InsightMath Texas, Grade 4

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

The materials present a structured framework that organizes instruction across the grade 4 course. The scope and sequence is organized into units and clusters, outlining a comprehensive, yearlong plan of instruction, showing how and when concepts are covered.

The materials also incorporate the Texas Essential Knowledge and Skills (TEKS) and English Language Proficiency Standards (ELPS) taught in the course. Within the grade 4 overview, the “Standards” tab outlines the TEKS and ELPS addressed in each unit and lesson. The scope and sequence includes TEKS and ELPS alignment for the course, showing how and when these concepts occur throughout the grade level.

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 InsightMath Program Overview Guide, Grade 4 outlines the concepts and the suggested number of days allotted for each unit. Additionally, the units are organized into clusters and lessons, giving further clarity to the pacing needed for the effective implementation of the program.

The Program Overview Guide provides pacing suggestions for a range of school-year lengths, including suggestions for 180-day and 165-day calendars. The two calendars are organized into units, accompanied by a recommended range of instructional days necessary to effectively implement the program. Additionally, the “Grade 4 Pacing Guide” in the Program Overview Guide provides a clear overview of the content standards addressed throughout the year and the time allotted to units and lessons with the material.

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 grade 4 materials explain the instructional progression of learning across the program. For example, the “Big Ideas and Course Organization” section provides the rationale of unit order as well as how concepts to be learned connect throughout the course. The material provides a graphic illustrating the progression of learning, outlining the units, big ideas, and connections across domains and clusters. The materials explain how and why units are ordered and contribute to overarching learning goals.

The materials describe how learning builds from one unit to the next across the course. Within the materials, the “Balanced Instruction” section explains the logic behind unit progressions about conceptual understanding, procedural skills, fluency, and application. The “Coherence” section within each unit specifically outlines for educators the connections among prior learning, the current unit, and future learning. The materials describe the intentional purpose of each unit and its sequence, explaining how concepts connect to future and prior learning.

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

Located in the Help Center, “Understanding the Structure of InsightMath” provides protocols for educators on internalizing the overall unit, cluster, and lesson structures of the materials. The article also provides guidance on effectively connecting content across lessons and highlighting the cluster and unit-level essential understandings and big ideas.

The Digital Planning Guide for each unit contains guidance to support educators in previewing the unit, understanding intended outcomes, and internalizing the sequence of learning within each unit and lesson. The guide provides key lesson information, including lesson timing, lesson overview, objectives, vocabulary, and brief activity descriptions. By expanding the individual sections, educators gather specific information about lesson delivery and student support, deepening their understanding of the overall lesson. Together, the structures provide support as educators gain an overall sense of the lesson and internalize its main aspects.

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

The materials include “Support for School-Level Leaders” in the Help Center for instructional leaders to support educators with implementing the materials as designed through the first year of the program’s implementation.

Within the Help Center, the “School Implementation Timeline and Checklist” provides a comprehensive list of action steps by month to help instructional leaders support educators in implementing the program effectively. Additionally, “Supporting Data-Driven Leadership for School-Level Leaders” establishes a systematic approach to collecting, analyzing, and acting on information to maximize instructional leaders coaching of the program.

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 grade 4 materials prepare educators with the content knowledge needed to introduce and develop the mathematical concepts within each unit. A “Schema Building” section in each unit introduction provides background knowledge regarding the development of content within the unit and how students’ schemas will grow and change relative to unit content. Additionally, each unit contains a “Math” tab that describes how math knowledge is balanced and connected to previous and future content, providing background for the educator on the extent of the content within each unit. Furthermore, an “At a Glance” section within each learning cluster outlines the essential understandings, schema building, and cluster outcomes necessary for mastery of the material. The materials provide educator guidance to support concept development by highlighting the background knowledge educators need to teach each lesson effectively.

The grade 4 materials identify and organize the mathematical language students encounter throughout instruction. The “At a Glance” tab summarizes the big idea driving each distinct unit of instruction. An overview of previously taught concepts appears at the beginning of each unit, describing connections students will build throughout the clusters and lessons. Furthermore, the materials provide a glossary explicitly defining mathematical terms, accompanied by the grade level at which each term is introduced and used in instruction. Each unit includes a list of vocabulary at cluster and lesson levels.

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.

Digital materials provide at-home Spanish- and English-language resources that help families reinforce mathematics learning throughout each unit. For example, the “Family Guides – Texas” web page contains links organized by unit in English and Spanish for supporting students’ growth. The grade 4 Family Guide offers key math ideas, tips for home support, and suggestions for at-home practice of skills and concepts. The various activities support students’ understanding of unit concepts while encouraging families to use mathematical vocabulary during learning.

The materials organize family resources so educators can access and share Spanish- and English-language supports throughout the materials. For example, each unit’s “Resources” section contains a link to the “Family Guide – Texas” grade 4 resources, enabling educators to review, print, or digitally share content with families to reinforce concepts introduced during instruction.

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

The materials organize daily instruction into a consistent sequence that supports effective teaching and learning. Each detailed lesson plan includes daily objectives, questions, tasks, materials, and formative instructional assessments required to meet the content and language standards of the lesson. In addition, the “Discourse Questions” and “Look-Fors” have an integral role in helping educators to ensure that each student meets content and language objectives.

