TX ClearMath 1e, Grade K

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

In the Texas ClearMath Grade K Scope and Sequence (165), the yearlong framework is organized into modules, topics, and individual lessons across 165 days of instruction. Each lesson overview identifies learning goals, connections to prior and future learning, and the grade-level Texas Essential Knowledge and Skills (TEKS) and English Language Proficiency Standards (ELPS) aligned to the instruction. This scope and sequence provides educators with a yearlong course map that outlines the TEKS, ELPS, and concepts taught throughout the instructional year.

In the Texas ClearMath Grade K Scope and Sequence (180), the yearlong framework is organized into modules, topics, and lessons across 180 days of instruction. Each lesson overview identifies learning goals and the grade-level TEKS and ELPS aligned to the instruction. This additional scope and sequence provides educators with another course-level map that outlines the TEKS, ELPS, and concepts taught throughout the instructional year.

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 feature a yearlong scope and sequence that aligns the TEKS, ELPS, and core concepts across 165 days of instruction. The Scope and Sequence (165) outlines the instructional framework by modules, topics, and individual lessons. Each lesson overview identifies learning goals, connections to prior and future learning, and the aligned grade-level TEKS and ELPS. This scope and sequence provides educators with a comprehensive yearlong course map that supports instructional planning and alignment with Texas standards.

The materials include additional scope and sequence documents for 180-day and 210-day instructional calendars. These documents outline the TEKS, ELPS, and mathematical concepts addressed throughout the kindergarten course and provide educators with alternative pacing guides that map the instructional progression across the school year. This additional scope and sequence provides educators with another course-level map that outlines the TEKS, ELPS, and concepts taught in the course.

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.

In the Texas ClearMath Grade K Teacher’s Implementation Guide Overview, the “Course Sequence” section explains the intentional progression of the curriculum and how understanding developed in earlier modules prepares students for more complex concepts and skills introduced later in the course. This overview supports educators in understanding the rationale of unit order and how concepts to be learned connect throughout the instructional year.

In the Teacher’s Implementation Guide, the “Intro to ClearMath Grade K — Course Design and Overview” section explains that modules are structured to center instruction around big mathematical ideas by grouping standards into coherent learning progressions. This framework organizes the course into a sequenced learning journey that highlights connections among topics and shows how concepts build across the instructional year.

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

The Texas ClearMath K–5 Teacher Topic Internalization Protocol provides a structured four-step process to support educators in internalizing each topic by explaining the importance of internalization, when to use the protocol, and why it matters for instruction. This protocol guides educators in preparing for instruction by engaging with key instructional components prior to teaching.

The Texas ClearMath K–5 Teacher Lesson Internalization Protocol provides a structured process for lesson internalization by guiding educators to examine learning goals, instructional moves, materials, and anticipated student thinking before instruction. Together, the topic and lesson internalization protocols provide corresponding guidance for internalizing the materials so educators can effectively prepare for implementation as designed.

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

The Texas ClearMath K–5 Coach Re-Engagement Protocol provides coach-facing guidance for supporting educators through a four-step reengagement process focused on reflecting on data, facilitating centers, and moving student learning forward. This resource supports instructional leaders by providing a structured protocol for coaching conversations and implementation support aligned with the design of the materials.

The Texas ClearMath Grade K Coach Topic Internalization Protocol is a structured framework used during individual or collaborative planning before each new topic. This coach-facing resource establishes a process for professional dialogue by supporting educators in defining the mathematical focus, clarifying success criteria, mapping the learning progression, and confirming instructional readiness across classrooms.

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 “Topic Overview” section of the Teacher’s Implementation Guide volume 1 includes an “About the Math” section for each topic. This section provides specialized instructional information by outlining vertical alignment, describing connections to prior and future learning, and explaining the mathematical progression across topics. This overview supports educators in understanding the background content knowledge necessary to effectively teach the concepts in the unit.

In the Teacher’s Implementation Guide, the “Partnering with Caregivers to Foster Success” section in the guide provides resources that support home-school collaboration by reinforcing topic-level understanding. The “Family Guides” section outlines key mathematical vocabulary and includes activities for at-home practice, while the “Conversation Starters” section provides caregivers with questions that prompt students to justify their thinking and connect concepts to real-world contexts. Additionally, the “Topic Summaries” section provides an overview of previously learned concepts and includes practice problems modeled after classroom tasks.

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.

In the Texas ClearMath Grade K Student Practice Book, module 2, topic 5, the “Spanish Family Guide” section provides families with information about the mathematical concepts students will encounter and suggestions for supporting student progress at home. This “Spanish Family Guide” provides unit-level family support connected to the learning students complete in the materials.

In the Student Practice Book, the “Spanish Family Guide” section for module 2, topic 5 provides families with information about the mathematical concepts students will encounter and suggestions for supporting student progress. Together, the English and Spanish “Family Guides” provide families with suggestions on how to support the progress of their students.

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).

In the Teacher’s Implementation Guide, module 1, topic 1, lesson 9 provides educator-facing instructional guidance, questions, tasks, lesson materials, and instructional assessments. The lesson overview includes clearly labeled sections that identify TEKS, ELPS, and objectives, and the lesson provides ongoing questions, tasks, and assessment opportunities to support implementation as designed.

In the Teacher’s Implementation Guide, module 5, topic 13, lesson 1 provides educator-facing instructional guidance for reengagement lessons aligned to the TEKS and ELPS. The lesson includes a structured progression through “Activate, Explore Centers, and Mindset Reflection” activities, as well as guidance for using prior assessment data to assign students to “Clarify Centers,” “Solidify Centers,” or “Stretch Centers.”

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.

In the Teacher’s Implementation Guide, module 3, topic 5, lesson 7, the “Lesson Structure and Pacing Guide” section identifies the sequence of instructional activities, required resources, and suggested timing for lesson components. This lesson overview helps educators prepare the materials and timing necessary to effectively deliver the lesson.

