HMH Into Math Texas, Grade 2

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

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


The scope and sequence charts describe how each module and lesson align to the TEKS and ELPS and identify the concepts taught throughout the instructional year. Additional materials support this alignment through TEKS and ELPS correlations as well as “Correlations by Lesson” documents that break down concepts taught by module. Under the program dropdown, the “Discover” tab outlines the TEKS, ELPS, and lesson concepts to 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 provide a “Scope and Sequence with Yearly Pacing” resource for 165-day and 210-day instructional calendars. The guidance provided in the calendar “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 materials include 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.

One example of unit order rationale appears in unit 1. The “Module Order Rationale” explains that students develop conceptual understanding of place value by composing and decomposing numbers before representing numbers in expanded form in module 2. Students then use number lines and symbols to compare and order numbers in module 3 before comparing fractional parts in module 4 and engaging with addition and subtraction in modules 5–9.

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

The materials support educators with unit and lesson internalization through comprehensive planning supports, structured instructional routines, and embedded educator guidance. The Teacher’s Guide provides planning support that 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 lesson sequencing explanations support educator preparation.

The “Step Through a Module” section of the Implementation Guide guides educators on internalizing module and lesson components, while “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 protocols to support module and lesson internalization through 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 the tools individually or collaboratively as note-taking 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 provided resources and guidance documents help instructional leaders support educators with implementing the program as designed. For example, the program includes implementation supports through the “Professional Learning” resource. In addition, the Coaching Guide includes instructional support, implementation guidance, pacing recommendations, and professional learning resources that 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 to 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, “Understand Equal Parts and Fractions,” includes guidance on prior learning and future learning connections to 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, “Understand Equal Parts and Fractions,” directs educators to use the “Words to Learn (WTL)” routine and the module’s WTL vocabulary cards to help students master review vocabulary and new vocabulary terms. The materials identify vocabulary connected to specific lessons, including eighths, equal parts, fourths, halves, whole, partition, and fractional part.

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

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, in module 18, the home activity prompts families to “give your child a problem such as, Missy has $43 in the bank. She makes a deposit of $12. How much does she have in the bank now? Discuss what the amount would be if she made a withdrawal instead of a deposit.”

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 lesson plans provide consistent objectives, questions, tasks, materials, and instructional assessments that meet the 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 “Coins Set.”

Each module includes a planning guide. For example, the module 12 guide provides a plan for lesson 12.2, “Represent Subtraction Word Problems to 20.” This lesson 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 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 lesson components. For example, the “What’s in Each Lesson” section of module 14 suggests approximately 45 minutes of an Essential Session and 15-plus minutes of “Differentiation and Practice” opportunities. Each part of lesson 14.1 includes suggested times such as one minute for “Learning Goal,” eight minutes for “Spark Your Learning,” nine minutes for task 1, and nine minutes for task 2.

The Teacher’s Guide includes overviews that identify the materials needed to deliver each lesson effectively. For example, the module 2 plan for lesson 2.1, “Use Expanded Form,” has a “Manipulatives & Materials” section that lists “foam base ten rods,” “foam base ten units,” and a “place-value chart (thousands, hundreds, tens, ones)” per student, as well as “foam base ten flats” and a “plastic base ten cube” per group. The 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 Teacher’s Guide includes a “Differentiation and Practice” section that provides multiple opportunities for continued learning beyond the Essential Session. This section identifies resources such as “Practice on Your Own,” “Practice Plus” homework, and independent practice activities to reinforce lesson concepts.

The materials guide educators on effectively using “Differentiation and Practice” activities to support students at varying levels of performance. For example, the module 2 guide for lesson 2.1, “Use Expanded Form,” includes a “Differentiation and Practice” section that guides educators in 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 include guidance on effectively using lesson materials available through the adaptive digital platform. The “Differentiation and Practice” section identifies resources such as “Personalized Practice in Waggle” and the “Program Activity Report.” The materials guide educators in 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 diagnostic assessments that vary in types of tasks and questions. For example, the module 11 “Prerequisite Check” reviews prior concepts and skills needed before beginning the module. The assessment includes tasks that require students to skip-count, join sets, separate sets, and solve multiplication and division situations. Students respond to questions such as “Which shows a correct way to skip count by fives?” and “There are 12 ducks in the pond. 4 separate and fly away. How many ducks are in the pond now?” These varied task types provide information about students’ readiness for upcoming learning.

The materials include lesson-level formative assessments that vary in types of tasks and questions. For example, the module 11 guide for lesson 1 includes a “Quick Check” that assesses mastery of the learning goal. Students demonstrate understanding by explaining how to put sets of objects together using equal groups and how to take sets of objects apart into equal groups. These formative assessment opportunities allow students to demonstrate understanding through explanation, modeling, and problem-solving tasks throughout instruction.

The materials include unit-level summative assessments that vary in types of tasks and questions. For example, the module 4 form A test includes multiple-choice questions, visual model analysis, contextual word problems, and fraction representation tasks. Students identify equal partitions, analyze shaded models, compare fractional parts in real-world contexts, and determine fractional quantities using visual representations. 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 provide the definition and intended purpose for the instructional assessments. In the Implementation Guide, the “Step Through a Module” section describes the “what,” “why,” and “how” for assessment components used throughout the program. 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. 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 needed 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 include educator guidance to ensure 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 to 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 include educator guidance to ensure consistent and accurate administration of 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.

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 align to the course TEKS and the objectives of each lesson. For example, the “Practice on Your Own” item guide in module 12, lesson 3 identifies the specific TEKS assessed for each item, including TEKS 2.7.B, 2.1.E, and 2.1.B. This guide shows how each item aligns to lesson tasks such as task 1, task 2, task 3, and task 4. The guide also identifies the corresponding Depth of Knowledge (DOK) level for each item. This alignment demonstrates that the assessment measures student understanding of both the grade-level TEKS and the lesson objectives taught during instruction.