The grade 4 materials provide educators with the instructional components needed to implement each lesson from beginning to end. Lessons are introduced with lesson and language objectives, key lesson questions, and aligned vocabulary needed for mastery of the content. Additionally, the grade 4 materials include clusters that contain materials and formative instructional assessments integrated into lessons required to meet the content and language standards of the lesson.

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 instructional materials prepare educators with the materials and planning information needed before instruction begins. For example, each “Preparing for This Lesson” section details the materials necessary to effectively deliver the lesson, along with prep notes, tools, templates, and “Practice Pages.”

The grade 4 materials include the suggested timing for each lesson component in the program. Within the Help components, “Understanding the Structure of InsightMath” outlines a consistent structure, including allotted time and guidance for the four lesson components, comprising “Launch, “Explore,” “Reflect,” “Connect,” and “Workshop.”

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

The materials include guidance on providing opportunities for students to extend and reinforce learning beyond the core lesson. Each lesson’s “Differentiation” section offers extension challenges to support educators in collecting evidence of progress toward mastery. Additionally, within each lesson, “Workshop Time” contains game assignments that give students opportunities to investigate and practice a unit concept.

The educator resources explain how to implement extended learning opportunities within the lesson structure. For example, the grade 4 materials include the article “Understanding the Structure of Insight Math,” which provides specific guidance for educators on the use of the activities in the “Workshop Time” section of the lesson. “Workshop Time” offers strategies for additional practice activities that may be completed simultaneously, independently, or in small groups for extension, enrichment, or homework opportunities.

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 assessment resources measure student understanding at key points throughout each unit using a range of question formats and mathematical tasks. For example, a diagnostic assessment at the beginning of each unit identifies prerequisite areas in which students may need additional support, and a summative assessment at the end of the unit assesses mastery of unit content. These assessments contain a wide variety of question types such as problem-solving tasks, concrete models, representational models, fill-in-the-blank, written response, true/false, multi-select, and real-world application to support educators in understanding students’ thinking and allowing students many ways to show understanding.

The materials provide frequent opportunities to monitor student learning and measure student understanding through various formative learning experiences integrated into daily instruction. For example, formative assessment opportunities highlighted throughout each cluster and lesson incorporate diverse task formats and question types.

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

The grade 4 materials explain how each instructional assessment supports teaching and learning throughout the program. Each unit of study contains an “Assessment” tab with detailed descriptions of the purpose of the diagnostic, formative, and summative assessments provided. The program defines formative assessments as useful for “observing, eliciting, and analyzing evidence of student thinking.” Additionally, the diagnostic assessments are “an opportunity for students to show the foundational skills previously mastered and to reveal areas in which they may need additional support.” Finally, summative assessment “provides an opportunity for students to demonstrate they have met the key learning objectives of the unit.”

The article “Making Assessments Accessible for All Students” describes formative assessments as “especially productive moments where students show their thinking on paper, on screen, through conversation with peers, and in whole-class discussions within the context of daily lessons.” The article explains diagnostic and summative assessment as “intended for students to take independently to demonstrate their understanding of prerequisites before the unit and mastery of content and skills learned from the unit.” The program’s materials and resources give clear definitions and purposes of the types of assessments to support educators in planning, delivering instruction, and using assessment data to monitor student progress.

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

The materials provide structured administration procedures that support consistent implementation across classrooms. The diagnostic “Assessment Guide” section for each unit includes explicit implementation instruction, materials, an item map aligned with the TEKS, and suggestions for supporting students. The materials provide a script to ensure consistent administration of assessments across examiners.

In addition, “Making Assessments Accessible for All Students” provides guidance for educators in determining how to accommodate students with special needs during assessments while ensuring that the content and rigor of an assessment remains the same. The article outlines considerations to support all students during formative, diagnostic, and summative assessments. The recommendations support accurate and reliable results for diverse students.

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

The material’s formative assessments are aligned to the TEKS and objectives of the course, unit, or lesson. Within each cluster, formative assessments at the lesson level align to the TEKS and lesson objectives, and the TEKS content and lesson objectives are clearly labeled. “Look-Fors” and “Discourse Questions” in the “Explore” block of each lesson contain activities, prompts, and questions directly aligned to the lesson objectives and the TEKS.

The diagnostic assessments identify students’ prerequisite knowledge before instruction begins and help educators plan targeted support. For example, the “Assessment Guide” correlates each item number with a specific Texas standard and suggests activities to help students build prerequisite skills, providing notes for educators to monitor emerging skills that will develop over the course of the unit.

Finally, the summative assessments measure student learning at the conclusion of each unit by evaluating mastery of unit objectives. Each summative assessment in the “Assessment Guide” includes an item map containing specific information on each item’s alignment to the TEKS.

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

The materials’ instructional assessments measure student understanding through multiple question formats and response types. For example, item types within the diagnostic and summative assessments vary in format and include matching, multi-select, fill-in, and open response. The TEKS-aligned instructional assessments within the program include two or more question types, providing a comprehensive view of student growth and learning.

Instructional assessments engage students in mathematical thinking across a range of cognitive demands. For example, assessment items vary in difficulty and ask students to create a model, choose a problem-solving strategy, write an equation, calculate, and solve real-world problems. “Assessment Guide” entries for each unit provide information on each item’s alignment to Webb’s Depth of Knowledge (DOK) levels, indicating the level of complexity of the cognitive processes used within each item.