In the Teacher’s Implementation Guide, module 3, topic 5, lesson 8, the “Lesson Structure and Pacing Guide” section identifies the sequence of instructional activities, required resources, and suggested timing for lesson components. This second lesson overview confirms that the materials consistently provide lesson structure, materials, and timing guidance for effective lesson delivery.

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

In the Teacher’s Implementation Guide Overview, the “Monitoring Student Progress” section explains how educators can use the Student Practice Book to monitor student progress and support continued practice and reinforcement aligned with lesson learning goals. This guidance supports the effective use of lesson materials for additional practice beyond core instruction.

The materials also include guidance on the effective use of lesson materials for extended practice through embedded differentiation supports. In the Teacher’s Implementation Guide, the embedded Differentiation Strategies identified in blue boxes provide “Assistance for All,” “Just-in-Time Supports,” and “Challenge Opportunities” to extend, reinforce, and enrich student learning during and beyond the lesson. Together, the Student Practice Book guidance and embedded differentiation supports provide structures for continued practice, reinforcement, and enrichment.

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.

In the Texas ClearMath Grade K Assessment Suite, module 3, topic 6, assessments include a “Snapshot Assessment,” “End-of-Topic Assessment,” and “Performance Task.” These assessments include matching, drawing, multiple-choice, and fill-in-the-blank items. Together, the assessment resources support educators in monitoring student progress and measuring mastery of mathematical concepts and skills throughout instruction.

The materials also include topic-level assessments that support diagnostic, formative, and summative evaluation of student learning. In the Assessment Suite, topics with 10 or more lessons include “Snapshot Assessments,” which serve as formative mid-topic checks of understanding and assess a combination of skills across a group of lessons to inform instructional adjustments. “End-of-Topic Assessments” and “Performance Tasks” function as summative assessments that measure mastery of the skills and concepts taught within the topic. “Performance Tasks” also provide opportunities for students to demonstrate application and reasoning in open-ended contexts.

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

In the Teacher’s Implementation Guide Overview, the “Comprehensive Assessment and Data-Driven Instruction” section explains the purpose and use of each component of the assessment suite, including diagnostic, formative, and summative assessments. This guidance supports educators in interpreting results and making instructional decisions based on student data.

The materials also include guidance for educators on the purpose and use of assessments throughout the curriculum. In the Assessment Guide, the assessment system describes course-level, module-level, topic-level, and lesson-level assessments and explains the purpose of each assessment type. The guide also identifies what each assessment measures, how educators collect assessment data, and how educators use student results to determine next steps for instruction.

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

The Texas ClearMath Grade K Year-at-a-Glance organizes the course by module and identifies the number of instructional days, review days, and assessment days within each module. This pacing structure helps educators administer assessments within a consistent instructional timeframe and supports reliable assessment practices.

The materials also provide pacing guidance that supports accurate assessment administration. In the Year-at-a-Glance, the course overview identifies lessons, assessments, and targeted instruction within each module. This structure helps ensure students receive similar instructional experiences and opportunities for practice before assessment, allowing assessment data to more accurately reflect student understanding of the concepts and skills taught.

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

In the Assessment Guide, module 1, topic 2, the “Snapshot Assessment Blueprint” and “End-of-Topic Assessment Blueprint” sections identify the TEKS and learning goals connected to assessment items. These assessment blueprints clearly identify the standards and objectives measured, supporting consistency between instruction and assessment and helping educators monitor student progress toward grade-level expectations.

The materials also include module-level and topic-level “ReadyCheck Assessments” administered before instruction to assess student readiness. In the Assessment Guide, the module and topic assessment guidance identifies the TEKS and topic objectives measured by each assessment. This information helps educators use diagnostic assessment results to plan instruction aligned with grade-level expectations and lesson objectives.

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

In the Assessment Guide, module 4, topic 10, the “End-of-Topic Assessment Blueprint” section includes a chart that identifies the TEKS aligned to each assessment item and the corresponding Depth of Knowledge (DOK) level. The blueprint includes items ranging from DOK 1 to DOK 3 and uses multiple item formats, including multiple-select, drawing, short-answer, and matching questions.

The materials also include “Beginning-of-Year Assessments,” “Middle-of-Year Assessments,” and “End-of-Year Assessments” with TEKS-aligned items that evaluate student understanding through varied item types and levels of complexity. These assessments include multiple-choice, short-answer, and fill-in-the-blank items. The items require students to demonstrate procedural understanding, apply concepts, and explain mathematical thinking. Together, these assessment components allow students to demonstrate understanding across a range of TEKS-aligned skills.

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

In module 5, topic 12, the “Performance Task: Partitioning in the Playground” section includes a scoring rubric with two criteria and descriptors for scores ranging from zero to two points for each criterion. These descriptors support accurate scoring by clearly defining performance expectations and levels of proficiency.

The materials also include guidance to help educators interpret student work. In module 5, topic 12, the “Performance Task: Partitioning in the Playground” section includes a scoring rubric, sample student responses, and Student Look-Fors that identify evidence of understanding. These supports help educators identify student strengths, misconceptions, and areas for continued growth.

Evaluation for 2.2b
Materials provide guidance for the use of included tasks and activities to respond to student trends in performance on assessments.

In the Assessment Guide, module 1, topic 1, the “Assessment Blueprints” and “Targeted Instruction Recommendations” sections align each assessment item to the TEKS and identify instructional supports connected to each skill. The “Targeted Instruction by TEKS” section provides educators with suggested tasks and activities to address specific areas of need based on assessment results.

The materials also include targeted instructional guidance following each assessment blueprint. In the Assessment Guide, the “Targeted Instruction Recommendations by TEKS” section helps educators analyze student performance by standard and identify next steps for instruction. Based on assessment results, educators can use the recommended activities and supports to provide additional practice and intervention aligned to specific TEKS and student 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 Assessment Guide directs educators to “Assessment Reports” that are available in the Clear Learning Center. These reports include customizable progress-monitoring charts that allow educators to track individual student and whole-class performance over time. The reports also provide instructional actions based on assessment results, supporting data-driven instructional decisions.