In addition to formative assessment alignment, the summative assessments align to the course TEKS and the objectives of the module. For example, the module 17 test answer key identifies the TEKS assessed by each item and the lesson in which the content was taught. Item 1 assesses TEKS 2.10A and aligns to lesson 17.3. 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 between the assessments, course standards, and instructional content.

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

The materials provide several examples of instructional assessments that include TEKS-aligned items at varying levels of complexity. For example, the “Depth of Knowledge Leveled Questions” in module 12, lesson 3 progress from level 1, where students compute sums involving place value, to level 2, where students explain how a base 10 model represents addition, and then to level 3, where students justify why only one digit changes when adding 10 or 100 using place-value evidence. This progression demonstrates increasing cognitive demand while remaining aligned to the lesson TEKS and objectives.

In addition to assessing varying levels of complexity, the instructional assessments include a variety of TEKS-aligned item types. For example, the module 18 form A test includes multiple-choice and numeric-response items that require students to solve financial literacy problems, analyze mathematical situations, and apply concepts related to earning, spending, saving, borrowing, producing, and consuming. The accompanying answer key identifies the TEKS assessed and the Depth of Knowledge (DOK) level for each item. These varied TEKS-aligned item types provide multiple ways 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. In the Teacher’s Guide, the “Practice on Your Own” section includes a scoring rubric that assigns point values, outlines performance criteria, and provides sample responses for assessment items. For example, module 10, lesson 3 includes descriptions of student responses earning zero, one, or two points and provides sample answers that illustrate each score level. This scoring guidance supports consistent and accurate evaluation of student work.

The materials provide guidance for interpreting student performance on instructional assessments. For example, the “Program Activity Report” displays student performance data and categorizes students based on instructional needs. The report guides educators in interpreting assessment results and determining appropriate supports, including small-group instruction, independent practice, collaborative activities, reteach lessons, and enrichment opportunities. This guidance helps educators interpret student performance and make informed instructional decisions based on assessment data.

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 guide educators on using tasks and activities to respond to student trends. For example, the module 9 data-driven support resource accompanying the “Module Review” assessment directs educators to use assessment results to identify specific content areas where students need additional support and to select corresponding reteach lessons and activities. This resource connects students who demonstrate difficulty solving multistep word problems involving addition to targeted reteach activities aligned to the assessed skill. This guidance helps educators use assessment data to plan instructional tasks that address misconceptions and learning gaps.

The materials guide educators on responding to student performance trends through the “Differentiation and Practice” section. Educators are directed to review data from the “Program Activity Report” to determine each student’s mastery of the Essential Sessions and identify students who may benefit from specific instructional supports. Based on assessment results, educators assign students targeted activities such as educator-led small-group instruction, independent practice, collaborative groups, reteach activities, or extension opportunities. This guidance helps educators use assessment data to match instructional tasks and activities to 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 “Learning Goal” routine is one example of program tools that help educators track student progress and growth. This routine provides educators with ongoing information about students’ understanding of lesson objectives. At the conclusion of lessons, students self-assess their learning, and the Teacher’s Guide directs educators to review class results and discuss how understanding has changed throughout the lesson. Educators then use these results and other assessment data to plan differentiated instruction and future learning. This routine provides an embedded tool for monitoring student progress and informing instructional decisions throughout the year.

Beyond educator-facing progress-monitoring tools, the materials include tools for students to track their own progress and growth. 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 module test scores 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 guide educators on differentiated instruction for students who have not yet reached proficiency. One example is the “Differentiation and Practice” section of module 6, lesson 1. This section directs educators to use the “Program Activity Report” to review student data and determine each student’s mastery of the Essential Sessions. Based on the data, educators identify students who will benefit from small-group instruction and assign differentiated learning pathways, including the educator-led “Almost There: Decompose Ones to Add” mini-lesson for students who need additional support.

In addition to providing guidance for identifying students who need 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: Problems with Even and Odd Numbers” provides explicit questioning, concrete models, and hands-on activities that help students analyze and represent even and odd numbers before writing equations independently. The materials also include “Intervention Activities” that provide structured practice through explicit directions and place-value models. Students identify hundreds, tens, and ones; analyze a base 10 model; and represent numbers using a place-value chart and expanded form. This provides scaffolded support as students develop 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).

One example of the preteaching and embedded supports for unfamiliar vocabulary is in module 4, lesson 2. This module directs educators to use the “Words to Learn” routine to introduce the term partition before students engage in the task and discuss equal parts. The materials also provide preteaching supports in module 13, lesson 2 by recommending the “Words to Learn” routine for terms such as classify, triangle, quadrilateral, pentagon, hexagon, and octagon. These supports help students develop an understanding of unfamiliar mathematical vocabulary before applying the terms during instruction.

The materials include embedded supports for unfamiliar references and academic language in text. For example, in module 13, lesson 1, the “Teaching Strategy: ELPS” guidance helps students distinguish between the everyday and mathematical meanings of the terms corners and vertices. The guidance explains that as students begin using the mathematical term vertices in place of the everyday term corners, they transition from everyday language to a mathematical register. These supports help students interpret unfamiliar references and use precise academic language when engaging with grade-level content.

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 educator 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 and recommends “Ready for More” small-group instruction for students who have demonstrated proficiency. In module 15, lesson 3, the “Ready for More: Use Square Units to Find Area” activity guides students to create rectangles using 12 square tiles, label the number of rows and columns, and explore multiple rectangle configurations using the same number of tiles. Students analyze whether rectangles of different shapes can have the same area, which extends learning beyond the lesson objective while providing 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 15, lesson 2, the “Ready for More: Relate Centimeters to a Number Line” activity guides students to measure classroom objects in centimeters, represent object lengths on a number line, compare measurements, and discuss relationships among the measured lengths. Students answer questions about combined lengths and differences in length and make comparisons between the longest and shortest objects. These opportunities encourage students to analyze measurement relationships 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.