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

Formative assessment resources help educators analyze student understanding and determine appropriate instructional next steps. For example, each formative assessment offers interpretive guidance for specific student actions and misconceptions to notice, look for, or listen for to determine student mastery. This guidance is followed by suggestions for supporting students and sometimes suggestions for extensions. The “Formative Assessment Recording Log” is provided for educators to record student performance.

“Assessment Guide” information in each unit offers scoring support that helps educators evaluate student responses consistently, including scoring information and guidance for interpreting student performance via detailed examples of student responses, particularly when there is more than one possible answer. The unit 7 “Assessment Guide” entry includes the following guidance for the unit’s diagnostic assessment: “Students may also answer with equivalent fractions, such as writing 1/3 instead of 2/6” as additional information following sample answers. The “Assessment Guide” for the unit 2 summative assessment explains, “The playground at Weaver School is 8 feet longer than the playground at Powell School. Answers should include the unit of measure. Students may also answer that the playground at Weaver School is 2 yards and 2 feet longer than the playground at Powell School.”

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 diagnostic assessment resources connect student results to targeted instructional supports. For example, the diagnostic “Assessment Guide” section for each unit provides guidance on supporting students with emerging skills for each item aligned to the TEKS.

The assessment resources include instructional recommendations that help educators address patterns in student learning. For example, the grade 4 materials contain educator guidance to support students whose summative assessment performance indicates “Areas of Struggle.” Additionally, the “Ways to Address” suggestions are designed to respond to the needs of individual students or groups of students according to trends in the assessment data.

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 resources provide documentation tools that help educators monitor student learning throughout each unit. For example, formative assessment opportunities are provided at each cluster level within every unit. The “Formative Assessment Recording Log” is available for educators to track student growth during the unit by documenting observations and planning next steps. The log has an area for each student’s name, whether the cluster objective was met, anecdotal notes, and if support was needed or provided.

The lesson resources incorporate structured reflection opportunities that encourage students to monitor their own learning throughout the year. For example, students have multiple opportunities throughout a unit to assess their learning of the unit’s content in “My Thinking Path” and to follow their development of math process strengths in “My Goal.” A Thinking Path activity appears midway through and at the end of each unit, and there are Goal activities at the beginning, middle, and end of each unit. Because students use the same strengths in Goal activities throughout the year, they have multiple opportunities throughout the course to reflect on their growth relative to the strength, tracking their progress throughout the school year. For example, “I learn from my mistakes” appears in units 1, 6, and 7, while “I use math to represent a real-life situation” appears in units 2, 6, and 11.

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 provide targeted instructional supports that help educators address unfinished learning and strengthen grade-level understanding. The “After this Unit” page in each unit includes “Areas of Struggle,” offering strategies for addressing and supporting students who have not yet reached proficiency on grade-level content and skills. For example, when students struggle to understand place value by patterns when multiplying by 10, in unit 4, the program prompts educators to “Continue to ask students to use precise language about how digits move to explain the shift in place rather than simply memorizing rules. Highlight connections between the number of zeros in the power of 10 and the number of places the digits shift, emphasizing that this pattern exists because of the base-10 structure, to prepare students for understanding that multiplying by 0.1 means making each digit one-tenth its original value.”

Furthermore, each grade 4 lesson includes a “Differentiation” section that provides educators with guidance on adjusting activities to support all students in meeting grade-level proficiency. For example, in unit 1, lesson 8, the “Differentiation” component of the lesson suggests using sticky notes or pieces of paper to reduce the amount of information on a page, placing the Playbook in a plastic sleeve for use with a whiteboard marker, and providing sentence frames to support students not yet reaching proficiency in the grade-level standard of using multiples to solve problems.

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

The materials provide instructional supports that help students understand unfamiliar language encountered during instruction. For example, within the “Differentiation” section of each lesson, “Supporting Language” includes sentence frames and key lesson vocabulary support. In addition, this section contains support for in-text references such as figurative language, idioms, and words with mathematical meanings that differ from colloquial meanings.

Furthermore, the article “Addressing the Needs of Special Populations in Texas” offers guidance for educators to support emergent bilingual (EB) students. For example, educators are encouraged to show central concepts multi-modally by using different types of sensory inputs: acting out scenarios or inviting students to do so; showing videos or images; using gestures; and discussing the context of what is happening.

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

The materials include educator guidance in the unit 6, lesson 3 “Differentiation” section for an “Extension” challenge, directing educators to “Challenge students to generate additional statements about factors and multiples using ‘always’ or ‘all,’ and ask them to explain how they know the statement is always true.” In the Program Overview Guide, The “Teaching Guide” suggests providing open-ended questions, tasks involving higher-order thinking, and real-world applications.

“Extension” activities include a financial literacy lesson in which students design their own one-year spending plan based on a set weekly allowance.

The grade 4 materials include educator guidance for differentiated instruction, enrichment, and extensions to support students who have demonstrated proficiency in grade-level content and skills. For example, while formative assessments for each lesson include a specific enrichment challenge activity for students, there is no explicitly labeled educator guidance for enrichment.

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

The lesson resources provide a structured framework that helps educators introduce and develop new mathematical concepts. Each activity within a lesson includes detailed steps to guide educators in modeling and explaining key concepts, including explicit prompts for educator use. For example, the “Explore” component within each lesson contains scripted explanations, details, and questions, emphasizing key learning moments, understanding, and vocabulary necessary for concept mastery.