In the Teacher’s Implementation Guide, the topic 8 overview includes a “Topic Self-Reflection” section with a student-friendly data tracker following each “Topic Assessment.” Students color a circle for each I Can statement to show their progress toward mastery of topic objectives. This tool supports student reflection, goal setting, and ownership of learning by helping students identify strengths and areas for continued growth.

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.

In theTeacher’s Implementation Guide, module 3, topic 5, lesson 12 includes educator guidance for differentiated instruction, activities, and scaffolded lessons for students who have not yet reached proficiency on grade-level content and skills. The “Lesson Structure and Pacing Guide” section includes differentiation supports through “Assistance for All” and “Just-in-Time Supports” strategies that provide targeted reteaching opportunities during instruction. These supports include explicit educator guidance, instructional prompts, and strategies designed to address misconceptions and build student understanding of the lesson concepts.

The Teacher’s Implementation Guide provides “Clarify Centers” within “Re-Engagement Lessons” that enable targeted, educator-facilitated support for students who need additional instruction by offering structured opportunities to revisit and strengthen their understanding of key concepts. For example, in module 1, topic 2, after lessons 1 and 2 regarding identifying numbers six and seven, lesson 3 provides a “Make the Number Clarify Center” in which the educator shows students a card with a number between one and seven and the students then make the number with connecting cubes and write the number on their whiteboard.

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).

In the Teacher’s Implementation Guide, module 3, topic 6, lesson 5 includes a “Language Link: Developing Contextual Language” section that has pre-teaching supports for unfamiliar references in text. This section provides guidance for addressing unfamiliar references that may interfere with students’ understanding of mathematical situations. For example, educators are guided to explain contextual references, such as baskets in a basketball scenario, before students engage with the task. These language supports help students develop an understanding of unfamiliar references that are essential for accessing grade-level content.

The Teacher’s Implementation Guide includes a “Language Links: Developing Mathematical Language” section that provides guidance for developing mathematical language, including strategies for using precise vocabulary and discussing mathematical reasoning. For example, in module 5, topic 12, lesson 5, this section guides the educator to explain that people often shorten the phrase 2-dimensional to 2-D and 3-dimensional to 3-D and then to relate the term 3-D to a book or movie that they may have seen in 3-D.

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.

In the Teacher’s Implementation Guide, the “Differentiation Strategy” section includes “Challenge Opportunity” tasks that provide enrichment activities designed to extend student thinking beyond grade-level expectations. These activities engage proficient students in deeper application of mathematical concepts through more complex problems and tasks that promote reasoning and conceptual understanding. Together, these supports ensure that students who demonstrate mastery are appropriately challenged through meaningful extension opportunities.

The Assessment Guide includes rubrics for various evaluations, including performance tasks. The “Recommendations for Future Topics” section provides educator guidance for differentiated instruction, including grouping strategies and suggestions for extension opportunities for students who have demonstrated proficiency in grade-level content and skills. These recommendations support educators in appropriately challenging proficient students by offering opportunities for deeper engagement and continued application of mathematical concepts beyond the core task. These supports ensure that students who demonstrate mastery are provided with meaningful extension experiences that promote higher-level thinking and sustained academic growth.

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.

Each task includes step-by-step instructional guidance in bullet-point format that outlines how educators should model and explain the concept. In addition, speech-bubble icons provide explicit educator prompts that can be used during instruction to support clear explanations and facilitate student understanding. Together, these supports guide educators in effectively modeling concepts and using consistent language to support student learning.

Facilitation notes also include Common Misconception embedded supports that identify likely student misunderstandings and provide guidance for addressing them during instruction. For example, in the Teacher’s Implementation Guide, module 5, topic 6, lesson 12, the educator is reminded that students may focus on the number of ducks instead of the action in the story and provides guidance for educators to prompt students to listen for what the ducks do before deciding whether the groups are “put together” or “take away.”

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

The Texas ClearMath Instructional Strategies Handbook provides educators with a range of instructional strategies organized into categories such as Authentic Problem Solving, Explaining Their Thinking, Guided Interactions, Math Talks, and Multiple Representations. Each strategy includes descriptions, examples, implementation guidance, and tips for strengthening instructional delivery over time. Together, these supports provide educators with multiple approaches for delivering instruction, engaging students in mathematical discourse, and facilitating learning through varied instructional methods.

Each lesson in the Teacher’s Implementation Guide includes a “Lesson Structure and Pacing Guide” section that highlights the specific strategy associated with each activity, illustrating a range of instructional approaches within a single lesson. This guidance supports educators in selecting and implementing appropriate strategies for individual lessons.

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 Teacher’s Implementation Guide volume 2 incorporates multiple forms of practice, including guided, collaborative, and independent learning opportunities that reinforce key concepts and skills. Clear educator guidance and recommended instructional structures, such as whole-group, small-group, partner, and individual activities, support effective implementation. These varied practice formats help students build understanding, apply learning, and develop confidence through meaningful engagement with the content.

The Teacher’s Implementation Guide volume 1 provides a variety of practice opportunities, including guided, collaborative, and independent tasks that strengthen student understanding of key concepts and skills. Embedded educator guidance outlines effective implementation through whole-group, small-group, partner, and individual learning structures. These diverse practice experiences support skill development, encourage active engagement, and help students apply their learning with increasing independence and confidence.

