HMH Into Math Texas, Grade K

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

The program’s scope and sequence resources 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 the Implementation Guide.


The scope and sequence charts describe the TEKS and ELPS alignment for each module and lesson and identify the concepts taught throughout the instructional year. Additional program materials support this alignment through the TEKS and ELPS correlations, as well as “Correlations by Lesson” documents that break down concepts taught by module. Under the program dropdown, the scope and sequence in 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).

Materials provide a “Scope and Sequence with Yearly Pacing” 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 guide educators 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.

The “Module Order Rationale” explains that “students begin the year by developing conceptual understanding of the numbers zero through five, focusing on counting, reading, and writing numbers in module 1 prior to applying their understanding of counting to compare and order numbers to five in module 2. The same pattern is followed as numbers are extended to 10 in modules 3 and 4 and ultimately to 20 in modules 5 and 6.”

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

The materials offer comprehensive planning supports, structured instructional routines, and embedded guidance to help educators internalize the units and lessons. 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 help educators plan instruction.

The materials include other resources to deepen educators’ understanding and help them internalize module and lesson components. These include the “Step Through a Module” section of the Implementation Guide and the “Teacher Background” sections, which feature mathematical rationales, examples, and summaries and explain the importance of course concepts. The “Module Internalization Tool” and “Lesson Internalization Tool” 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 can 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 Professional Learning and Coaching Guide and other materials offer instructional support, implementation guidance, pacing recommendations, and professional learning resources to help leaders guide educators in implementing the materials as designed.

Other tools include the Look-Fors and Reflection Guide, which 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 supports educators in effectively teaching course concepts. The guide’s comprehensive overviews include necessary background knowledge and academic vocabulary. The module planning sections include guidance on the mathematical focus, instructional progression, and vocabulary connected to the learning goals. For example, module 4, “Explore Numbers to 10,” 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, “Explore Numbers to 10,” directs educators to use the “Words to Learn” (WTL) routine and the module’s WTL vocabulary cards to help students master review and new vocabulary terms. The materials identify vocabulary connected to specific lessons, including recognize and order.

The Teacher’s Guide includes a glossary with academic vocabulary and mathematical definitions to support educator content knowledge. The materials state that the glossary “aims to provide educators with specific mathematical definitions to support their understanding of the mathematics in their lessons.” The provided definitions 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 home activities to support student learning beyond the classroom. For example, a home activity in module 6 directs caregivers to “gather 20 coins and 20 pasta pieces. Line them up in groups of different quantities. Ask your child how many are in each set, and if there are more coins or pasta. Change the number in each set and repeat the activity.”

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 provided materials include daily objectives, questions, tasks, materials, and instructional assessments that meet the content and language standards aligned with the TEKS and ELPS. For example, in lesson 12.1, the “Manipulatives and Materials” section of “Before You Teach” lists “20 pennies and 20 Foam Two-Color Counters.”

Each module includes a “Planning Guide” section. For example, the module 7 “Planning Guide” provides a lesson plan for lesson 7.1, “Compose Numbers to 5.” The lesson plan identifies three tasks to facilitate mastery of the content objective. These tasks include questions for educators to ask students and instructional routines such as “Three Reads,” which supports students in understanding the problem.

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 timing lesson components. For example, the “What’s in Each Lesson” section of module 17 recommends “approximately 45 minutes of an Essential Session and 15+ minutes of suggested Differentiation and Practice opportunities.” Each part of lesson 17.1 includes suggested times, including 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 overviews identify materials educators need to deliver lessons effectively. For example, the module 2 “Planning Guide” provides a lesson plan for lesson 2.2, “Identify a Greater Number of Objects to 5.” The “Manipulatives & Materials” section lists “Crayons,” “10 Foam Two-Color Counters,” “10 Linking Cubes,” and “Counters” available through HMH Ed™. 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 Teacher’s Guide includes a “Differentiation and Practice” section that provides multiple opportunities for continued learning beyond the Essential Session. The section identifies resources such as “Practice on Your Own,” “Practice Plus” homework, and independent practice activities to reinforce lesson concepts.

The materials guide educators to effectively use “Differentiation and Practice” activities to support students at varying levels of performance. For example, in module 2, lesson 2.2, “Identify a Greater Number of Objects to 5,” the “Differentiation and Practice” section directs educators to use the “Program Activity Report” to review student mastery and determine which students will benefit from small-group instruction. The materials provide leveled practice opportunities, including “Almost There” reteach activities and “Extension” challenge activities.

The materials guide educators on effectively using lesson materials available through the adaptive digital platform. For example, the “Differentiation and Practice” section identifies “Personalized adaptive practice HMH Waggle” as an ongoing practice resource. The materials guide educators to use student performance data from the “Program Activity Report” to select appropriate digital practice opportunities that 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 “Prerequisite Check” at the beginning of module 8 assesses students’ prior knowledge before instruction. Students complete tasks that require them to count objects, compose numbers, represent quantities, and order numbers. The assessment includes prompts such as “Count each set. Write how many” and “Compose numbers to 5.” 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 “Assess” section in module 3, lesson 1 includes a “Quick Check” that measures students’ mastery of the lesson objective. Students respond to the prompt “Show how you can use an object to represent each broom” by creating a model to represent a set of six objects. Additionally, students demonstrate understanding through the “Learning Goal” routine and independent tasks in “Practice on Your Own.” These opportunities allow students to demonstrate understanding through modeling, discussion, and problem-solving tasks throughout the lesson.