The materials support effective instructional delivery through structured questioning and examples that build student understanding. For example, lesson activities include “Discourse Questions,” which offer more prompts for educators to use when modeling and explaining concepts. Additionally, the “Look-Fors” provide student exemplars to support students in consolidating their understanding and restating it in clear mathematical language. Each phase of the lesson plan is summarized concisely and clearly, giving models and clear explanations to use while explaining the concept.

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

The grade 4 materials prepare educators to facilitate instruction through a range of instructional routines used throughout the program. Unit 0 introduces educators to various instructional approaches used in lessons and offers guidance in facilitating activities, preparing educators for the types of learning interactions that they will facilitate throughout the year. For example, an instructional approach described in lesson 3 is “Puzzle Talk,” in which students engage in a whole-class discussion, sharing strategies and analyzing feedback.

Additionally, the grade 4 materials incorporate multiple instructional routines such as virtual manipulatives, “Discourse Questions,” writing to justify answers, puzzles, and “Practice Pages” that support student engagement and mathematical understanding. For example, unit 1, lesson 7 uses “Puzzle Talk,” collaborative exploration, small-group and class discussion, Playbook assignments, and open-ended writing to teach representing multiples.

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 engage students in learning through a balance of instructional experiences designed to build understanding and reinforce new concepts. For example, lessons include a combination of guided, collaborative, and independent learning opportunities with detailed steps for implementing those activities and facilitating discussions about the underlying mathematics.

The grade 4 materials organize instruction using flexible grouping formats that support a variety of learning experiences throughout each lesson. Within each lesson’s “Workshop Time,” activities vary in structure and include a game or a “Practice Page” completed independently to enable students to extend practice at their own pace. “Explore” activities within lessons are suggested for use in a small group setting. Lastly, the “Reflect and Connect” phase of each lesson requires individual reflection followed by whole-group discussions, providing opportunities for students to share their written responses and hear multiple ways to justify an answer.

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

The materials include instructional guidance to support language development for EB students. The article “Addressing the Needs of Special Populations in Texas” offers educator guidance on linguistic accommodations for various levels of language proficiency, such as a list of universal language supports not identified in the “Differentiation” sections of specific lessons, as well as essential information for educators about the language supports within “Differentiation” sections. However, the ELPS proficiency levels are not explicitly referenced in educator guidance to support EB students.

The materials do not include linguistic accommodations differentiated for an additional language proficiency level. While there are supports such as sentence frames, visual cues, and vocabulary guidance, the materials lack accommodations for multiple proficiency levels as defined by the ELPS.

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

The materials explain how to adapt and implement the program to meet the needs of emergent bilingual and ESL classrooms. For example, “Addressing the Needs of Special Populations in Texas” includes implementation guidance to support educators in effectively using the materials in state-approved bilingual/ESL programs.

Additionally, the Universal Design for Learning (UDL) provides further guidance on how to implement lessons to reach all students, detailing design elements that enhance accessibility for EB students and the rationale for their recommended use.

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.

Each lesson includes embedded guidance for educators to support EB students through the “Supporting Language” category within the “Differentiation” section. However, the materials do not support students in making cross-linguistic oral and written connections.

The materials encourage mathematical discussion that strengthens academic language and conceptual understanding. For example, the grade 4 materials include activities within a lesson that provide opportunities for oral discourse through “Discourse Questions” that develop academic vocabulary, increase comprehension, and build background knowledge.

The materials include embedded guidance for educators to support EB students in developing academic vocabulary, increasing comprehension, and building background knowledge through written discourse. Multiple lessons in each unit also provide opportunities for students to use written discourse to develop academic vocabulary, increase comprehension, build background knowledge, and make cross-linguistic connections.

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.

Practice opportunities throughout lessons require students to apply their learning in ways that demonstrate understanding of the grade-level TEKS. For example, in lesson 9, “Exploring Multiplication and Division Relationships,” students first solve multiplication problems using mental math before applying their understanding to solve related division problems. They then represent a word problem with multiplication and division equations and use mathematical tools to justify their solutions. Finally, students write corresponding multiplication and division equations with variables, demonstrating their understanding of the inverse relationship between multiplication and division.

The materials include instructional assessments that allow students to demonstrate their understanding of grade-level mathematical concepts and skills aligned to the TEKS. In grade 4, practice opportunities throughout unit 1 require students to develop conceptual understanding of multiplication and division through a progression of learning experiences. Students first explore factors and factor pairs to understand multiplicative relationships, then apply this understanding to identify multiples and solve multiplication problems. Students extend their understanding to division with remainders, requiring them to apply multiplication and division relationships to solve complex problems.

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

Learning experiences are sequenced to build students’ mathematical understanding from concrete exploration to increasingly complex application of grade-level concepts. For example, when addressing TEKS 4.3C “determine if two given fractions are equivalent using a variety of methods,” students progress from supported exploration to independent reasoning. In unit 7, students use number lines and visual models to explore fractions equal to zero, one, and whole numbers; identify equivalent fractions and mixed numbers; and add and subtract mixed numbers by regrouping. As instruction progresses, students transition from using models to solving problems mentally and independently.

In unit 8, students build on these understandings by using strip diagrams, set models, and number lines to generate and identify equivalent fractions before connecting visual models to the numerical process of multiplying the numerator and denominator by the same factor. They then use numerator–denominator relationships and mental strategies to recognize equivalent fractions, ultimately selecting from numerical methods, set models, or number lines independently.