Explicit prompts support educators in modeling and explaining the concepts that students will learn. For example, in module 6, lesson 5, task 2, the materials provide direct questioning prompts such as “What place value will you look at to determine if Mateo needs to regroup to add?” and “How does the quick picture help you check your answer?” The materials provide possible responses and encourage students to defend their reasoning, which helps educators explain regrouping and connect visual models to place-value concepts during addition.

Module 5, lesson 7, task 1 directs educators to use the “Three Reads” routine and the “Process Standard: Analyze” step to help students make sense of the problem before solving it. The materials guide educators to ask questions about the addends, model different strategies for combining three numbers, and facilitate discussion about why changing the order of addends does not change the sum. Through this sequence of prompts, explanations, and discussion opportunities, educators support students in developing an understanding of addition strategies and mathematical reasoning.

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

Module 13 offers one example of how the materials guide educators on effective lesson delivery with a variety of approaches. The module includes mathematical language routines (MLRs) such as “Three Reads,” “Discussion Supports,” “Compare and Connect,” “Critique, Correct, and Clarify,” and “Stronger and Clearer Each Time.” The materials also direct educators to use “Peer Coach Videos” to support implementation of the routines. These supports provide guidance for facilitating discussion, collaboration, language development, and mathematical reasoning through a variety of instructional approaches.

The materials include educator guidance and recommendations for lesson facilitation through concrete and visual representations. For example, in module 7, lesson 5, the Universal Design for Learning (UDL) support strategy recommends using base 10 blocks, base 10 units, a place-value chart, and a number line to support students’ understanding of subtraction with regrouping. By incorporating hands-on and visual models into instruction, the materials provide educators with multiple approaches to facilitate learning and support students’ conceptual understanding of mathematical concepts.

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 guide educators on using multiple types of practice. For example, in module 7, lesson 1, the “What Does This Lesson Look Like in My Classroom?” section guides 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 HMH Waggle” activities. These opportunities support differentiated instruction, independent application, collaboration, and enrichment based on student needs.

The materials include recommended instructional structures to support effective implementation. For example, in module 13, lesson 1, the “Differentiation and Practice” section first directs educators to use the “Program Activity Report” and review the data to determine a student’s individual mastery of the Essential Session. The materials then guide educators to determine which students will benefit most from small-group instruction, providing opportunities for educator-led small-group activities, independent practice, and collaborative groups. The materials also include leveled instructional pathways through “Almost There,” “On Track,” “Extension,” and “Math Language Routine” activities that support differentiated instruction and flexible grouping.

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 guide educators on how to accommodate various levels of language proficiency as defined by the ELPS. For example, the “Emergent Bilinguals: Supporting All Language Learners” teaching strategy in module 13, lesson 1 directs educators to use the “Supporting All Language Learners” chart to let students choose the language scaffolding that they need. The chart provides differentiated supports for pre-production/beginning, intermediate, and high intermediate/advanced students. Pre-production/beginning students create simple models by tracing shapes and counting corners; intermediate students use sentence starters to explain how shapes are sorted; and high intermediate/advanced students generate their own explanations using precise mathematical language. These supports provide linguistic accommodations across multiple levels of language proficiency.

The materials engage students in using more academic language across language proficiency levels. For example, the emergent bilingual teaching strategy in module 7, lesson 1 provides targeted linguistic accommodations that move students from using models and drawings to explaining mathematical reasoning through equations and complete mathematical explanations. Students at the pre-production/beginning level “use linking cubes or make a drawing to show the problem,” while students at the high intermediate/advanced level are prompted to “include equations to represent their model” and explain how the model helps solve the problem. The materials further support academic language development by directing educators to model and practice connecting words such as because, so, then, and and during mathematical explanations. These strategies support increasingly sophisticated oral language and 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 guide educators in effectively using the program in state-approved bilingual/ESL programs. For example, the “Language Development Resource Guide” includes the “Building Reading Fluency” routine, which explains the purpose of fluency instruction for language learners and provides guidance for implementation. The guide directs educators to use “Tracked Reading,” “Echo-Reading,” and “Oral Cloze” routines and explains when they should use each routine during instruction. The materials also provide step-by-step procedures for implementing the routines and describe how they support students’ language development, fluency, and comprehension.

The materials provide educators with embedded implementation guidance for state-approved bilingual/ESL programs. For example, the “Emergent Bilinguals: Supporting All Language Learners” teaching strategy in module 13, lesson 1 directs educators to use the “Supporting All Language Learners” chart to let students choose the language scaffolding that they need. The chart provides differentiated implementation guidance for pre-production/beginning, intermediate, and high intermediate/advanced students. Guidance tells educators to support beginning students with simple models and gestures, provide intermediate students with sentence starters, and encourage advanced students to develop precise mathematical explanations using academic language. These supports help educators implement language scaffolds aligned to students’ proficiency levels during mathematics instruction.

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 embedded guidance helps educators support emergent bilingual students in increasing comprehension through oral and written discourse. For example, in module 17, lesson 2, the Teacher’s Guide directs educators to use the “Three Reads” routine while students solve a pictograph word problem about classmates’ favorite breakfast foods. Students read and discuss the problem multiple times to develop an understanding of the context, quantities, and question being asked.

The embedded guidance helps educators support emergent bilingual students in developing academic vocabulary and building background knowledge through oral and written discourse. For example, in module 14, lesson 2, the Teacher’s Guide explicitly defines the academic vocabulary term estimate as “a number that is close to the exact amount” and directs educators to consider using the “Words to Learn” routine for estimate with emergent bilingual students before instruction begins. Students discuss the meaning of the term and apply it while solving measurement problems. Through explicit vocabulary instruction and opportunities to use the term in context, students build a foundational understanding of measurement concepts while developing academic language.