The materials include unit-level summative assessments that vary in types of tasks and questions. For example, in the module 9 form A test, students complete picture-based subtraction problems, number-sentence-matching tasks, modeling situations, and written-response items. Students solve problems such as “There are 3 dogs playing. 1 dog leaves. How many dogs are left?” “Which number sentence matches the story?” and “Chris has 4 bats. He gives 2 bats to his sister. How many bats does he have now?” These varied assessment formats allow students to demonstrate understanding through visual models, equations, and real-world problem-solving situations.

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

In the Implementation Guide, the “Step Through a Module” section describes assessment components used throughout the program. For example, 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. This guidance defines the assessments and explains their intended purpose within instruction.

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 skills needed for upcoming learning and helps educators build on students’ strengths to support instruction. Additionally, the guidance explains when to administer the assessment and how educators can use the results, along with the accompanying data-driven support resources, to address identified learning gaps.

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

In the Implementation Guide, the “Step Through a Module” section guides educators on administering 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 five 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.

The materials guide educators on administering summative assessments as well as formative assessments. 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.

Formative assessments align to the course TEKS and the lesson objectives. For example, the “Practice on Your Own” item guide in module 18, lesson 2 identifies the TEKS assessed for each item, the corresponding Depth of Knowledge (DOK) level, and the lesson task to which each item aligns. The guide shows that items 1–3 assess TEKS K.1.D and K.8 standards and align to tasks 1 and 2 from the lesson. This alignment demonstrates that the assessment measures student understanding of both the TEKS and the lesson objectives.

Summative assessments align to the TEKS as well. For example, the module 17 test answer key identifies the TEKS assessed by each item and the lesson in which the content was taught. For example, item 1 assesses TEKS K.7A and aligns to lesson 17.01. The answer key identifies the standard measured by each assessment item and connects the assessment to the 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. The “Benchmark Assessments” include answer keys with a TEKS correlation table that aligns each assessment item to the corresponding TEKS and specific lessons.

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

The materials require students to demonstrate understanding through varying levels of cognitive demand, from recalling mathematical concepts to applying relationships and comparing quantities. One example is the module 4 form A test answer key, which identifies the TEKS assessed and the corresponding DOK level for each item. This assessment includes items aligned to TEKS K.2.B–K.2.H and evaluates students at DOK levels 1 and 2. Specifically, item 1 assesses TEKS K.2.B at DOK level 1, while items 5, 6, and 8 assess TEKS K.2.F and K.2.G at DOK level 2.

In addition to evaluating varying levels of complexity, the instructional assessments include a variety of TEKS-aligned item types. For example, in module 18, lesson 2, students complete “Practice on Your Own” activities and DOK-leveled questions that include selected-response, short-answer, and constructed-response items. Students identify information from picture graphs, explain how they determined their answers, and justify their conclusions using evidence from the graph. These varied item types provide multiple opportunities for students to communicate mathematical thinking, support responses with evidence, and demonstrate mastery of the standards in different ways.

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 scoring criteria and sample responses for assessment items. For example, module 10, lesson 1 provides point values, performance descriptors, and possible student responses that distinguish between complete, partial, and incorrect answers. This scoring guidance supports consistent and accurate evaluation of student work.

Throughout the modules, the materials guide educators on interpreting student performance and determining next steps for instruction. For example, the module 10 review and accompanying data-driven support resources identify the content focus and the TEKS assessed and recommend reteach activities for each assessment item. Educators use this information to analyze assessment results, identify misconceptions and learning gaps, and determine targeted instructional supports.

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 to use assessment results to address misconceptions and learning gaps through focused instructional support. For example, the module 18 data-driven support resource identifies the content focus and TEKS assessed for each module review item and recommends specific reteach activities based on student performance. This resource connects students who demonstrate difficulty with skills such as making and reading picture graphs or collecting and sorting data to targeted instructional activities aligned to the assessed content.

The materials guide educators on responding to student performance trends through the “Differentiation and Practice” section. This resource directs educators to review student assessment data to determine each student’s level of mastery and identify students who may benefit from targeted instructional support. Based on assessment results, educators select course activities such as educator-led small-group instruction, leveled practice, collaborative groups, independent practice, and extension opportunities. This guidance helps educators use assessment data to assign 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 “Program Activity Report” provides information about student participation, self-evaluation, assessment performance, and TEKS proficiency. Educators use these data to monitor progress over time, analyze mastery of lesson objectives, and plan differentiated instruction. The report supports ongoing progress monitoring and instructional decision-making.

Every lesson provides students with opportunities to track their own progress and growth. For example, the “Learning Goal” routine prompts students to reflect on their understanding of lesson objectives at the conclusion of instruction. Students self-assess their learning by identifying whether they “don’t understand,” “need more practice,” or “have got it.” Because the routine is embedded throughout the lessons, students regularly evaluate their understanding and identify areas for continued growth. This tool supports student self-monitoring and ownership of learning.

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 to use differentiated instruction, activities, and paired (scaffolded) lessons to support 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 can benefit from small-group instruction and assign differentiated learning pathways, including the educator-led “Almost There: Count and Order to 20” mini-lesson.

In addition to providing differentiated instructional guidance, the materials include scaffolded lessons and intervention activities for students who have not yet reached proficiency in grade-level content and skills. For example, the educator-led small-group lesson “Almost There: Count Forward to and Backward from 10” provides explicit instructional guidance and scripted prompts, linking cubes, number tiles, and 10 frames to support students as they develop counting skills. The materials also include “Intervention Activities” that break learning into sequenced steps with hands-on modeling and educator guidance. For example, students use cubes to model subtraction, remove a cube, count the remaining cubes, and complete a subtraction sentence. These activities provide scaffolded support as students develop proficiency with 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).

A variety of pre-teaching strategies help students understand unfamiliar academic vocabulary and references. For example, in module 18, lesson 2, educators use the “Words to Learn” routine to introduce the term picture graph before students engage in the task. Educators also support emergent bilingual (EB) students by connecting the English term to the Spanish cognates gráfica and pictográfica and explaining that both words mean “a graph that uses pictures to show information.”