Furthermore, the grade 4 “Discourse Questions” progressively increase in rigor and complexity by requiring students to move beyond identifying factor pairs to explaining and justifying their mathematical reasoning. Students analyze which side lengths are factors of a number, determine whether all possible rectangles have been identified, and connect rectangle representations to factor pairs.

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

The materials establish clear connections among mathematical concepts throughout the course, reinforcing important patterns and relationships as students progress from one unit to the next. The “At a Glance” section of each unit provides the big idea, describes how concepts grow over time in the “Schema Building” section, and then lists the “Essential Understanding” and lessons in each cluster. In unit 1, students develop an understanding of multiplication as a way to discover and explain relationships between numbers. In unit 2, students apply this understanding to compare quantities and measurements using multiplication, helping students build on prior learning and recognize relationships between mathematical concepts.

The grade 4 materials demonstrate consistency and clarity across units by connecting patterns, big ideas, and relationships. For example, in unit 3, lesson 1 students’ knowledge of place value connects to their use of partitioning two-digit numbers into tens and ones later in unit 4, lesson 10. The coherence of mathematical concepts explicitly connects, as students create four partial products that represent the total product, leading to understanding of the standard algorithm.

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 grade 4, the materials connect content and academic language learned in previous grade levels to current grade-level learning. The “Schema Building” sections state that students enter each unit with multiplication schemas developed in grade 3, including equal groups, arrays, area models, and single-digit multiplication. Students build on previously learned concepts and vocabulary while extending their understanding to multi-digit multiplication, place-value reasoning, partial products, and distributive property.

Additionally, the materials build on students’ prior mathematical language by reinforcing familiar vocabulary while introducing new terminology in context. In unit 4, students build skills for multiplying multi-digit whole numbers using the distributive property. Students’ understanding of the distributive property also becomes more sophisticated through work with parentheses and strategic decomposition. This expanded multiplication schema forms the foundation for grade 5 work with fractions, decimals, and even larger whole numbers. The materials provide consistent mathematical vocabulary that connects to future learning, including a glossary of academic language indicating which terms were introduced, reinforced, and developed across the grades.

Lastly, the materials explicitly state in the grade 4 Program Overview Guide that students’ expanded multiplication schema lays the foundation for grade 5 work with fractions, decimals, and larger whole numbers. These connections help students understand how current learning supports future mathematical concepts and procedures.

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

The materials connect previously learned and current mathematical concepts to new content, enabling students to build on existing knowledge as they develop deeper mathematical understanding. In the grade 4 materials, unit lessons are grouped into clusters. Just as clusters within units work together to build the big idea of the unit, lessons within the same cluster work together to build the “Essential Understanding” of that cluster, which conveys coherence. For example, in unit 3, cluster 1, the “Essential Understanding” states, “A digit in any place in the base-10 place value system represents 10 times the value of the same digit in the next place to the right.”

The materials connect mathematical procedures from current and previous grade levels to new learning, supporting students as they apply and extend procedural knowledge in increasingly complex situations. For example, in unit 1, lesson 1, students make connections to their understanding of factors from grade 3 when exploring how factor pairs can be used to make rectangles. In unit 1, lesson 4, students build on their knowledge of factors to explore multiples and discuss that multiples are infinite. In addition, there are lesson descriptions at the beginning of each lesson in the “Digital Planning Guide.” Lesson descriptions situate the lesson’s content relative to that of previous and future lessons. “Discourse Questions” on each slide support students in making connections between prior learning and new skills. For instance, unit 2, lesson 7 states, “In previous lessons, students found unknown values by interpreting multiplicative comparisons. In this lesson, students extend their multiplicative thinking to convert yards to feet.”

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

Grade 4 materials incorporate spaced retrieval opportunities that reinforce previously learned skills. Units and clusters conclude with one or more lessons featuring a mixed review of content from throughout the unit. This cumulative review prompts students to determine which operations or strategies best fit each task while recognizing the distinguishing features that guide their mathematical decisions. For example, in the final two lessons of unit 4, students review multiplication strategies from throughout the unit to solve two-by-two-digit and one-by-four-digit word problems, combine those strategies with multi-digit subtraction from previous units, and apply them to solve perimeter and area problems involving rectangles.

The lesson resources integrate ongoing review into daily instruction to strengthen student recall of previously learned concepts. Each lesson includes a student “Practice Page” with spaced, spiral review problems. For example, in the unit 4, lesson 5 “Practice Page, students review two unrelated concepts from earlier in the year, subtracting multi-digit numbers and converting from cups to pints. Students also multiply using the horizontal partial products algorithm from the current lesson, then review interpreting a remainder in a word problem from earlier in the year.

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

The materials reinforce previously taught skills by integrating review opportunities into daily instruction. Each lesson includes a student “Practice Page” with spaced, spiral review problems to interleave with the targeted practice aligned to the day’s focus and word problems. In the “Practice Page” for unit 3, lesson 12, students review two unrelated concepts from earlier in the year, shape attributes and multiplicative comparisons, then add and subtract four-digit numbers on an open number line from the current lesson. Lastly, students review an addition word problem from earlier in the year.

The materials revisit mathematical concepts throughout the course to strengthen connections across lessons and units. Lessons include a mixed review of content from across the unit, providing interleaved practice in which students determine appropriate operations or strategies for each task, supporting students in identifying distinguishing features of tasks to choose relevant approaches. In two lessons at the end of unit 4, students review multiplication strategies from across the unit to solve two-by-two-digit and one-by-four-digit word problems, combine them with multi-digit subtraction from previous units, and use them to solve rectangle perimeter and area problems.