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 Texas ClearMath Grade K Emergent Bilingual Student Support Handbook includes educator guidance for each lesson on providing linguistic accommodations for multiple levels of language proficiency. The “Emergent Bilingual Student Support” section provides connected ELPS-aligned scaffolds and supports for Pre-Production/Beginning, Intermediate/High Intermediate, and High Intermediate/Advanced learners. These supports include leveled sentence stems, reminders, and structured prompts that guide student discussion and participation in mathematical discourse. Across proficiency levels, the materials progressively increase expectations for students to use more complex and academic language, supporting students in developing and applying increasingly sophisticated language structures as they engage with grade-level content.

The Emergent Bilingual Student Support Handbook provides guidance for implementing linguistic accommodations that support students at varying levels of English language proficiency in alignment with the ELPS. Embedded supports—including sentence stems, visual representations, structured discussion opportunities—and targeted academic vocabulary instruction, help students access grade-level content while developing language skills. These scaffolds encourage students to progressively strengthen their use of academic language across listening, speaking, reading, and writing tasks.

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

The Teacher’s Implementation Guide includes implementation guidance to support educators in effectively using the materials in state-approved bilingual and English as a second language (ESL) programs. The “Empowering Emergent Bilingual Students” section in both the Teacher’s Implementation Guide and Emergent Bilingual Student Support Handbook provide educators with structured strategies to support multilingual learners during instruction. This includes embedded ELPS-aligned guidance, sentence frames for verbalizing mathematical thinking, word banks to support academic vocabulary development, and language goals that define expected language use within each topic. Together, these supports provide clear implementation guidance for adapting instruction to meet the linguistic and academic needs of emergent bilingual (EB) students while maintaining access to grade-level content.

The Emergent Bilingual Student Support Handbook provides clear guidance for implementing instruction within state-approved bilingual and ESL programs. Embedded supports include language development strategies, ELPS-aligned instructional recommendations, and opportunities for students to build both academic content knowledge and language proficiency. These resources help educators effectively support multilingual learners while ensuring access to rigorous, grade-level 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 Emergent Bilingual Student Support Handbook offers comprehensive topic-level resources that effectively address the needs of EB students. In topic 12, instructional supports build background knowledge and comprehension through concrete demonstrations and visual references, while opportunities for home-language use encourage meaningful cross-linguistic connections. Additional scaffolds, including sentence frames and word banks, provide targeted support for developing academic vocabulary.

The educator facilitation notes in the Teacher’s Implementation Guide include guidance for supporting EB students. In module 3, topic 5, lesson 11, the “Emergent Bilingual Student Support” section suggests that educators help students make connections to background knowledge by having students point to the pictures and review weather phrases and short sentences. This activity also supports students with vocabulary and comprehension as they utilize academic vocabulary in their written answers about their picture graph.

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.

In the Assessment Suite, module 3, topic 6, students demonstrate depth of understanding aligned to the kindergarten TEKS by connecting quantities, models, and number sentences. The “End-of-Topic Assessment” asks students to count a group of bears, identify which 10 frame represents 7 as 4 and 3, draw a picture to model the sentence “3 and 6 is 9,” and choose a picture that matches “7 take away 2 is 5.” Students also draw a picture to represent “10 take away 2 is 8,” solve addition and subtraction story problems, determine how many more are needed to make 10, and complete number sentences. These assessment tasks require students to apply conceptual understanding of joining, separating, composing, and decomposing quantities using pictures, ten frames, connecting cubes, story contexts, and number sentences.

The Student Practice Book provides practice opportunities that require students to demonstrate depth of understanding across module 3, topic 7. In lesson 1, students combine quantities to complete sentence frames and represent joining situations with pictures and number bonds. In lesson 2, students complete models that represent adding quantities and numbers. In lesson 5, students draw pictures to represent equations and write equations with sums up to 10. These practice opportunities require students to move among concrete quantities, pictures, number bonds, sentence frames, and equations rather than only finding an answer.

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

In the Teacher’s Implementation Guide, module 3, topic 7, lessons 1–3, questions and tasks progressively increase in rigor and complexity as students move from combining quantities to representing addition with numbers. In lesson 1, students use farm animal counters, sorting tables, number bonds, and sentence frames to combine quantities and represent joining situations. In lesson 2, students use number bond models to put together a quantity and a number. In lesson 3, students use sorted groups, tables, number bonds, and numeral cards to represent totals with numbers.


The lesson sequence in module 3, topic 7 continues to increase in complexity as students move from concrete and pictorial representations toward symbolic addition. Students first count and combine objects, then represent quantities with number bonds and sentence frames, and later use numbers to model addition situations. By lesson 5, students are introduced to the addition sign and use equations to represent addition situations. This progression moves students from concrete joining experiences to number bonds, sentence frames, and equations, supporting grade-level proficiency with addition within 10.

The “Emphasizing Focus, Coherence, and Balance” section of the Teacher’s Implementation Guide “Overview” demonstrates an intentional progression of rigor by integrating conceptual understanding, procedural fluency, and real-world application throughout instruction. Students first develop conceptual understanding by composing and decomposing numbers using multiple representations, such as fingers, dominoes, and visual models. They then build procedural fluency through games, number bonds, and composing and decomposing activities that strengthen connections among quantities, numerals, and operations. Finally, students apply their understanding in real-world story contexts by composing and decomposing numbers to solve and create problems with the same total. This progression intentionally moves students from conceptual exploration to procedural fluency and authentic application, supporting grade-level proficiency aligned to the kindergarten TEKS.

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

In the Teacher’s Implementation Guide, the module 2 overview demonstrates coherence across units by connecting patterns, big ideas, and relationships between mathematical concepts. The module overview explains that students build on earlier counting and number work from module 1 as they compare and describe quantities and begin organizing objects by attributes. The overview also identifies key concepts such as comparing and describing quantities, sorting and classifying two-dimensional shapes, and using mathematical language and reasoning.


The “Mathematical Progressions Across Modules” chart in module 2 connects kindergarten learning across the year by showing how counting and comparison concepts develop across modules. It shows that module 1 focuses on reading, writing, and representing numbers, while module 2 extends that work into comparing quantities and sorting objects. The chart also shows later connections to module 4 and module 5. This progression shows how the materials connect counting, comparing, sorting, classifying, and attribute-based reasoning across 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.