The materials include embedded supports for text references. For example, in module 5, lesson 2, picture supports accompany a word problem, allowing students to connect the text to the mathematical situation described. The “Mathematical Language & Emergent Bilinguals” section prompts educators to use the “Words to Learn” routine and vocabulary cards to introduce and review key terms before instruction, supporting students’ understanding of language they encounter throughout the lessons.

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 “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. For example, in module 14, lesson 5, the “Ready for More: Create Two-Dimensional Shapes” activity directs educators to provide foam pattern blocks and have students compose a larger shape, determine which shapes to use, and compare the shapes they created. This educator-guided activity extends learning beyond the lesson objective while providing an additional challenge for proficient students.

The materials include enrichment and extension activities for students who have demonstrated proficiency in grade-level content and skills. For example, in module 14, lesson 1, the “Ready for More: Identify and Describe Circles” activity includes an “I Spy” game in which one student chooses an object in the room and describes its shape while other students identify the object. This activity requires students to apply geometric vocabulary, describe shape attributes, and communicate mathematical thinking, extending learning beyond the core lesson.

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.

Direct prompts help educators model and explain learning concepts. For example, in module 11, lesson 5, task 1, the Teacher’s Guide provides direct questioning prompts such as “How can you use objects to model the problem?” “How many children are in the art group?” and “What kind of number sentence will you write?” These prompts guide educators in helping students represent a subtraction situation, connect concrete models to equations, and explain their mathematical thinking while developing an understanding of subtraction within 10.

Module 12, lesson 1, task 2 directs educators to use the “Three Reads” routine to help students make sense of the problem, determine whether Jasmine has enough pennies to buy a pencil, and evaluate the reasonableness of their answers. The “Discussion Supports” routine offers additional support and opportunities for students to justify their thinking, which helps educators explain problem-solving processes and mathematical reasoning throughout the lesson.

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

Through manipulatives, technology, questioning, and structured discussion, the materials support educators in facilitating lessons across a variety of instructional approaches. For example, module 15 includes multiple Mathematical Language Routines (MLRs), including “Three Reads,” “Compare and Connect,” “Discussion Supports,” “Collect and Display,” and “Stronger and Clearer Each Time.” The materials also direct educators to use “Peer Coach Videos” to reinforce routines.

In module 10, lesson 3, task 3, educators have students use objects or digital tools to model a problem and then participate in the “Three Reads” and “Stronger and Clearer Each Time” routines to discuss and refine their thinking.

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 “Differentiation and Practice” section in module 15 directs educators to review student performance data to determine each student’s mastery of the Essential Sessions and instructional needs. Based on that data, students may engage in educator-led small-group activities, collaborative “Math Language Routine” activities, and independent practice through resources such as “Practice on Your Own,” “Practice Plus,” homework, and personalized adaptive practice. Educators also can use the module’s project-based learning opportunities flexibly throughout instruction.

The “Differentiation and Practice” section in module 6, lesson 2 uses student performance data to recommend educator-led small-group instruction through the “Almost There,” “On Track,” and “Ready for More” pathways. The materials guide educators on collaborative learning through a “Math Language Routine” activity and independent learning through resources such as “Practice on Your Own,” “Practice Plus,” and personalized adaptive practice. This guidance supports instruction in small-group, collaborative, and individual settings.

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 provide linguistic accommodations across multiple levels of language proficiency. For example, the “Emergent Bilinguals: Supporting All Language Learners” section in module 15, lesson 1 provides differentiated language scaffolds for preproduction/beginning, intermediate, and high intermediate/advanced students. Preproduction/beginning students use sentence frames and a word bank to explain how to identify a cylinder. Intermediate students use sentence frames to explain the attributes of a cylinder. High intermediate/advanced students use sentence frames to explain why some objects with flat and curved surfaces are not cylinders.

Students increase their use of academic language across language proficiency levels. For example, in module 10, lesson 5, the emergent bilingual teaching strategy guides educators on providing students time to consult with a partner about the problem before comparing models and discussing strategies for finding the missing addend. The guidance notes that students may begin by listening for evidence of good reasoning and later share their ideas with the class. The lesson also incorporates the “Stronger and Clearer Each Time” routine, in which students discuss their reasoning, ask questions about each other’s thinking, and use what they learn to better understand the problem. These activities support increasingly sophisticated mathematical language and communication.

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

The “Language Growth for All Learners” section explains how the program consistently embeds language supports. The guidance explains how educators use “Observable, Measurable Language Objectives within Each Lesson,” “Texas English Language Proficiency Standards,” and “Teaching Strategies that Support Mathematical Communication” to support language development. Lesson-level language objectives, ELPS-aligned supports, and embedded instructional guidance help students develop mathematical language and content knowledge simultaneously.

In module 13, lesson 1, the “Emergent Bilinguals: Supporting All Language Learners” section directs educators to “use the Supporting All Language Learners chart to let children choose the language scaffolding that they need.” The materials provide differentiated guidance for pre-production/beginning, intermediate, and high intermediate/advanced students. Educators support students through phrases and keywords, sentence frames, and detailed explanations that use academic language. They provide clear guidance for implementing language supports based on students’ English language proficiency levels.

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.

By engaging students in discussions about how vocabulary transfers across languages, educators promote cross-linguistic connections, strengthen comprehension, and develop academic vocabulary through oral and written discourse. For example, in module 18, lesson 2, task 1, students create and interpret a picture graph while learning the term picture graph. The ELPS support directs educators to connect the English term to the Spanish cognates gráfica and pictográfica and guide students in discussing how the words are related across languages. Educators ask, “How do a gráfica or a pictográfica in Spanish help you understand the word graph in English?” They also ask students to explain how the cognates support their understanding of the mathematical concept represented in the graph.