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

Questions and tasks require students to interpret models and representations of mathematical concepts and situations. Across a cluster, unit, or group of related units, students begin by making sense of concepts through manipulatives and visual models, then progress toward flexibly using numerical or symbolic representations and strategies. Students interpret, analyze, and evaluate a range of base 10 blocks models to compose the number 30,000 and make connections among various models and strategies. For example, “Discourse Questions” in unit 4, lesson 1 such as “What is the value of these blocks?” “How do you know?” “How did you determine how many of each value it would take to make 30,000?” and prompts such as “Describe how knowing the number needed of one base 10 block type can help you figure out another” require students to interpret representations, analyze place-value relationships, and justify their mathematical reasoning.

Questions and tasks also require students to analyze models and representations for mathematical concepts and situations. For example, in unit 4, lesson 17, “Students engage in a whole-class Puzzle Talk to identify which operation and amount will complete or clear the path for JiJi. They share strategies for comparing answer options and analyze the feedback of the game to evaluate why their choice was correct or incorrect. The discussion focuses on multiplicative and additive comparisons shown in the puzzles as well as in a strip diagram. This prepares students to model and solve multi-step problems in the activities that follow.”

Lastly, questions and tasks require students to evaluate models and representations for mathematical concepts and situations. In unit 4, lesson 17, students participate in a “Puzzle Talk” game in which they must analyze visual feedback to evaluate why a chosen mathematical path or operation was correct or incorrect. Students also interpret relationships between different colored bars within a representation by answering “Discourse Questions” such as “What is the relationship between the total length of the blue bars and the orange bar?” and “What is the relationship between the pink bar and the total length of the blue bars?” Students evaluate multiplication and subtraction equations to determine which one accurately matches a provided strip diagram.

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

The materials contain questions and tasks that provide opportunities for students to construct mathematical models to represent and communicate real-world and mathematical situations. In unit 2, lesson 5, students analyze and interpret mathematical representations using visual data displays to model multiplicative comparisons, generate equations and comparison statements, and communicate mathematical relationships through written explanations.

Furthermore, tasks require students to create models representing mathematical situations. Across a cluster, unit, or group of related units, students begin by exploring and demonstrating understanding of concepts through manipulatives and visual models, then progress toward flexibly using numerical or symbolic representations and strategies. Students create a range of models and make connections among various models and strategies. In unit 4, lesson 2, students create base 10 block models to represent multiplying single-digit numbers by multiples of powers of 10; for example, 3 x 40 can be represented by three groups of four 10s to get 12 10s, or 120.

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

The materials include questions and tasks that encourage students to extend their mathematical understanding by applying previously learned concepts to unfamiliar situations and meaningful contexts. Within and across lessons, students are introduced to concepts through simple examples, then have the opportunity to transfer and reinforce their understanding with additional tasks with less scaffolding and/or greater challenge. In unit 4, lesson 5, students explore area models to represent one-digit by two-digit multiplication side by side with distributive property equations, starting with heavy guidance and moving toward independence by applying the same concepts to new problems with decreased support. Students apply their conceptual understanding in the following lesson, “Multiplying Two-Digit Numbers with Multiple Strategies,” when they review these multiplication strategies, then continue to apply them in new situations to explain how the vertical partial products algorithm and standard algorithm use place value.

The culminating lessons for unit 4 provide opportunities for students to apply conceptual understanding to new problem situations and contexts. Students first analyze relationships using strip diagrams to represent multiplicative comparisons and additive relationships. Next, students apply these models to solve increasingly complex multistep, real-world problems involving carnival games, ticket sales, food sales, restaurant pricing, perimeter, and area. Students choose appropriate solution strategies, justify their reasoning, explain how mathematical models support their thinking, and reflect on the effectiveness of different problem-solving approaches. These lessons require students to transfer conceptual understanding across multiple real-world contexts rather than relying on memorized procedures.

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

The materials provide tasks to build the student automaticity needed to complete grade-level tasks. Targeted lessons support developing grade 4 fluency with one- and two-step problems involving multiplication and division, including interpreting remainders. In unit 4, lesson 12, students practice multiplying two-digit by two-digit numbers fluently, emphasizing the efficiency of area models/partial products and the standard algorithm by discussing the relationship between the two models. Students first solve on paper and upload images from their math notebooks, then play an ST Math game that supports using the standard algorithm side by side with an area model to provide multiple opportunities to practice the steps online.

The materials include tasks that promote fluent use of mathematical strategies and procedures to solve grade-level problems accurately and efficiently. In unit 4, lesson 12, students engage in sequenced activities that develop computational fluency through repeated use of mental math strategies. Students decompose numbers, estimate sums and differences, use number lines to reason about operations, and solve multi-digit addition and subtraction problems mentally. The lesson encourages students to select efficient strategies and explain their reasoning, strengthening flexibility, accuracy, and efficiency with grade-level computations.

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.