Beyond supporting comprehension and vocabulary development, the materials include embedded guidance for educators to support emergent bilingual students in making cross-linguistic connections through oral and written discourse. For example, in module 8, lesson 3, the emergent bilingual teaching strategy provides sentence frames to support students’ discussions and written explanations about regrouping. The guidance encourages students to speak in their home language and use models to support their explanations before writing responses about how they know whether regrouping is needed. By connecting students’ home language to mathematical discussions and written justifications, the materials promote cross-linguistic connections while strengthening academic vocabulary, comprehension, and mathematical communication 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 9 form A test, students solve one-step and multistep addition and subtraction word problems, interpret number sentences, determine appropriate operations, and identify mathematical situations represented by equations. Students also analyze real-world contexts, solve problems involving three-digit numbers, and justify solutions by connecting operations to problem situations. These assessment tasks require students to apply conceptual understanding, problem-solving strategies, and computational reasoning across multiple representations, demonstrating depth of understanding aligned to the TEKS.

Module 13 offers further opportunities to demonstrate depth of understanding. For example, the “How Does the Module Support the Conceptual and Procedural Emphasis of the TEKS?” section explains that students develop conceptual understanding of two-dimensional shapes and three-dimensional solids by learning to sort and classify shapes and solids, draw shapes, and create shapes. Students apply this understanding through tasks aligned to TEKS 2.8A–2.8E. The “How Are the Process Standards (PS) Connected to the Content in This Module?” section explains that students apply mathematics, choose tools, share ideas, use representations, and communicate with precise mathematical language while working with geometric concepts. These opportunities require students to analyze attributes, classify figures, create representations, and justify their thinking, demonstrating depth of understanding aligned to the TEKS.

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

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 3, lesson 3, students begin by comparing and ordering four-digit numbers using place-value reasoning. Students then complete comparison statements, determine numbers that are greater than or less than given values, and order multiple numbers from least to greatest. This progression requires students to apply place-value understanding to increasingly complex comparison tasks, supporting grade-level proficiency in the TEKS.

Module 11 offers further opportunities for increasing rigor and complexity. For example, in lesson 1, “Practice on Your Own,” students begin by representing equal groups using objects or drawings. They then describe their models using numbers to complete multiplication sentences before creating and solving their own equal-group situations. This progression moves students from representing mathematical ideas with models to explaining relationships symbolically and applying their understanding in new contexts, increasing rigor and complexity while supporting grade-level proficiency in the TEKS.

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

The materials explicitly connect prior learning to new concepts, as shown in module 5, lesson 3, task 1. In “Connect to Prior Learning,” students use their understanding of the addition fact 6 + 4 = 10 to explain how it helps them solve the related subtraction fact 10 – 6. Students connect addition and subtraction through related facts and use a bar model to represent the relationship between the operations. These opportunities reinforce mathematical connections and support a coherent progression of learning across lessons and units.

Module 11, lesson 5 offers further opportunities to connect mathematical concepts across lessons and units. The “Connect to Prior Learning” prompt asks students, “If Jamal had 20 pencils to divide equally into five cups, how many pencils would go into each cup? Explain.” The accompanying guidance directs educators to facilitate a “Turn and Talk,” listen to students’ explanations, and encourage students with different responses to share their thinking. By connecting previously learned ideas about equal groups to new situations with different values, the materials reinforce relationships among equal groups, division concepts, and mathematical reasoning while supporting a coherent progression of mathematical understanding 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 language learned in previous grade levels to current instruction while preparing students for future learning. For example, in module 12, “What Will Students Learn in This Module?” the materials identify prior learning by reminding educators that students have counted to 120, represented numbers to 1,200 using base 10 models and place-value charts, and related skip-counting by tens and hundreds to adding and subtracting groups of 10 and 100. The module builds on this foundation as students classify even and odd numbers, identify numbers that are 10 or 100 more or less than a given number, extend number patterns, and solve addition word problems using mathematical language to explain their reasoning. The “Future Connections” section notes that students will later interpret products of whole numbers, estimate and round using place-value understanding, efficiently add and subtract multiples of 10 and 100, and solve multistep word problems involving place-value shifts. 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 by maintaining consistent mathematical language that supports learning across grade levels. For example, the “Teacher’s Glossary” section provides mathematical definitions to support educators’ understanding of the mathematics taught in lessons while also indicating that the vocabulary cards and “Words to Learn” routine offer student-friendly definitions. As students progress through grade levels, they encounter consistent mathematical vocabulary that is reinforced and expanded while remaining developmentally appropriate. These supports promote coherence by connecting mathematical language learned in 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 doubles facts and addition strategies to new mathematical knowledge and skills. In module 5, lesson 1, “Spark Your Learning,” students use previously learned doubles facts to solve near-doubles addition situations. During “Spark Discussions” and “Spark Your Learning: Turn and Talk,” students explain how known doubles facts help them solve related addition problems and justify their reasoning. These lesson activities intentionally build on familiar addition concepts and procedures to develop more efficient addition strategies and strengthen mathematical understanding.

Module 9, lesson 1, “Rewrite Addition Problems” offers further opportunities to connect students’ prior knowledge of concepts and procedures to new mathematical knowledge and skills. Students build on previously learned experiences representing addition situations with concrete models and equations as they solve one-step addition word problems by modeling with base 10 blocks, writing equations in expanded form, and representing solutions on a number line. By extending familiar addition concepts and procedures to more sophisticated place-value representations and problem-solving strategies, the lesson intentionally develops students’ mathematical reasoning while strengthening coherent connections between prior learning and new mathematical knowledge and skills.

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 5, “Recall Basic Facts to Subtract Within 20,” students retrieve addition and subtraction strategies while practicing subtraction fluency. Students developed these skills through earlier learning in addition and subtraction within 20, properties of operations, and the relationship between addition and subtraction. This strengthens procedural fluency and long-term retention in a later unit.

The materials continue to provide spaced retrieval opportunities across lessons through the “Train Your Memory” section. In module 7, lesson 2, students revisit the decomposition strategy introduced in lesson 6.2 by breaking apart numbers to solve 32 + 14. They then apply previously learned addition and subtraction fluency to solve equations. These retrieval opportunities reinforce conceptual understanding, procedural fluency, and long-term retention by connecting previously learned strategies to later lessons.