In the Teacher’s Implementation Guide, the module 5 overview connects current kindergarten content to previous and future learning. The overview explains that module 5 supports students as they build connections between counting, comparison, geometry, and story problems by identifying names, exploring shapes and solids, and modeling addition and subtraction within 10. The “Mathematical Progressions Across Modules” chart shows that students revisit earlier number, operations, geometry, and personal financial literacy concepts while extending those ideas into new contexts.

In the Teacher’s Implementation Guide, module 5, topic 13, the “Topic Overview” section connects prior and future learning to current grade-level content. The “Connection to Prior Learning” section explains that in topic 6, students learned to represent and solve addition and subtraction story problems within 10 and to compose and decompose numbers with 10. The “Connection to Future Learning” section explains that in grade 1, students will solve joining, separating, part-part-whole, and take-apart story problems. This shows a clear vertical connection from kindergarten story problems with objects, pictures, and equations to grade 1 problem types with unknowns in different positions.

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..

In the Teacher’s Implementation Guide, module 3, topic 7, lesson 5, students build on their understanding of combining quantities and finding totals within 10 to learn how equations represent addition situations. The lesson uses familiar procedures, including counting objects, joining two groups with manipulatives, and modeling addition with pictures before introducing the addition symbol (+), equal sign (=), and equations such as 3 + 2 = 5. Students connect the concrete models and pictorial representations to the corresponding equation by identifying the two parts and the whole represented in each addition situation. These concepts and procedures extend students’ kindergarten experiences with joining situations and prepare them to solve addition story problems and represent mathematical situations using equations.

In the Teacher’s Implementation Guide, module 5, topic 12, lesson 1, the “About the Math” section highlights the relationship between what students learned in topic 11 about measurable attributes, while the facilitation notes and discussion questions prompt students to consider how to apply their understanding of attributes to identify, sort, and compare two-dimensional shapes based on their attributes. This intentional connection supports students in leveraging prior knowledge to develop a deeper understanding of shapes and shape attributes. The materials demonstrate coherence within this lesson by explicitly connecting prior concepts and procedures in topic 9 “Introduction to Measurement” to new learning in topic 12 “Introduction to 3-Dimensional Solids.”

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

The Teacher’s Implementation Guide provides spaced retrieval opportunities through “Daily Math Routines” and “Re-Engagement Lessons.” In module 3, topic 7, lessons 1–3, students revisit previously learned counting, sorting, and number bond concepts through daily routines such as “Headline Story” and “Mental Math.” These routines are placed before new lesson instruction so students retrieve prior knowledge before extending it to new addition and subtraction representations.


The materials also provide spaced retrieval through “Planning to Re-Engage” and “Re-Engaging” lessons. For example, module 3, topic 7, includes a “Planning to Re-Engage” section after lesson 2 that directs educators to use the “Reflect” activity to assess students’ current understanding by modeling addition using quantities and numbers. Lesson 4 then has students revisit and strengthen prior learning before moving forward. This structure provides students with opportunities to retrieve and refine previously taught concepts after initial instruction.

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

The Student Practice Book provides interleaved practice by mixing current lesson content with previously learned skills. In module 3, topic 7, lesson 1, the Student Practice Book identifies interleaved practice that reviews counting a set of objects and knowing the last number counted is the number of objects in the set while students work on combining quantities and completing sentence frames. This requires students to apply prior counting concepts while working in a new addition context.

In the Student Practice Book, “Concept Lesson” activities incorporate purposeful interleaved practice, identified with a pink IP leaf icon in the answer key. In module 3, topic 7, the Student Practice Book continues to provide interleaved practice across the topic. In lesson 2, the Student Practice Book identifies interleaved practice that reviews sorting data into two categories while students complete models that represent adding quantities and numbers. In lesson 5, the Student Practice Book identifies interleaved practice that reviews using data to create a picture graph while students draw pictures to represent equations and write equations with sums up to 10. These tasks mix current addition work with previously learned counting, sorting, and data skills. These tasks are well designed and strengthen learning by consistently requiring students to connect and apply previously learned skills within new instructional contexts, supporting deeper understanding across lessons and topics.

In the Assessment Suite, students engage in interleaved practice by applying previously learned addition, subtraction, geometry, and personal financial literacy concepts within the same assessment. In the “End-of-Module Assessment,” students write and solve addition and subtraction equations from story problems, identify two-dimensional shapes found on the faces of three-dimensional solids, and distinguish between needs and wants in real-world situations. These varied problem types require students to recall and apply previously learned concepts and skills from multiple mathematical domains within the same assessment. By alternating among operations, geometry, and personal financial literacy tasks, students apply concepts and skills across lessons and units in new contexts.

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

In the Teacher’s Implementation Guide, module 3, topic 6, lesson 8, students interpret and analyze models that represent taking-apart situations. Students use connecting cubes to model taking-apart trains, connect the model to a number bond, and identify the whole and the parts. The lesson guides students to explain what each part of the model represents and how the number bond shows the relationship between the whole number and the two parts.

In the same lesson, students continue interpreting and evaluating mathematical representations using sentence frames and part-part-whole models. Students complete sentence frames such as “5 take away 2 is 3,” use connecting cubes to represent the taking-apart situation, and explain how the model matches the sentence frame. Students also use a part-part-whole model to take apart numbers and discuss how each representation shows the same mathematical relationship.

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

In the Teacher’s Implementation Guide, module 3, topic 6, lesson 2, students create models to represent mathematical situations. During Act It Out!, students use transportation counters and a Transportation Story Mat to model joining stories. For example, students act out a situation with vehicles at the playground where additional vehicles join the group, then determine the total number of vehicles. These tasks require students to create concrete models that represent addition situations.