The materials provide opportunities for students to strengthen efficient problem-solving by applying mathematical procedures throughout lessons and across the unit. The culminating lessons in unit 4 provide students with repeated opportunities to develop efficient, flexible, and accurate mathematical procedures through guided instruction, independent practice, and real-world application. In lesson 17, students analyze multiplicative relationships during the “Comparison Bridge Puzzle Talk” and solve multistep multiplicative comparison problems using strip diagrams, such as determining how many people played carnival games based on comparison statements. Students also complete strip diagrams with missing values and independently solve additional comparison problems. Lesson 18 extends procedural fluency when students apply multiplication, perimeter, and area in real-world contexts. Students calculate the total cost of meals using menu prices, determine the new perimeter of a rectangular menu sign after increasing its width, and find the area of a seating space by using the given perimeter and the side length to determine the missing dimension. The Thinking Path provides an additional opportunity for students to independently apply efficient procedures.

Additionally, students use and compare flexible solution strategies while applying mathematical procedures throughout instruction. Students practice flexible strategies through specific focus on individual skills. In unit 4, lesson 13, students choose among the strategies they have learned for multiplying two-digit by two-digit numbers to efficiently solve contextual problems, then share and compare their strategies. Students further apply flexible procedures to multiply multi-digit numbers in unit 4, lesson 3, displaying their understanding of partial product strategies, area models, and the standard algorithm as they solve contextual multiplication problems.

Lastly, students reinforce procedural accuracy through repeated application of mathematical procedures within lessons and across the unit. Students solve multistep word problems regarding food truck costs and earnings in unit 4, lesson 18, in which they must use a “range of multiplication strategies” to find accurate answers and move away from relying on just one specific method. Later in the lesson, students choose a specific strategy from the unit and explain how and why it helped solve a complex, multistep problem, ensuring that they deliberately evaluate and identify the most efficient and accurate ways to solve the problem.

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

Students evaluate procedures, processes, and solutions for efficiency within lessons and throughout units. For example, In unit 4, lesson 3, students consider the strategies that they used to solve two problems and discuss why they might choose other multiplication strategies depending on the numbers involved; specifically, 5 x 365 might be solved with mental math, taking half of 365 x 10, or other flexible strategies, while 39 x 365 might be solved with the standard algorithm or an area model/partial products.

Students also evaluate procedures, processes, and solutions for flexibility within the lessons and throughout the units. Unit 2, lesson 6 provides multiple opportunities for students to evaluate multiplication procedures while solving problems. Students estimate products, solve using horizontal partial products and the standard algorithm, and compare the efficiency of each method. They then reflect on which strategy they prefer and justify their choice, demonstrating flexibility in selecting procedures. Students also verify the accuracy of their work by comparing estimates with exact products, identifying the smallest product among multiple expressions, and creating multiplication problems that satisfy a specified product range.

Lastly, students evaluate procedures, processes, and solutions for accuracy within the lessons and throughout the units. In unit 4, lesson 6, students build upon their understanding of the distributive property by solving one-digit by two-digit multiplication problems using area models, horizontal and vertical partial products, and the standard algorithm. They compare these strategies and recognize how each strategy uses place value to break apart numbers and leads to the same product. Students also use estimation strategies to find low and high estimates, supporting them in checking the reasonableness of their answers. The lesson structure provides opportunities for students to evaluate processes and solutions for efficiency and flexibility throughout the lesson.

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

The materials include embedded support for educators to guide students toward efficient approaches. In many lessons, the “Details,” “Look-Fors,” and “Discourse Questions” support the educator in guiding students toward a more efficient strategy in a learning trajectory that progresses across each cluster, unit, or group of related units. In unit 4, lesson 16, the “Discourse Questions” and “Look-Fors” support educators in guiding students to notice how the formulas for the perimeter and area of a square can be written more efficiently than the formulas for non-square rectangles, including using multiplication instead of repeated addition.

Furthermore, unit 4, lesson 3 provides embedded instructional supports that develop increasingly efficient multiplication strategies. Students progress from multiplying ones and tens to multiplying multiples of 10, use decomposition and equivalent expressions to reason about products, and apply these strategies in contextual problems before completing independent practice. The lesson builds procedural efficiency through conceptual understanding of place value and the associative property.

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

The program directly addresses the conceptual and procedural TEKS emphases at the unit level. Each unit includes a “Coherence” section that explains the relevant content that students learned in prior grades and units, the progression of concepts and skills that build across the unit, and how these will support students in future grades and units. For example, in unit 2, the “Conceptual Understanding” states, “In this unit, students develop a deep understanding of multiplicative comparison as a distinct way of thinking about relationships between quantities. In grade 3, students described multiplicative comparison using language such as times as many, but they did not yet solve problems involving these relationships. Now in grade 4, students build conceptual understanding by distinguishing between additive comparisons (more than, less than) and multiplicative comparisons (times as many as), and they recognize that these comparisons represent fundamentally different relationships.”

The materials communicate how students develop procedural knowledge and apply the mathematical skills required by the grade-level TEKS. Each grade 4 unit includes a section that explains the conceptual and procedural emphasis of the unit. In unit 8, students generate equivalent fractions using visual models and patterns, explain why multiplying or dividing the numerator and denominator by the same number preserves the value of the fraction, and justify that equivalent fractions represent the same point on the number line (conceptual emphasis). Students then build fluency by generating equivalent fractions through multiplication and division and connect that procedure to the concept of creating different-sized parts that represent the same quantity (procedural emphasis).

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.