The materials include embedded guidance to support emergent bilingual students in increasing comprehension through oral and written discourse. For example, in module 10, lesson 1, the materials direct educators to “use the Three Reads routine to support children in understanding the problem.” During the first read, students focus on the problem’s context and discuss what it is about. During the second read, students discuss the quantities represented in the problem and explain why the numbers are important. During the third read, students focus on the problem question and explain how they can use addition to represent the situation. Through repeated readings, educator questioning, and discussion routines, students develop comprehension and communicate mathematical thinking through oral and written discourse.

Beyond supporting comprehension, the materials include embedded guidance to help emergent bilingual students develop academic vocabulary and build background knowledge through oral and written discourse. For example, in module 3, lesson 5, the Teacher’s Guide defines the academic vocabulary term ten as “one more than nine; a group of ten ones; 10.” The materials advise educators to “consider using the Words to Learn routine for ten” before instruction begins if the class includes emergent bilingual students. Through explicit vocabulary instruction prior to the lesson, students build a foundational understanding of key mathematical concepts while developing academic language. These supports help students build background knowledge and communicate mathematical ideas using precise academic vocabulary 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 16 form A test, students classify and sort two-dimensional and three-dimensional figures by identifying the defining attributes. Students determine whether shapes have four sides or curved edges, classify groups of circles and cubes, identify cones and cylinders, distinguish shapes with three sides, and select figures based on their geometric attributes. These assessment tasks require students to apply conceptual understanding of shape attributes across multiple representations rather than simply recognize vocabulary, demonstrating depth of understanding aligned to the TEKS.

Module 8 offers one example of how students demonstrate depth of understanding aligned to the TEKS. In lesson 5, “Practice on Your Own 1,” students solve an addition situation involving four gray bunnies and one white bunny. Using counters, students represent the problem, write a number sentence, solve the problem, and explain how their model helped them find the solution. By connecting concrete models, symbolic representations, and mathematical explanations, students demonstrate conceptual understanding of addition while making connections among visual, concrete, and symbolic representations as described in TEKS K.3A and K.2C.

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

In module 6, lesson 2, students begin by comparing two sets of objects to determine which has the greater number and defend their reasoning. Students then count and compare additional sets, record the quantities, and identify the greater set. As the lesson progresses, students extend their reasoning by determining how many more objects are in the greater set. This progression requires students to compare quantities, justify their thinking, and apply increasingly complex reasoning, demonstrating the level of rigor specified in the TEKS.

Module 15 offers further opportunities for increasing rigor and complexity. The “How Does the Module Support the Conceptual and Procedural Emphasis of the TEKS?” section explains that students first develop an understanding of the attributes of three-dimensional solids. Students then identify and describe the attributes of cylinders, cones, spheres, and cubes, identify two-dimensional components of three-dimensional real-life objects, and apply their understanding to explain why solid figures are three-dimensional. The “How Are the Process Standards (PS) Connected to the Content in This Module?” section explains that students apply the problem-solving model and justify their reasoning while using precise mathematical language to classify, describe, and identify two-dimensional shapes and three-dimensional solids. With increasing rigor and complexity, students move from identifying attributes to analyzing relationships and justifying mathematical thinking.

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

Students have opportunities to apply conceptual understanding, communicate mathematical reasoning, and demonstrate depth of understanding aligned to the TEKS. For example, in module 7, lesson 4, task 1, “Turn and Talk: Connect to Prior Learning,” students explain how they decomposed numbers using objects or pictures and compare their representations with a partner. They justify their thinking, discuss multiple ways to decompose a number, and make connections to prior learning using mathematical language.

In module 7, lesson 1, students have additional opportunities to connect mathematical concepts across lessons. Students compose numbers to five by representing the same quantity with cubes, drawings, and number pairs while exploring multiple ways to make a number. The lesson concludes with “Review Spark Your Learning,” where students revisit the opening problem and identify another way to represent the same quantity, reinforcing connections between prior understanding and new learning. These opportunities help students connect multiple mathematical representations and strengthen conceptual understanding across the lesson.

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 in the current grade level to future learning. For example, the “What Will Students Learn in This Module?” section in module 2 explains that students use counting and numbers to determine quantities up to five. Students answer “how many?” questions and count out a given number of objects. The module then extends these understandings as students count and order numbers from one to five, compare numbers and quantities to five, and model equal sets. “Future Connections for Students” explains that students will later compare numbers to 20 using comparative language and count and order numbers to 20. These explicit connections support a coherent progression of mathematical content and language across grade levels.

The materials consistently use mathematical language, demonstrating the program’s coherence across grade levels. The “Teacher’s Glossary” provides educators with definitions to support instruction, while the vocabulary cards and “Words to Learn” routine provide student-friendly definitions for the same mathematical terms. When definitions differ, the glossary explicitly identifies those differences so educators can connect instructional language with the vocabulary students use during lessons. These consistent language supports help connect mathematical language across multiple concepts while establishing a foundation for future mathematical 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..

Activities intentionally build students’ conceptual understanding and procedures to support new mathematical knowledge and skills. For example, in module 11, lesson 1, “Spark Your Learning,” students practice representing subtraction situations with objects, drawings, and number sentences before learning to solve subtraction word problems within 10. During “Spark Discussions” and “Spark Your Learning: Turn and Talk,” students explain their thinking, apply familiar subtraction strategies, and connect prior representations to new problem situations.