In the Teacher’s Implementation Guide, module 3, topic 6, lesson 4, students create models to represent part-part-whole addition situations. Students use connecting cubes and a part-part-whole mat to model two parts and a whole. They identify the first part, the second part, and the total and then connect the model to a sentence frame. These tasks require students to create mathematical models that represent put-together situations within 10.

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

In the Teacher’s Implementation Guide, module 3, topic 6, lesson 2, students apply conceptual understanding to new problem situations and contexts. Students use transportation counters and a Transportation Story Mat to act out joining story problems. They model situations such as vehicles at the playground where more vehicles join the group and then determine the total. Students explain what happened in the story, how they modeled the joining action, and how they determined the answer.

In the same lesson, students extend their conceptual understanding by creating and telling joining stories. In “Tell a Joining Story,” students use car quantity cards to create joining situations, place cars on the story mat, and describe what happens as more cars join the group. Students then determine the total number of cars and explain their reasoning. These tasks require students to apply addition concepts in new story contexts rather than only count objects in isolation.

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

In the Teacher’s Implementation Guide, module 3, topic 6, lesson 13, students build automaticity through the “Quick Images: Soccer Balls” activity. Students briefly view structured arrangements of soccer balls, identify the total number of objects, and explain how they saw the quantity. This activity supports subitizing and helps students recognize quantities efficiently without counting each object one at a time.

The Teacher’s Implementation Guide also supports fluency development through the “Daily Math Routines” activities. The overview explains that daily routines include brief, repeated practice such as “Headline Story” and “Mental Math.” These routines give students ongoing opportunities to practice number recognition, subitizing, counting, and mental math outside of the main lesson, supporting automaticity needed for grade-level tasks.

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.

In the Teacher’s Implementation Guide, module 3, topic 6, lesson 4, students practice efficient, flexible, and accurate mathematical procedures. Students use part-part-whole models, connecting cubes, number cards, and sentence frames to represent put-together problems. They move between concrete models and symbolic representations as they determine the total and explain how the two parts make the whole.

In the same lesson, students practice flexible procedures through the “Are They Equal within 10?” and “Splitting Counters: Combinations within 10” activities. Students match models and sentences that represent equal quantities and then use two-color counters to create combinations within 10. These activities require students to compare representations, identify equivalent relationships, and use accurate strategies for composing numbers within 10.

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 the Teacher’s Implementation Guide, module 3, topic 6, lesson 4, students evaluate procedures, processes, and solutions for efficiency, flexibility, and accuracy. During “Modeling Part-Part-Whole,” students compare how a part-part-whole model represents the same joining situation shown with connecting cubes. The educator guidance asks students to explain what is similar and different about the models and how each model represents the two parts and the whole.

The lesson also provides opportunities for students to evaluate strategies during “Reflect and Summarize.” Students determine the total of two groups, explain how they combined the quantities, and discuss strategies for adding numbers. Students also connect the model to a statement and explain how they know the representation is accurate. These tasks require students to evaluate whether models, sentence frames, and totals match the mathematical situation.

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

In module 3, topic 6, lesson 4, educator guidance supports students as they move from concrete joining with counters and cubes to part-part-whole models and sentence frames. The lesson prompts educators to ask how the parts and whole are represented and how the same relationship can be shown in more than one way.

In module 3, topic 6, lesson 13, the reengagement structure also provides embedded supports for educators. Students are grouped into “Clarify Centers,” “Solidify Centers,” and “Stretch Centers” based on evidence from prior learning. The centers guide students from solving addition and subtraction word problems with objects to discovering combinations that make 10 and then to creating and interpreting addition and subtraction story problems. This structure helps educators move students toward more efficient and flexible approaches based on demonstrated need.

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

The Teacher’s Implementation Guide explicitly states how the “Foundations for Effective Math Instruction” addresses the conceptual and procedural emphasis of the TEKS. The overview identifies rigor as a three-legged stool made up of conceptual understanding, procedural fluency, and real-world application. It explains that students develop conceptual understanding by composing and decomposing numbers through multiple representations, such as fingers, familiar visual representations, and dominoes.

The same “Foundations for Effective Math Instruction” section explains how students develop procedural fluency alongside conceptual understanding. The overview describes students building procedural fluency by exploring and applying strategies, using different representations, playing games that reinforce relationships, and practicing procedures in meaningful contexts. This guidance explicitly identifies how the materials balance conceptual understanding, procedural fluency, and application in grade-level mathematics instruction.

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.

In the Teacher’s Implementation Guide, module 3, topic 6, lesson 2, students use concrete models, pictorial representations, and abstract representations. Students use transportation counters as concrete models and a Transportation Story Mat as a pictorial representation to act out joining stories. They then determine the total and explain the joining situation using mathematical language.

In module 3, topic 6, lesson 4, students continue using concrete, pictorial, and abstract representations. Students use connecting cubes to model parts, part-part-whole mats to organize the relationship, and sentence frames to record the mathematical structure. They also match models to statements and use number cards to represent put-together problems. These tasks connect concrete manipulatives, visual models, and symbolic number relationships 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.

In the Teacher’s Implementation Guide, module 3, topic 6, lesson 4, the materials include supports for students in connecting, creating, defining, and explaining concrete and representational models to abstract number relationships. Students first use connecting cubes to create concrete models of two parts being put together. They then use a part-part-whole mat as a representational model to define the relationship between the parts and the whole. Educator prompts guide students to explain what each part represents, how the parts combine to make the whole, and how the model matches a sentence frame. These supports help students connect concrete manipulatives and representational part-part-whole models to abstract symbolic and numeric addition concepts.