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

The materials guide educators to provide students with opportunities that interleave previously learned skills and concepts. In lesson 4.3, the “Train Your Memory” section requires students to compare sets using more and fewer, identify a number based on place-value clues from lesson 2.4, solve missing-addend and subtraction fluency equations, and solve a comparison word problem. By incorporating counting, comparison, place-value reasoning, addition, subtraction, and problem-solving within the same practice set, educators interleave practice across lessons.

The materials continue interleaved practice across lessons and units by presenting varied problem types within a single lesson. During the “Differentiation and Practice” portion of lessons, educators can assign “Practice Plus” to reinforce practice concepts across lessons and units. For example, in lesson 9.4, the “Train Your Memory” section asks students to create models to represent and solve subtraction problems. These tasks revisit previously introduced modeling strategies from lesson 12.3 before switching to different types of problems, such as fluently finding the missing addend in number sentences.

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 2, lesson 1, task 3, students match numbers written in expanded form to their corresponding standard form and explain their reasoning. Students respond to the prompt “Analyze: Read the problem again. What do you know? What do you need to do?” This task requires students to analyze mathematical representations to determine the relationship between expanded and standard forms before modeling the number with concrete materials.

In module 17, lesson 3, students interpret, analyze, and evaluate mathematical models and representations using bar graphs. In task 1, students interpret the “Favorite Vegetables” bar graph to identify quantities, analyze relationships between categories, and determine how many classmates chose each vegetable. Students then evaluate the reasonableness of their response by answering the prompt “Does your answer for part C make sense? Explain.” In task 2, students interpret and analyze the “Soccer Goals Scored” bar graph by comparing quantities, identifying differences between players’ scores, evaluating how the graph would change if another goal were scored, and supporting their conclusions with evidence from the representation.

In module 5, lesson 7, task 1, students interpret, analyze, and evaluate mathematical models and representations while solving a problem involving three addends. Students respond to the prompt “Analyze: What are you trying to solve? What tools can you use to show each addend?” They determine how to group the addends by responding to “How can you use these tools to group the two addends to add first? Draw to show what you did.” After solving the problem, students evaluate their mathematical representation by explaining how well their tool worked and what other tool they could have used.

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 1, task 2, students model a situation by showing how 16 animal stickers can be placed equally into two rows and describe the model using numbers to complete a sentence. Students also complete the “Show Another Way” prompt by modeling the stickers in a different arrangement of equal rows and creating their own equal-group problem using objects or drawings. These tasks require students to create multiple mathematical models to represent and communicate mathematical situations.

In module 9, lesson 1, task 1, students create multiple models to represent an addition situation involving building bricks. Students rewrite the numbers in a place-value chart to represent the addition algorithm, draw a pictorial model to represent the problem, and solve for the total number of bricks. During “Turn and Talk,” students use complete sentences and mathematical reasoning to explain how their pictorial model matches the addition algorithm.

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 conceptual understanding to new problem situations and contexts. For example, in module 8, lesson 4, task 2, students use representations to estimate the total number of coins, explain their estimate, determine when regrouping is needed, and solve the addition problem using a place-value chart. Students then compare their estimate to the solution during the “Turn and Talk” discussion. These tasks require students to apply their understanding of place value and addition strategies in a new mathematical context.

In module 9, lesson 2, students apply their conceptual understanding of subtraction to a new real-world situation involving trading cards. Students use an open number line to solve the problem, complete the subtraction algorithm, and then extend their learning in the “Practice On Your Own” section by solving a different subtraction problem involving apples. Responding to the prompt “Use two different strategies to find the answer,” students apply their understanding of subtraction strategies to solve a new problem situation.

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 that provide repeated practice to build the automaticity that students need to complete grade-level tasks. In “Fluency Practice: Using Doubles to Add, Part 2,” students repeatedly solve doubles facts and use those known facts to determine related addition facts. This repeated practice strengthens automatic recall of doubles facts and supports efficient retrieval of basic addition facts needed for grade-level mathematics.

The materials provide tasks that offer repeated practice to build the fluency that students need to complete grade-level tasks. In module 10, lesson 1, “Practice Plus,” students repeatedly determine the value of collections of coins by counting on and then complete the “Solve (Fluency)” problems, including equations such as “___ = 9 + 7” and “___ = 6.” These repeated fluency tasks strengthen students’ ability to accurately and efficiently apply addition and subtraction strategies while reinforcing flexible computation needed for 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.

Students have opportunities to practice applying efficient mathematical procedures. In “Practice on Your Own,” students solve two-digit subtraction problems with and without regrouping, determine when regrouping is required, and solve real-world subtraction situations using place-value charts. These repeated opportunities strengthen efficient subtraction procedures while reinforcing the mathematical skills needed to solve grade-level tasks.

Additionally, students have opportunities to practice applying flexible mathematical procedures within a lesson. In module 17, lesson 5, the “Show Another Way” routine asks students to “rewrite your subtraction number sentence as an addition number sentence.” Students then consider why it is important to show another way to represent the number sentence before participating in the “Collect and Display” routine to communicate their reasoning. These opportunities develop flexible mathematical procedures by encouraging students to represent mathematical relationships in multiple ways and explain their thinking.

Students have opportunities to practice applying accurate mathematical procedures through additional independent practice. In “Practice Plus: Represent Regrouping for Addition,” students solve two-digit addition problems that require regrouping, represent regrouping using place-value charts, and apply regrouping in multiple computation and word-problem contexts. These repeated opportunities reinforce accurate mathematical procedures while providing additional practice with regrouping across multiple contexts.

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

Students have opportunities to evaluate procedures, processes, and solutions. For example, in module 9, lesson 7, task 2, students respond to the “Evaluate Process” prompt by reflecting on their strategy to solve a subtraction problem and describing what they would do differently the next time. Students evaluate the effectiveness of their mathematical process by reflecting on their solution strategy and considering improvements to their approach.