In module 18, lesson 1, “Make and Read a Real-Object Graph,” students build on their understanding of sorting, classifying, comparing objects, and counting quantities as they organize data into categories, create real-object graphs, and interpret the information represented. By applying familiar classification and counting procedures to develop a new understanding of graphing and data analysis, the lesson extends students’ mathematical thinking while reinforcing coherent connections between mathematical 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. For example, in module 18, “Practice Plus: Make and Read a Real-Object Graph,” students retrieve counting and number-representation skills as they determine quantities shown in graphs and record the corresponding numbers. They first developed these skills in module 1, “Count, Read, and Write Numbers 0 to 5.” This opportunity allows students to revisit foundational counting concepts in a later unit and strengthen long-term retention.

The materials provide spaced retrieval opportunities with previously learned concepts and skills across lessons and units through the “Train Your Memory” section. For example, in module 18, lesson 2, “Practice Plus: Make and Read a Picture Graph,” students identify the shape that does not have three equal sides from lesson 16.2 and retrieve previously learned subtraction fluency to complete a subtraction sentence. By revisiting geometry concepts and computational skills in a new context, the materials reinforce prior learning while supporting mathematical fluency and long-term retention.

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

In module 13, lesson 1, “Practice Plus: Recite Numbers to 50 by Ones,” students practice reciting numbers to 50 while completing addition within five and fluency problems introduced in earlier modules. By combining counting, addition, and fluency in a single practice set, the materials require students to draw on multiple previously learned skills and concepts rather than focus on a single topic, thereby reinforcing flexible mathematical thinking across units.

The materials extend interleaved practice across lessons and units through the “Train Your Memory” section of independent practice. For example, in module 3, lesson 5, “Practice Plus: Represent 10,” students revisit the comparison strategy from lesson 2.5 by drawing two sets of triangles, comparing the sets by matching, and recording the quantity in each set. Students then shift to fluency tasks that require counting collections of up to five. By requiring students to move between comparison, representation, and counting within the same practice set, the materials provide interleaved practice that strengthens flexible application of 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.

Students have regular opportunities to interpret, analyze, and evaluate mathematical models and representations throughout the lesson tasks. For example, in module 8, lesson 3, task 2, students create an addition word problem using a drawing to represent a set of animals and model the situation with a corresponding number sentence. Students then respond to the prompt “Analyze: What information should you include in your addition word problem?” This task requires students to analyze the mathematical representation they create to figure out what information they need to model the situation accurately.

In module 18, lesson 2, students interpret, analyze, and evaluate mathematical models and representations using picture graphs. Students create a picture graph showing the number of birds and rabbits, analyze the graph to organize and compare categories, and explain how they know how many of each animal to record. Students further evaluate information in the “Favorite Pets” picture graph by determining which pet is most popular, comparing categories, and justifying their conclusions using evidence from the graph.

In module 9, lesson 5, task 3, students interpret a subtraction word problem by using a picture to represent the situation and writing a corresponding number sentence. Students use the visual representation to determine how many students remain after two are on the swings and solve the problem by representing the situation with the equation 5 − 2 = __.

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

In module 8, lesson 5, task 1, students use objects or drawings to represent an addition situation, write a corresponding number sentence to model the problem, and explain their strategy for solving the problem. Students create mathematical models to represent real-world situations involving pieces of fruit before responding to the “Show Another Way” prompt to demonstrate an additional representation.

In module 11, lesson 11.2, students create models to represent subtraction situations. In task 1, students use objects to model a problem involving 10 pinecones, draw their own model to represent the situation, and write a corresponding number sentence to determine how many pinecones remain. These tasks require students to create multiple mathematical representations to solve a real-world situation.

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

In module 7, lesson 3, task 3, students solve a new problem by determining possible combinations of brown and black horses that add up to 10. Students then respond to the “Argue” prompt: “Adam says there could be 4 brown horses and 6 black horses. Is he correct? Why or why not?” They answer the prompt and explain their reasoning. These tasks require students to apply their understanding of number composition to solve a new mathematical situation.

In module 7, lesson 3, task 2, students apply their conceptual understanding of composing 10 to a new problem situation involving balloons at a fair. Students are asked to “draw to show two ways to make 10” and complete the corresponding statements before responding to the questions “What is the most important information in the problem?” and “How do you use that information to solve the problem?” These tasks require students to apply their understanding of number composition in a new mathematical 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. For example, in “Fluency Practice: The Ten-Frame Model, Part 1,” students repeatedly identify the quantity shown on 10 frames by selecting the correct numeral from multiple choices. This repeated practice strengthens automatic recognition of quantities and supports automatic recall of numbers within 10.

The materials include tasks designed to build the fluency that students need to complete grade-level tasks through repeated practice. For example, students repeatedly compare sets of objects up to 10 using one-to-one correspondence and determine which set has the greater quantity across multiple tasks. Students compare a number of ribbons, circle the set with the greater number, compare sets of teddy bears, and complete a “Quick Check” by identifying which set is “greater.” These opportunities strengthen fluency with comparing quantities while supporting efficient and accurate identification of greater amounts.

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 represent combinations that make four and five using connecting cubes and 10 frames. Students use efficient counting and representation procedures to model quantities and compose numbers. These opportunities reinforce efficient mathematical procedures by helping students apply representations to solve grade-level tasks.

The “What Is the Rationale for the Order of the Lessons in This Module?” section explains that the module develops counting, representing, reading, and writing numbers in a logical progression before students apply these understandings through the problem-solving model. For example, in lesson 3.6, task 2, students use a problem-solving model and then evaluate the reasonableness of their solutions by explaining how their answers make sense. Educators facilitate discussion through the “Discussion Support” routine as students justify their approaches, compare their thinking with classmates, and refine their reasoning. These opportunities develop flexible mathematical procedures by encouraging students to evaluate, justify, and refine their problem-solving approaches.