In the Teacher’s Implementation Guide, module 3, topic 6, lesson 8, the materials include supports for students in connecting, creating, defining, and explaining models for decomposition and subtraction. Students create concrete models by using connecting cubes to show a train being taken apart. They then connect the concrete model to a number bond and a sentence frame, identifying the whole number and the parts that remain after taking away. Educator questions guide students to define what the number bond shows, explain how the parts relate to the whole, and connect the concrete cubes and representational number bond to abstract symbolic number relationships such as “5 take away 2 is 3.” These supports help students move from concrete modeling to representational models and then to symbolic and numeric subtraction concepts.

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

In the Teacher’s Implementation Guide, module 2, topic 4, lesson 1, students use triangle cutouts to examine triangles in different sizes and orientations. Students point to vertices, trace each side with their fingers, compare triangle attributes, and describe their shapes using academic vocabulary such as triangle, side, and vertex. The “Language Link” section guides educators to support students in comparing triangles and explaining that although triangles may look different, they all have three sides and three vertices.

In module 3, topic 6, lesson 1, students develop academic mathematical language through story mats, counters, visual representations, and structured oral language. Students use farm animal counters and the Farm Story Mat to act out joining stories, tell what happened in the story, and explain how many animals are in each group and in all. Additional centers also support positional vocabulary as students tell joining stories using picture cards and counters. These tasks support students in developing and using language such as joining, together, in all, group, first, next to, in front of, and behind while connecting mathematical vocabulary to concrete and visual models.

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

In the Teacher’s Implementation Guide, module 2, topic 4, lesson 4, the materials include embedded educator guidance to scaffold students’ development and use of academic mathematical vocabulary in context. In “Explore 1: Describing Circles,” students use circle cutouts to describe circle attributes and compare circles of different sizes. Educator prompts guide students to explain how they know each shape is a circle, and the “Language Link” section supports students in using complete sentences and precise language to describe circle attributes.

In module 2, topic 4, lesson 2, the materials scaffold students’ use of geometry vocabulary in context. Students use rectangle and square cutouts, sort and describe rectangles, and discuss how rectangles can be different sizes and orientations while still sharing defining attributes. Educator guidance prompts students to describe shapes using words such as rectangle, side, vertex, corner, same, different, and equal. These embedded supports help students use academic mathematical vocabulary while examining, sorting, and explaining two-dimensional shapes.

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.

In the Teacher’s Implementation Guide, module 2, topic 4, lesson 2 includes embedded educator guidance to support the application of appropriate mathematical language through vocabulary, syntax, and discourse. Students participate in a Think-Pair-Share routine to discuss different ways to sort rectangles before recording their ideas with words and pictures. Educator prompts ask students to explain how they sorted the rectangles, describe how rectangles can be alike and different, and justify how they know each figure is a rectangle. Sample responses model complete mathematical explanations, giving students opportunities to hear, refine, and use academic language with peers.

In the Teacher’s Implementation Guide, module 2, topic 4, lesson 4 supports mathematical conversations using vocabulary, syntax, and discourse. Students use circle cutouts to describe circle attributes and share observations with a partner. Educator prompts guide students to identify and describe attributes using mathematical vocabulary, and sample responses model precise language for explaining how students know a shape is a circle. As educators monitor partner discussions, students hear, refine, and apply mathematical language while communicating their mathematical thinking about circles.

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

In the Teacher’s Implementation Guide, module 3, topic 6, lesson 1, the “Mathematical Process Standards” section identifies standards connected to using a problem-solving model and selecting tools, strategies, and models. Students use farm animal counters, the Farm Story Mat, and the Problem-Solving Model to represent joining situations and determine the total number of animals. Educator questions prompt students to explain how their models represent the story and discuss the strategies they used.

In the Teacher’s Implementation Guide, module 2, topic 4, lesson 1, TEKS mathematical process standards are integrated as students analyze, describe, and communicate geometric relationships. The lesson identifies Mathematical Process Standard K.1.F as students examine triangle cutouts, compare attributes, and explain how they know a shape is a triangle. Students use visual models, manipulatives, and precise language to analyze relationships among sides and vertices, supporting the integration of process standards within the geometry lesson.

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

The “Topic Overview” for module 1, topic 1 includes a “Mathematical Process Standards” section that describes how TEKS mathematical process standards are incorporated and connected throughout the topic. The overview lists the TEKS mathematical process standards and provides Student Look-Fors that describe how students demonstrate each process standard during instruction. This provides educators with a course- and topic-level description of how students apply mathematics, use problem-solving processes, select tools, communicate ideas, create representations, analyze relationships, and justify mathematical thinking.

The materials also describe TEKS mathematical process standards through the lesson design and assessment structure. The topic overview shows where TEKs mathematical process standards connect to student actions and educator observations, while individual lessons include a “Mathematical Process Standard” section within instructional activities. Together, these features show that standards are intentionally incorporated across the course through topic overviews, lesson guidance, Student Look-Fors, and embedded process-standard callouts.

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’s Implementation Guide, module 1, topic 1, the “Mathematical Process Standards” section describes how TEKS mathematical process standards are incorporated and connected throughout the topic. The table identifies each standard and includes Student Look-Fors, such as applying learning to problems, identifying relationships, using tools and manipulatives, communicating mathematical ideas, and explaining thinking. These Student Look-Fors provide consistent expectations for how students demonstrate the TEKS mathematical process standards across the lessons within the topic.

In module 2, topic 4, the lesson structure shows how TEKS mathematical process standards are connected throughout the topic. Lessons on triangles, rectangles, and circles include “Mathematical Process Standard” sections connected to specific activities, such as analyzing relationships among shape attributes, selecting tools and strategies, communicating mathematical ideas, and using precise language. This topic-level design shows that the standards are incorporated across lessons as students identify, describe, compare, sort, and justify classifications of two-dimensional shapes.

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

In the Teacher’s Implementation Guide, module 3, topic 6, lesson 1, the lesson overview identifies the TEKS mathematical process standards incorporated into the lesson. The “Texas TEKS” box lists the TEKS mathematical process standards alongside the content TEKS and ELPS, allowing educators to identify the standards addressed before instruction begins. This lesson-level overview supports consistent access to the TEKS mathematical process standards incorporated into each lesson.

