of mathematics.

Collaborative mathematical discourse strengthens students’ understanding by requiring them to make sense of mathematics through opportunities to discuss math with peers and educators. In module 20, lesson 3, task 2, students use the problem-solving model to determine who is saving money and who is spending money by analyzing, planning, and solving the problem. Students explain how they know who is saving and who is spending. They tell a partner how their plan helped them solve the problem and respond to the “Turn and Talk” prompt “How can you use what you already know when you make choices about saving or spending?” These structured discussions require students to explain their reasoning, justify their solutions, and engage in meaningful mathematical conversations with peers and educators.

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

The materials support educators in guiding students to share their problem-solving approaches through structured mathematical discussions. For example, in module 9, lesson 3, task 1, the educator guidance directs students to use the “Process Standard: Share Ideas” routine to explain the subtraction number sentence they created and discuss the meaning of the mathematical symbols they used. Students then participate in the “Stronger and Clearer Each Time” routine, where they share their subtraction number sentences with a partner, discuss other ways to solve the problem, and refine their responses. These opportunities support educators in guiding students to share their mathematical thinking through explanations, arguments, and justifications.

The materials provide program-wide guidance to help educators support students in reflecting on their problem-solving approaches. The “Texas Problem-Solving Model” in the Implementation Guide directs educators to use student responses to facilitate discourse and reflection while asking questions throughout each stage of the problem-solving process, such as “Can I explain or generalize my thinking?” and “Does my solution make sense? Does it answer the question?” The guidance also encourages educators to have students explain how they used the problem-solving model within a module, lesson, and task using verbal descriptions and representations. These supports help educators guide students in reflecting on their mathematical thinking through explanations, arguments, and justifications.

Educators guide students to share and reflect on their problem-solving approaches through structured discussion and mathematical argumentation. For example, in module 16, lesson 2, students explain how they know a shape has four equal parts during “Spark Your Learning.” In task 1, they justify why shapes do or do not represent fourths and compare their reasoning with classmates through “Turn and Talk.” In task 2, the guidance incorporates the “Discussion Supports” routine, where students explain why their drawings represent equal parts and discuss different solution approaches with peers. These structured opportunities support educators in guiding students to share and reflect on their mathematical thinking through explanations, arguments, and justifications.

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

The materials offer prompts and guidance to support educators in providing explanatory feedback based on anticipated misconceptions. For example, in module 1, lesson 5, “Spark Discussions,” the “Addressing Common Errors” section anticipates that students may incorrectly read 96 as nine ones and six 10s. The guidance directs educators to ask questions such as “What does the digit 9 represent?” “What does the digit 6 represent?” and “How can you show 9 tens and 6 ones?” The guidance also provides possible student responses to help educators address the misconception. The lesson reminds educators that place value determines the value of each digit, supporting explanatory feedback that strengthens students’ understanding of tens and ones.

The materials provide prompts and guidance to help educators provide explanatory feedback based on students’ responses and anticipated misconceptions. For example, in module 2, lesson 2.5, task 3, educators ask questions throughout the analyze, plan, solve, justify, and evaluate stages while using possible student responses to guide instruction. If students incorrectly identify 102 as the least number by comparing only the first digit, the guidance directs educators to model 99, 102, and 120 with tens and ones blocks so that students recognize that 102 represents 10 tens and 2 ones. These prompts, possible student responses, and instructional supports help educators provide explanatory feedback that addresses misconceptions while strengthening students’ understanding of place value.

The materials provide guidance to help educators provide explanatory feedback based on students’ responses through the program’s “Differentiation and Practice” structure, which is embedded throughout the materials. Educators use the “Program Activity Report” to review student performance and determine which students will benefit from educator-led small-group instruction. The materials then direct educators to provide targeted support through “Almost There,” “On Track,” and “Ready for More” or “Extension” activities. These allow educators to deliver explanatory feedback and instruction that responds to individual student needs.