Students also evaluate procedures, processes, and solutions in module 9, lesson 2, task 1. In this task, 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 by writing a matching number sentence and then respond to the “Show Another Method” prompt by solving the problem using a different method. These opportunities require students to evaluate the flexibility of multiple solution strategies and mathematical representations.

In module 8, lesson 8, task 1, the Teacher’s Guide directs educators to have students justify how they used regrouping to solve the problem by supporting their solution with evidence and reasoning. Students then participate in the “Evaluate Reasonableness” routine, in which they discuss their thinking with peers, refine their responses based on the discussion, and respond to the “Show Another Way” prompt by representing and solving the problem using a different method. These opportunities require students to evaluate the accuracy of their solution, the effectiveness of their mathematical process, and the flexibility of multiple solution strategies.

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, in module 3, lesson 2, task 1, the Teacher’s Guide provides questioning, modeling, and discussion prompts that support students in comparing numbers using place-value reasoning. These embedded supports guide educators in developing students’ conceptual understanding before transitioning students toward increasingly efficient comparison strategies based on place value rather than counting.

The “Teacher Background” section of module 8 provides additional embedded supports that explain 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 representing three-digit addition to decomposing addends, representing regrouping in addition, adding three-digit numbers, representing three-digit subtraction, regrouping in subtraction, subtracting three-digit numbers, and regrouping to subtract from numbers with zeros. These embedded supports help educators build students’ conceptual understanding through a purposeful instructional sequence before guiding students toward increasingly efficient addition and 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 8, the “How Does the Module Support the Conceptual and Procedural Emphasis of the TEKS?” section explains that students first develop a conceptual understanding of three-digit addition and subtraction by recognizing when regrouping is necessary. Students then build procedural proficiency by representing, recording, and solving three-digit addition and subtraction problems using place-value concepts and standard algorithms. This guidance supports educators in developing students’ conceptual understanding before procedural proficiency.

Another example appears in module 11, in the section “How Does the Module Support the Conceptual and Procedural Emphasis of the TEKS?” This section explains that students first develop a conceptual understanding of the relationship between equal groups and multiplication and division by understanding why multiplying equal groups finds the total and why dividing equal groups finds the number in each group. Students then build procedural proficiency by modeling equal groups, joining equal groups (multiplication), and separating equal groups (division). This guidance supports educators in developing students’ 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.

Students have opportunities to use pictorial and abstract representations as required by the TEKS. For example, in module 9, lesson 3, task 1, students create and draw a base 10 model, write a number sentence, represent the addition on an open number line, and solve the problem using the standard algorithm. These activities require students to represent mathematical thinking using pictorial models and abstract numerical representations.

In module 6, lesson 4, task 1, students use tools to model the number of pages that Eli reads each night, and then they draw their model and determine the total number of pages read. These activities provide students with opportunities to use concrete models to represent and solve addition problems.

In module 3, lesson 3, students use concrete models to represent and compare numbers, organize numbers in a place-value chart, compare using the symbols >, <, and =, and justify their reasoning. Together, these examples demonstrate that the materials consistently provide opportunities for students to use concrete, pictorial, 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 provide activities in which students connect concrete and representational models to abstract symbolic and algorithmic representations while solving multi-digit subtraction problems. For example, in module 9, lesson 2, task 1, students represent a subtraction situation using base 10 blocks, solve the problem on an open number line, complete a subtraction algorithm, and compare the effectiveness of the different strategies.

In module 12, lesson 5, task 2, students also create concrete and representational models of abstract mathematical concepts. In that task, students create and draw a pictorial model using counters or cubes, write a matching number sentence with an unknown addend, explain how they organized their counting, and defend their solution using a pictorial model.

The digital student experience extends these opportunities by providing interactive activities that reinforce mathematical understanding through multiple representations. For example, Waggle “Understand Place Value” activities reinforce TEKS 2.2A and 2.2B 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.

Throughout the materials, vocabulary cards introduce academic mathematical vocabulary using a consistent instructional routine in which students hear each term, learn its meaning, discuss it, and apply it in mathematical contexts. Each card incorporates “Say It,” “Define It,” “Discuss It,” and “Use It” sections. In this way, the cards pair vocabulary with visual representations to reinforce mathematical language and support students as they communicate with precise mathematical vocabulary.

In module 10, lesson 1, students have opportunities to develop academic mathematical language through visuals, manipulatives, and structured language routines. Educators use the “Words to Learn” routine to introduce vocabulary such as cent, cent sign, value, penny, dime, nickel, and quarter while students identify coin values and communicate their mathematical thinking. Students then participate in the “Compare and Connect” routine, where they compare the value of individual coins to the total value, discuss their reasoning with partners, and refine their mathematical explanations.

In module 4, lesson 1, students develop academic mathematical language through visual models, manipulatives, and embedded language development strategies. Students use arrays, visual models, and concrete representations to explore multiplication concepts and describe mathematical patterns. Educator guidance incorporates guided questioning, “Spark Your Learning,” and emergent bilingual supports that encourage students to explain and justify their reasoning using precise mathematical vocabulary.

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 guide educators on how to scaffold and support students’ development and use academic mathematical vocabulary in context. For example, module 10, lesson 3 incorporates the “Turn and Talk” routine to support students as they explain different ways to write money amounts using mathematical vocabulary. Guidance for the ELPS helps students learn the pronunciation and meaning of dollar, while UDL supports provide sentence frames that scaffold students’ mathematical explanations using precise academic language.

The Language Development Resource Guide provides embedded guidance that supports educators in intentionally developing academic mathematical vocabulary through the “Words to Learn” routine. Educators receive explicit guidance for introducing vocabulary, facilitating meaningful discussion, and encouraging students to apply new mathematical terms through the “Say It,” “Define It,” “Discuss It,” and “Use It” instructional sequence. Because the routine is embedded throughout the lessons, educators have consistent support for developing students’ mathematical language in context.

In module 18, lesson 1, instructional supports help educators strengthen students’ academic mathematical vocabulary during lessons on financial literacy. Educators prompt students to compare the meanings of save and accumulate. They encourage students to restate the meaning of accumulate in their own words before applying the vocabulary in a discussion about how savings grow over time. These embedded prompts scaffold students’ understanding and use of academic mathematical vocabulary within meaningful mathematical contexts.