The same lesson also includes an embedded “Mathematical Process Standard” section within instructional activities. For example, in “Explore 1: Act It Out!,” the box identifies the TEKS mathematical process standards addressed as students use farm animal counters, the Farm Story Mat, and the Problem-Solving Model to solve joining story problems. These embedded boxes provide an activity-level overview of the standards incorporated into the lesson and show how the standards connect directly to student tasks.

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

In the Teacher’s Implementation Guide, module 3, topic 7, lesson 8, students think mathematically, persevere through solving problems and make sense of mathematics as they estimate and count collections of objects. Students first estimate the number of objects in a collection and then count and record the actual quantity. Educator questions prompt students to explain the strategies they used to keep track while counting, compare their estimate to the actual count, and describe how grouping objects helped them determine the total. The “Ongoing Assessment” section directs educators to monitor whether students create groups, count by ones or fives, and then adjust their strategies as needed. These supports encourage students to reason about quantities, refine counting strategies, and make sense of the mathematics throughout the lesson.

In the Teacher’s Implementation Guide, module 3, topic 7, lesson 7, students work with a partner to sort equation cards into addition and subtraction groups based on the operation represented. Educator questions prompt students to explain how they categorized the equations and compare how addition and subtraction are alike and different. Students discuss their reasoning with a partner and justify their classifications before reaching agreement. These learning experiences provide opportunities for students to think mathematically, persevere through problem-solving, and make sense of mathematics.

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.

In the Teacher’s Implementation Guide, module 3, topic 7, lesson 7, students develop an understanding that there can be multiple ways to represent and solve mathematical situations. Students use counters and number bonds to decompose a whole into two parts, record different combinations, and explain how each representation shows the relationship between the whole and its parts. Educator questions prompt students to identify what each part of the number bond represents, explain how they determined the missing part, and justify that a number can be decomposed in more than one way. During the closing discussion, students explain and justify multiple decompositions, recognizing that different representations and solutions can correctly represent the same whole.

In the Teacher’s Implementation Guide, module 4, topic 8, lesson 8, students explain and justify that there can be multiple ways to solve addition and subtraction facts within five. Students play an independent group game in which they solve facts before advancing on the game board. Before moving forward, students must agree on each answer, providing opportunities for peers to discuss, explain, and justify their mathematical thinking. During the closing discussion, educator questions prompt students to share and compare the different strategies they used, reinforcing that mathematical tasks can be represented and solved in more than one way.

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.

In the Teacher’s Implementation Guide, module 2, topic 4, lesson 8, students make sense of mathematics through opportunities to do, write about, and discuss mathematics with peers and educators. Partners use two spinners to determine the attributes of a shape, then work together to draw a shape that matches both attributes. Students revise their drawings when a combination of attributes cannot be represented and discuss their reasoning with a partner before recording the completed shape. Educator questions prompt students to explain how they selected the shape attributes and describe combinations of attributes that could not be drawn. These opportunities support students in making sense of mathematics through collaborative problem-solving, recording, and discussion.

In the Teacher’s Implementation Guide, module 5, topic 13, lesson 5, students make sense of mathematics through opportunities to do, write about, and discuss mathematics with peers and educators. Students work with a partner to match related addition and subtraction equations by playing the “Make a Match!” game. As an extension, students write the related fact for an opposite-operations card. During the activity, students read equations aloud, discuss why equation pairs match or do not match, and respond to educator questions by explaining their reasoning.

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

In the Teacher’s Implementation Guide, module 3, topic 6, lesson 1, educators are provided guidance to support students in sharing and reflecting on their problem-solving approaches through explanations, arguments, and justifications. Students use the Problem-Solving Model and manipulatives to solve joining story problems, explain how they modeled each situation, identify the problem and the question being asked, and discuss possible solution strategies during a Think-Pair-Share. Educator questions prompt students to explain how the Problem-Solving Model helped them solve the problem, justify how they know their answer is correct, and reflect on what was the same and different across the joining stories. These embedded supports guide students in sharing and reflecting on their problem-solving approaches.

In the Teacher’s Implementation Guide, module 3, topic 7, lesson 2, students share and reflect on their problem-solving approaches through explanations, arguments, and justifications. During educator modeling, students explain strategies they can use to determine how many more counters are needed to make 10. Students then work with a partner to represent a quantity on a 10 frame, determine the remaining counters needed to make 10, and justify their reasoning by explaining how they found the missing amount. During the closing discussion, educator questions prompt students to share the strategies they used and reflect on their approaches by explaining and justifying how they determined the number of counters needed.

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

In the Teacher’s Implementation Guide, module 3, topic 6, lesson 12, educators are provided prompts and guidance to support explanatory feedback based on student responses and anticipated misconceptions. The lesson includes a “Common Misconception” section that anticipates students may focus on the number of ducks instead of the action in the story. Educator guidance provides prompts to redirect students to determine whether more ducks joined the group or ducks separated before students select an operation. Throughout the lesson, educator questions and sample responses guide educators in responding to student thinking as students explain what happened in the story, determine whether the ducks joined or separated, and identify how the story supports choosing addition or subtraction.

In the Teacher’s Implementation Guide, module 1, topic 1, lesson 6, the materials provide prompts and guidance that support educators in giving explanatory feedback based on student responses and anticipated misconceptions. During the “Reflect and Summarize” activity, students draw different ways to represent the quantity five using fingers or objects and share their representations during an educator-facilitated discussion. Educator questions prompt students to explain and compare the different ways they represented the number five. The lesson also includes a “Common Misconception” section that prepares educators to address the misconception that groups of five must contain identical objects. Educator guidance reminds students that a collection of five can be made using different objects, providing explanatory feedback that reinforces students’ understanding of representing quantities.