Students have opportunities to practice applying accurate mathematical procedures. For example, they begin with “Spark Your Learning” and continue through tasks 1–3 by modeling subtraction situations, writing subtraction equations, and connecting pictures to number sentences. Students solve a subtraction story by completing an equation such as “4 − 1 = ___” and use a picture to represent the situation. They then revisit the original problem during “Review, Spark Your Learning.” These repeated opportunities reinforce accurate mathematical procedures by requiring students to correctly model subtraction situations, write corresponding equations, and connect visual representations to symbolic notation throughout the lesson.

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.

In module 10, lesson 2, students solve addition problems using multiple representations. In task 1, students use objects or drawings to represent and solve the problem before modeling the same situation with a number sentence, which allows them to evaluate the flexibility of different mathematical representations. In task 3, students again represent an addition situation with drawings and a number sentence before responding to the prompt “Is writing a number sentence a simpler way to represent addition than using objects? Explain your thinking.” This prompt requires students to evaluate the efficiency of different representations. In the “Quick Check” routine, students solve an addition problem and explain how the model they chose helped them find the solution, providing an opportunity to evaluate the accuracy of their representation and solution.

In module 16, lesson 4, task 3, students evaluate whether Adam’s solution of four brown horses and six black horses correctly represents a group of 10 horses. They also justify whether their reasoning accurately satisfies the problem’s conditions.

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

The Teacher’s Guide contains embedded supports that help educators guide students toward increasingly efficient approaches. For example, in module 8, lesson 1, educators use prompts, questioning, and modeling to guide students in connecting concrete representations to addition number sentences. Educators develop students’ conceptual understanding before transitioning students toward increasingly efficient symbolic representations of addition.

The “Teacher Background” section of module 11 provides additional embedded supports. It 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 describes how students progress from representing subtraction with concrete actions and finding differences within 10 to writing subtraction number sentences, representing subtraction situations, and solving subtraction word problems. These embedded supports help educators build students’ conceptual understanding through a purposeful instructional sequence before guiding students toward increasingly efficient symbolic 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 11, the “How Does the Module Support the Conceptual and Procedural Emphasis of the TEKS?” section 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 subtraction within 10 by understanding subtraction as separating a set into smaller parts. Students then build procedural proficiency by solving subtraction problems using spoken words, concrete models, pictorial models, and number sentences with abstract symbols. This guidance supports educators in developing conceptual understanding before procedural proficiency.

Module 13 offers another example. The guidance explains that students first develop a conceptual understanding of patterns and sequences in numbers to 100, including why numbers ending in zero appear in the last column of a hundred chart. Students then use this conceptual understanding to build procedural proficiency by reciting numbers to 50 and 100 by ones, reciting numbers to 100 by tens, and reciting numbers from a given number. 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.

Activities require students to represent mathematical thinking using concrete manipulatives and abstract numerical representations as required by the TEKS. For example, in module 6, lesson 6, task 3, students use counters to model 20 red peppers and an unknown number of yellow peppers, write the number of yellow peppers, compare the quantities using comparison words, and circle the number that is less.

In module 10, lesson 1, “Practice on Your Own,” students draw a picture to represent an addition situation, write a number sentence to model the problem, and explain how they solved it.

In module 11, lesson 2, task 1, students use objects to model a subtraction situation, draw their model, and write a number sentence to represent the problem. 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 include activities that help students connect, create, define, and explain concrete and representational models in relation to abstract mathematical concepts. For example, in module 11, lesson 2, task 1, students use objects to model a subtraction story, draw a representation of the solution, and write a corresponding number sentence.

Another example is in module 11, lesson 2, task 1, where students use objects to model and solve a subtraction situation, draw their model, and write a corresponding number sentence.

The digital student experience extends these opportunities by providing interactive activities that reinforce mathematical understanding through multiple representations. For example, Waggle provides engaging videos and adaptive learning games that build students’ conceptual understanding of mathematics. The “Subtraction Within 5” activities support TEKS K.3B and K.3C by engaging students in solving subtraction word problems using objects and drawings and explaining their strategies using spoken words, concrete and pictorial models, and number sentences.

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

In module 15, the vocabulary cards introduce mathematical terms using a consistent instructional routine in which students hear each term, learn its meaning, discuss it using visuals and manipulatives, and apply it in mathematical contexts. The materials direct educators to reinforce vocabulary through oral repetition, sentence frames, partner discussions, and visual representations. In this way, educators support students as they develop and use academic mathematical language in context.

In module 16, lesson 1, students expand their academic mathematical language through visuals, manipulatives, and structured language routines. Educators use the “Words to Learn” routine to introduce vocabulary such as sort, regular shape, and category while guiding students to use precise mathematical language to describe and classify shapes. Students then apply the vocabulary during the “Compare and Connect” and “Turn and Talk” routines as they justify how they sorted shapes and communicate their mathematical reasoning with partners.

In module 12, lesson 2, students have additional opportunities to develop academic mathematical language. Educators use the “Words to Learn” routine to introduce the term nickel while students examine pictures and physically manipulate a nickel to identify its name and attributes. Students then apply precise mathematical vocabulary during the “Compare and Connect” routine as they discuss similarities and differences with a partner. ELPS and Universal Design for Learning (UDL) support further develop mathematical language.

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

In module 16, lesson 1, the “Turn and Talk” routine encourages students to use lesson vocabulary to explain how they sorted shapes. Embedded educator guidance further supports vocabulary development through emergent bilingual sentence frames and UDL strategies that provide multiple ways for students to communicate their mathematical thinking using precise mathematical language.