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.

Embedded guidance throughout the materials helps educators facilitate conversations while modeling appropriate mathematical language through exemplar responses to questions and tasks. For example, module 4, lesson 5 provides guiding questions, possible student responses, and the “Stronger and Clearer Each Time” routine to help students explain and justify how shapes are partitioned into equal parts. Students discuss their reasoning with peers, revise explanations using precise mathematical vocabulary, and participate in the “Turn and Talk” routine to communicate mathematical thinking.

In module 16, lesson 1, educators promote mathematical discourse through the “Turn and Talk” routine. Students explain how they determined where to draw the hour and minute hands while educators encourage the use of formal mathematical language during discussions. Sample responses and sentence starters support students as they hear, refine, and use mathematical language with peers while communicating their mathematical reasoning.

The Implementation Guide’s “Language Growth for All Learners” section supports educators in developing mathematical language. Each lesson includes language objectives aligned to the Texas ELPS and teaching strategies that provide differentiated scaffolds and instructional supports for mathematical communication. For example, the language objective for module 10, lesson 1 is that students will explain orally and with drawings how to determine the total value of a collection of coins. This guidance supports students as they develop and apply increasingly precise mathematical language across lessons and over time.

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

The materials intentionally integrate the TEKS process standards into grade-level instruction by embedding them within mathematical problem-solving tasks. For example, in module 6, lesson 5, task 2, students complete a process standards representations activity in which they draw quick pictures to model adding two-digit numbers; determine whether regrouping is necessary; defend their reasoning; solve the problem; and discuss an alternative addition strategy during a “Turn and Talk.” The task integrates the process standards by requiring students to represent mathematical ideas, justify their reasoning, communicate their thinking, and apply problem-solving strategies as they engage with grade-level content.

The Student Edition demonstrates the intentional integration of the TEKS process standards by embedding multiple process standards within lesson activities. For example, “Practice on Your Own” in module 10, lesson 3 directs students to use a problem-solving model, analyze, plan, solve, and justify while completing mathematical tasks. Embedding these process standards throughout student learning activities demonstrates that the materials consistently integrate standards into grade-level instruction rather than presenting them as separate skills.

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

In the Implementation Guide, the “Mathematical Connections” section explains how mathematical topics intentionally build across modules while being connected to the TEKS. For example, place-value concepts introduced in module 1 are extended through two- and three-digit addition and subtraction in modules 6–8. In module 9, addition and subtraction situations connect prior learning to real-world contexts. In modules 14–15, students apply mathematical process standards through multiple representations, communication, and reasoning.

The materials describe how the course incorporates the TEKS process standards throughout the course. In the Implementation Guide, the “Step Through a Module: Lesson Planning” section explains that the process standards guide every lesson as students engage with the content. The Teacher’s Guide provides strategies to reinforce mathematical communication and reasoning, includes reflection questions in every lesson for students to evaluate and clarify their understanding, and regularly asks students to explain their thinking using multiple representations. Every process standards icon identifies where students use mathematical processes to demonstrate mathematical understanding. This guidance helps educators intentionally embed the process standards 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 organizes each TEKS process standard with guiding questions that support students’ mathematical thinking. For example, under “Apply Mathematics in Everyday Life,” students are prompted to ask “What is the problem about?” “How does this math help someone?” and “Why does my solution make sense?” The chart also encourages students to reflect by completing statements such as “Someone could use this math to ___” and “I use math in this problem to ___.” The chart provides consistent support for applying the process standards throughout the course.

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

In each unit, the materials describe how the course incorporates and connects the TEKS process standards. For example, in module 5, the “How are the Process Standards (PS) Connected to the Content in This Module?” section explains how the module weaves the process standards throughout the instructional sequence. The materials state that students will learn the steps of the problem-solving model (PS 1.B). Then they will use all the steps together in lesson 7 to solve a problem related to using basic facts to add and subtract. The module overview identifies opportunities for students to select tools, analyze relationships, use representations, apply mathematics in everyday life, and justify their thinking using precise mathematical language.

Another example appears in module 10. The materials explain that students will learn the steps of the problem-solving model (PS 2.1.B), and then they will use all the steps together in lesson 3 to solve a problem related to the total value of a coin collection. The overview identifies how specific lessons incorporate additional process standards, including sharing mathematical ideas (PS 2.1.D), using representations (PS 2.1.E), and applying the problem-solving model (PS 2.1.B), demonstrating 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.

Throughout the course, materials explain how the course intentionally incorporates the TEKS process standards into each lesson. For example, the “Before You Teach” pages for lesson 8, “Measure in Centimeters and Meters,” identify the TEKS process standards at the beginning of the lesson, including 2.1.B, 2.1.C, and 2.1.D. The lesson overview includes “Mathematical Standards in This Lesson,” the learning objective, and the language objective.

Module 16, lesson 2, task 1 offers another example of how the course embeds the process standards. In that task, students use the problem-solving model to read and write time to the nearest minute by completing the steps to analyze, plan, solve, justify, and evaluate a process. 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 consistently prompt students to think mathematically, persevere through solving problems, and make sense of mathematics. For example, in module 11, lesson 5, task 1, students solve this problem: “Maya has 12 buttons. There are 3 art stations. Help Maya divide the buttons into equal groups for each station.” Students work through the problem-solving model by responding to these prompts: “Analyze: What information do you have?”; “Plan: What do you have to do to solve this problem? Make a plan and show your work with counters”; “Solve: Divide the counters. How many counters go in each station?”; “Justify: Explain why your answer makes sense”; and “Evaluate Process: Would you rather use a different strategy to divide the counters?” Students extend their thinking through the “Turn and Talk” prompt “How would your model change if Maya had to divide the buttons into 6 stations instead of 3?” These opportunities encourage students to reason through the division problem, persist as they develop a solution, and reflect on their mathematical thinking.