The Language Development Resource Guide provides educators with embedded guidance for scaffolding academic mathematical vocabulary through the “Words to Learn” routine. The guide explains when educators should implement the routine and outlines the instructional purpose of each step. The guide also supports educators in introducing, discussing, and reinforcing new vocabulary through the “Say It,” “Define It,” “Discuss It,” and “Use It” sequence. These embedded supports help educators develop students’ understanding and use of mathematical vocabulary during instruction.

In module 19, lesson 3, the materials prompt educators to introduce the terms wants and needs using the “Words to Learn” routine before students begin the task. Emergent bilingual sentence frames then support students as they explain their thinking and apply academic mathematical vocabulary while distinguishing between wants and needs.

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 guide educators to apply appropriate mathematical language through vocabulary and syntax that promote mathematical conversations. For example, in module 10, lesson 1, the “Three Reads” routine helps students make sense of the problem before engaging in mathematical discussions. Educators use questioning prompts, the “Stronger and Clearer Each Time” routine, and the “Turn and Talk” routine to encourage students to explain their reasoning using mathematical vocabulary and complete mathematical statements while discussing different representations of the problem.

In module 16, lesson 4, educators provide opportunities for students to hear, refine, and use mathematical language with peers. Through the “Stronger and Clearer Each Time” routine, students discuss their reasoning with partners, ask questions about one another’s thinking, and use insights from the discussion to refine their responses and mathematical explanations. These structured discussions help students strengthen their mathematical language toolkit over time.

In module 2, lesson 6, educators support student responses through questioning strategies, exemplar responses, and UDL sentence frames. The materials provide sample responses that model the use of vocabulary such as greater than, less than, and equal to, while sentence frames support students as they compare sets and explain their reasoning. These embedded supports help educators scaffold mathematical conversations and strengthen students’ application of appropriate mathematical language.

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

The materials integrate the TEKS process standards appropriately into instruction by embedding process standards directly within lesson tasks. For example, in module 9, lesson 3, task 1, students solve a subtraction story problem, write a matching number sentence, and explain their thinking to a partner. The lesson identifies the process standard with the “PS” designation, demonstrating that mathematical communication, representation, and problem-solving are integrated into grade-level instruction rather than taught separately.

The materials intentionally integrate the TEKS process standards through educator guidance at the beginning of each lesson. The lesson’s introduction identifies the specific TEKS process standards the lesson addresses. For example, in lesson 12.3, the introduction references K.1.B, which requires students to use a problem-solving model that incorporates analyzing information, formulating a strategy, determining and justifying a solution, and evaluating the reasonableness of the result. This consistent lesson-level identification helps educators intentionally integrate the process standards throughout instruction.

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 topics intentionally build across modules while connecting to process standards to strengthen problem-solving, reasoning, communication, and coherence. For example, students develop counting, reading, and representing numbers in modules 1, 3, and 5 before applying those understandings to comparing numbers, decomposing numbers, addition and subtraction, geometry, measurement, and data in later modules. This guidance demonstrates a coherent progression of content and process standards throughout the kindergarten course.

In the Implementation Guide, the “Step Through a Module” section explains that the Texas process standards guide every lesson by identifying where students use mathematical processes to demonstrate understanding. The guide introduces the Texas problem-solving model in module 1 and explains that students continue practicing the individual steps and complete problem-solving model throughout the remainder of the program, demonstrating consistent integration of the process standards across the course.

The recurring “Process Skills Anchor Chart” in each module describes how the course consistently incorporates and connects the TEKS process standards. This chart prompts students to apply the process standards as they solve problems. For example, students answer questions 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 and throughout the kindergarten 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 the “Teacher Background” for module 2, the “How Are the Process Standards (PS) Connected to the Content in This Module?” section explains how the process standards are intentionally embedded across the lessons. It states that “throughout module 2, children learn the steps of the problem-solving model (PS 1.B), and then they use all the steps together in lesson 5 to solve a problem related to matching sets of objects to compare.” The module overview further describes how individual lessons incorporate additional process standards, including selecting tools, using representations, communicating mathematical ideas, analyzing relationships, and using precise mathematical language.

Another example appears in the “Teacher Background” for module 3, in the section “How Are the Process Standards (PS) Connected to the Content in This Module?” The materials explain that “throughout module 3, children learn the steps of the problem-solving model (PS 1.B), and then they use all the steps together in Lesson 6 to solve a problem related to representing numbers and counting forward to 10.” The overview also identifies specific lessons that incorporate additional process standards, including applying mathematics to everyday problems (PS 1.A), selecting tools (PS 1.C), communicating mathematical ideas (PS 1.D), using representations (PS 1.E), and analyzing mathematical relationships (PS 1.F). In this way, the overview 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 make it clear that the process standards are incorporated within the lesson’s mathematical content and instructional goals. For example, the “Before You Teach” pages for lesson 3, “Write Addition Number Sentences Within 10,” identify the TEKS process standards at the beginning of the lesson, including K.1.A, K.1.C, and K.1.G. The lesson overview also includes “Mathematical Standards in This Lesson,” the learning objective, and the language objective.

The process standards are embedded throughout the lesson tasks. For example, in module 10, lesson 2, task 1, students are prompted to “Choose Tools” and “Plan” as they solve an addition problem by representing the sets with objects or drawings. 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.

In module 7, lesson 6, task 1, students think through the problem “Mel takes care of 9 horses. 3 horses are white. The other horses are brown. How many horses are brown?” To solve the problem, they respond to these prompts: “Analyze: What information does the problem give you?” “Plan: How can you use the picture and linking cubes to solve the problem? Show your thinking” “Solve: Complete the statements about the horses” “Justify: Does your answer make sense? How do you know?” and “Evaluate Reasonableness: What can you do to check your answer?” These opportunities encourage students to reason through the problem, persist as they develop a solution, and reflect on the reasonableness of their mathematical thinking.

Students have opportunities to persevere through structured mathematical discussions. For example, in module 12, lesson 3, the “Spark Discussions” routine directs educators to have students “brainstorm possible strategies and engage in independent think time before solving the problem.” After solving, students discuss their thinking, justify their answers, ask questions about one another’s solution strategies, and refine their responses throughout peer conversations. These routines support students as they persist in problem-solving while strengthening their mathematical reasoning and understanding.

Module 3, lesson 1 offers further opportunities for students to think mathematically, persevere through solving problems, and make sense of mathematics. The “Spark Your Learning” routine uses the “Three Reads” routine to help students understand the problem before they brainstorm possible strategies and engage in independent think time before solving. Students then participate in the “Stronger and Clearer Each Time” and “Turn and Talk” routines to explain their reasoning, justify their solutions, and refine their mathematical thinking through peer discussions. These opportunities promote sustained problem-solving while helping students deepen their understanding of mathematical concepts.

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.

Students have opportunities to understand that there are multiple ways to represent and solve problems and complete tasks. For example, in module 7, lesson 2, task 3, students represent the number eight using different combinations of pencils and pens. They compare Katie’s and Em’s solutions, determine whether both representations show eight, and create another way to represent the same quantity using drawings or objects. Students respond to prompts such as “Do Katie and Em both have 8 pencils and pens? How do you know?” and “Use a drawing or objects to show another way to make 8.” These opportunities help students recognize that the same mathematical idea can be represented in multiple valid ways.

Another example is in module 10, lesson 5, task 1, where students analyze an addition word problem by explaining what the problem is asking, choosing objects or drawings to represent and solve the problem, writing a matching number sentence, and describing how they solved the task. Students then respond to the prompt “Show Another Way: What is another way you could solve it?” These opportunities encourage students to explain how they can use different representations and strategies to solve the same problem.

The materials reinforce this expectation by supporting students in justifying that there can be multiple ways to represent and solve problems and complete tasks. For example, in module 12, lesson 3, task 2, educators ask, “What is another way you can solve the problem?” Educators then direct students to use the “Stronger and Clearer Each Time” routine to discuss their thinking, justify their answers, evaluate the problem-solving process, ask questions about different solution methods, and refine their responses through discussion. These opportunities encourage students to justify why different approaches can be appropriate for solving the same mathematical problem.

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 opportunities to make sense of mathematics through problem-solving with peers and educators. For example, in module 6, lesson 6, task 2, students solve a comparison problem by counting purple carrots, using counters to represent a set with more carrots, writing the number of orange carrots, and determining which quantity is greater. Students then tell a partner the steps they took to solve this problem. Educators direct students to use their own words to describe how they showed a number that is more and how they found the number of carrots in each set.

Students also make sense of mathematics by writing about math with peers and educators. For example, in module 10, lesson 5, task 1, students analyze an addition word problem by responding to prompts such as “How can you use objects or drawings to represent and solve the problem?” “Write a number sentence to model how to join the sets,” and “How did you solve this task?” Students also respond to “Show Another Way: What is another way you could solve it?” by recording an additional representation.

Collaborative mathematical discourse strengthens students’ understanding through meaningful discussions with peers and educators. For example, during the “Spark Your Learning” routine in module 3, lesson 1, students represent quantities using concrete models. They then participate in the “Turn and Talk” routine to explain whether they used six red apples and one yellow apple or seven red apples and describe how they counted the objects. The lesson also incorporates the “Stronger and Clearer Each Time” routine, where students discuss their reasoning, ask questions about classmates’ thinking, and refine their responses.

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, educators 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.

In addition to lesson-level discussions, the materials provide program-wide guidance to help educators support students in reflecting on their problem-solving approaches. In the Implementation Guide, the “Texas Problem-Solving Model” directs educators to use student responses to facilitate discourse and reflection while asking questions throughout each stage of the problem-solving process. Suggested questions include “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 by 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 19, lesson 2, task 1, where students determine whether a picture shows someone earning income or receiving a gift and then respond to prompts such as “How do you know which picture shows Rami earning income? Persuade a partner about your answer” and “Argue: Dan says that the picture of selling apples shows a gift. Is Dan correct? Explain your thinking.” Educators then direct students to reflect on their problem-solving strategies and participate in the “Stronger and Clearer Each Time” routine, where they share their reasoning, ask one another questions about how they made their choices, and refine their explanations.

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

Prompts and guidance help educators deliver explanatory feedback based on anticipated misconceptions. For example, in module 7, lesson 4, “Spark Discussions,” the guidance identifies a common error in which students compose two sets instead of decomposing the total to find the number left. The lesson directs educators to address this misconception through prompts such as “How many turtles are at the lake?” “How many turtles are in the water?” and “If 2 turtles are separate or apart from the others, what should you do with the number 2?” The guidance includes sample responses that help educators explain why “5 break apart 2 is 3.” These prompts and recommendations prepare educators to provide explanatory feedback that addresses anticipated misconceptions.

Another example is in module 10, lesson 3, task 1, where students write an addition number sentence to model a word problem and explain what each number represents. Guidance prompts educators to offer probing questions, possible student responses, and guidance for a common error in which students solve the problem correctly but do not understand how to represent the situation with a number sentence. Guidance tells educators to point out the joining sets and explain how the plus and equal symbols represent addition before discussing how the symbols correctly model the situation. These prompts, possible student responses, and corrective guidance help educators provide explanatory feedback based on student responses while addressing anticipated misconceptions.

The materials support educators in providing explanatory feedback based on student 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, allowing educators to deliver explanatory feedback and instruction that responds to individual student needs.