Additionally, the materials provide structured discussions that help students persevere through solving problems and making sense of mathematics. For example, in module 10, lesson 2, 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, guidance prompts educators to monitor responses, address common errors through purposeful questioning, and encourage students who use correct strategies to share their thinking. The “Stronger and Clearer Each Time” and “Turn and Talk” routines further support students as they explain how they used counting on, ask questions about one another’s strategies, refine their responses, and justify their mathematical reasoning.

Further opportunities occur in module 11, lesson 3. During the “Spark Your Learning” routine and tasks 1–4, students solve multiplication problems using equal groups, arrays, drawings, and equations while explaining and refining their reasoning through purposeful educator questioning. Students represent equal groups in multiple ways, compare strategies, and answer prompts such as “How do you know?” and “How are the representations alike?” They also justify why different representations produce the same product as they progress through increasingly complex multiplication tasks. These opportunities encourage students to reason through division problems, persist as they develop solutions, and reflect on their mathematical thinking.

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

The materials guide students to understand that there can be multiple ways to represent and solve problems and complete tasks. For example, in module 1, lesson 4, task 2, students represent the same number using different place-value models by writing the number as hundreds, tens, and ones, trading tens and ones to create an equivalent representation, and responding to “Show Another Way: What is another way you could show the hundreds, tens, and ones?” Students then discuss “How do you know both your drawings show the same total?” These opportunities help students recognize that the same quantity can be represented in multiple valid ways.

As students deepen their mathematical reasoning, the materials guide them in learning the multiple ways to represent and solve problems and complete tasks. During the “Spark Your Learning” routine in module 11, lesson 3, students investigate multiplication situations by modeling equal groups with arrays, drawings, and repeated addition while discussing the advantages of each representation. Students compare visual models that represent the same situation and explain how each representation demonstrates the total number of objects. These structured discussions help students explain how different mathematical representations communicate the same mathematical concept.

To extend this learning, the materials guide students in justifying the multiple ways to represent and solve problems and complete tasks. For example, the Teacher’s Guide for module 10, lesson 3, task 1 directs educators to have students justify why they can write the total value of coins one way using the cents symbol and another way using a dollar sign, decimal, and leading zero. Students then participate in the “Stronger and Clearer Each Time” routine to explain their reasoning, ask questions about one another’s strategies, and refine their responses. These opportunities reinforce that different representations can be justified when they accurately convey the same mathematical value.

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

Students have multiple opportunities to engage with peers and educators to make sense of math. For example, in module 8, lesson 1, task 1, students use concrete and pictorial models to represent the addition problem about the pages that Clara reads in June and July before identifying the hundreds, tens, and ones represented in their model and solving the problem. Students then explain how the concrete and pictorial models helped them solve the problem and participate in a “Turn and Talk” to discuss how many longs are needed to represent the value of a hundreds flat.

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 2, students represent a number using hundreds, tens, and ones; trade tens and ones to create an equivalent representation; show another way to represent the same number; and write the number represented. Students record multiple representations and matching number sentences before participating in a “Turn and Talk” where they explain how they know that both of their drawings show the same total. These opportunities require students to organize and communicate their mathematical thinking through written representations while making sense of mathematics.

Collaborative discourse strengthens students’ understanding of mathematics. For example, in module 9, lesson 7, task 1, students write a subtraction problem situation to match a given number sentence, solve the problem using a concrete model, and “Show Another Way” to represent the subtraction problem. Students then participate in a “Turn and Talk” to explain how they know their problem situation matches the given number sentence. These structured discussions require students to explain their reasoning, compare mathematical representations, and engage in meaningful mathematical conversations with peers and teachers.

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 guide educators in prompting students to share their problem-solving approaches through structured discussions about strategies, arguments, and justifications. For example, in module 9, lesson 4, task 1, students solve a problem about reading and writing time. Educators prompt students to discuss their problem-solving model and reflect on which strategy they chose and why and how they will keep track of counting minutes. Students explain their reasoning, describe their chosen strategies, and justify how they determined the correct time.

In addition to lesson-level discussions, the materials provide program-wide guidance to help educators support students in reflecting on their problem-solving approaches. The 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 materials encourage 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.

Another example is in module 11, lesson 3, where students solve multiplication problems using equal groups before participating in educator-facilitated discussions about their strategies. The educator guidance prompts students to explain why different representations produce the same product, compare multiple solution methods, defend the efficiency of their chosen strategy, and evaluate alternative approaches during class discussions. These 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 guide educators on how to deliver explanatory feedback based on anticipated misconceptions. For example, in module 7, lesson 5, “Spark Discussions,” the educator guidance identifies a common error in which students write two digits in one place-value column when regrouping. The materials guide educators to address this misconception through prompts such as “How many digits can be in each place value in a two-digit number?” “How can you write 13 as tens and ones?” and “How can you show a regrouped ten when adding?” The guidance includes sample responses that explain that 13 is composed of one 10 and three ones, and that only one digit belongs in each place-value column. These prompts and recommendations prepare educators to provide explanatory feedback that addresses anticipated misconceptions.

In module 17, lesson 1, task 1, the materials also prompt educators to provide feedback on anticipated misconceptions. Students interpret a picture graph to answer questions about the data. The Teacher’s Guide provides prompts and possible student responses as educators ask questions such as “What does the picture graph show?” “What does each basketball picture stand for?” and “How can you tell how many points each player scored?” The lesson also identifies a common error in which students misinterpret the picture graph or select the incorrect operation. The guidance has educators remind students to examine the picture graph carefully and use problem wording such as “How many points in all?” to indicate addition and “How many more points?” to indicate subtraction. These prompts, possible student responses, and instructional recommendations help educators provide explanatory feedback based on student responses while proactively addressing anticipated misconceptions.

The program’s “Differentiation and Practice” structure, which is embedded throughout the materials, also guides educators in providing feedback. 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 activities allow educators to deliver explanatory feedback and instruction that responds to individual student needs.