Throughout grade 4, questions and tasks include the use of concrete models and manipulatives, pictorial representations, and abstract representations. In lessons, units, and clusters, students begin with concrete representations and models, then transition to more abstract representations. In unit 5, lesson 12, students use base 10 blocks to represent multi-digit dividends grouped into equal parts with regrouping as necessary, and record their partial quotient steps side by side with abstract multiplication expressions.

Additionally, in unit 5, lesson 13, students use pictorial area models and abstract equations side by side to model division steps, beginning by completing a few steps with models and equations that are mostly complete, and using the strategies independently by the end of the lesson.

Lastly, unit 5, lesson 13 develops conceptual understanding of multi-digit division through the use of area models. Students estimate unknown side lengths, partition rectangles, connect visual representations to multiplication and division expressions, identify remainders, explain their reasoning, and solve equations symbolically. Students then create their own area models to solve new division problems and demonstrate understanding through independent practice. The lesson intentionally progresses from visual models to abstract mathematical expressions.

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.

Lessons include opportunities for students to connect, create, define, and explain concrete and representational models to abstract concepts. The “Differentiation” sections of many lessons offer additional educator guidance to support students in connecting these representations. For example, in unit 5, lesson 13, the activities on the slides and the “Discourse Questions” prompt students to use, create, and explain how virtual concrete models represent division into equal groups with remainder, then connect this to abstract notation with the division symbol and R to represent the remainder. The “Differentiation” section provides additional strategies to support students in connecting models to abstract representations.

Additionally, in unit 5, lesson 1, the activities on the slides and the “Discourse Questions” prompt students to use, create, and explain how virtual concrete models represent division into equal groups with a remainder, then connect this to abstract notation with the division symbol and R to represent the remainder. The “Differentiation” section provides additional strategies to support students in connecting models to abstract representations.

Lastly, the materials include supports that encourage students to define and explain abstract mathematical concepts by using concrete and representational models to justify their mathematical thinking. For example, the “After This Unit” educator suggestions in unit 5 offer support for students struggling to use partial-quotients strategies efficiently, stating, “Encourage students to start with the greatest possible partial quotient without going over the dividend. Guide students to look for multiples of the divisor that are close to the value of each place in the dividend. Provide additional practice with decomposing dividends by place value when each digit is a multiple of the divisor, as well as practice with nonstandard partitioning when digits are not multiples of the divisor.”

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

The materials provide educators with prompts encouraging students to communicate mathematical thinking through precise vocabulary, complete mathematical statements, and purposeful classroom discussions. Students have opportunities to engage with new mathematical language by using manipulatives such as AngLegs. In unit 2, lesson 10, students use AngLegs to create and name triangles based on their angles. Students discuss how to classify the triangles into three categories. After students have used their own language to explain their thinking, the vocabulary terms obtuse triangle, right triangle, and acute triangle are introduced. The use of the concrete manipulative AngLegs helps students visualize the mathematical terms they are learning.

Additionally, the materials encourage collaborative mathematical discussions in which students listen to, build on, and strengthen their use of mathematical language through ongoing peer interactions. In unit 1, lesson 1, students develop academic mathematical language by using a visual grid model to investigate all possible rectangles that can be formed with 24 square units. Through educator-facilitated discussions, students describe and justify their strategies using precise mathematical vocabulary such as factor, factor pair, side length, dimensions, rectangle, and multiplication facts. Educator guidance includes “Look-Fors” that monitor students’ use of academic language as they explain why certain side lengths do or do not create valid rectangles; distinguish unique factor pairs; and describe rectangles by their dimensions, such as 8 x 3, 6 x 4, 12 x 2, and 24 x 1. “Discourse Questions” require students to explain their reasoning; defend their conclusions; and connect mathematical vocabulary to the visual representations, strengthening conceptual understanding and mathematical communication.

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

The materials explain how the TEKS mathematical process standards support instruction across lessons and learning experiences throughout the course. During unit 1, lesson 4, on introducing multiples, the educator guidance scaffolds new vocabulary by prompting students to examine a set of numbers such as skip-counting sequence 7, 14, 21, and so on, and share what they have in common before the formal term is ever defined. The embedded questions What do these numbers have in common? and How could we extend this pattern? include educator guidance to let students use informal language first, such as “Skip-counting by 7s” or “Adding 7 each time.” The educator then attaches the formal label—multiple—to this commonality.

The materials embed educator prompts and instructional routines that encourage students to develop and apply precise mathematical terminology within mathematical contexts. For each new vocabulary term, guidance for educators is embedded within the “Details,” “Look-Fors,” and “Discourse Questions” to support all students in using new mathematical language in context. Within the “Differentiation” section of each lesson, the “Supportive Language” suggestions provide sentence frames, additional important language, and other strategies to support expressive and receptive mathematical language and scaffold language development to meet each student’s 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.

Embedded educator guidance in the materials supports the application of appropriate mathematical language to include vocabulary, syntax, and discourse to support mathematical conversations. The “Details” section introduces new vocabulary, encouraging students to describe new terms in their own words and connect them with formal definitions, after which “Discourse Questions” and “Look-Fors” support students in using the language in context. The “Differentiation” section of each lesson provides sentence frames; guidance on how to rephrase student thinking; and other strategies for supporting receptive and expressive mathematical language, including addressing vocabulary, syntax, and discourse. For example, unit 7, lesson 2 features sentence frames such as “The model shows the fraction ____.” “In the fraction ____, the number ____ represents ____,” and “The model shows the fraction ____ because ____” to support the application of mathematical language. Additionally, unit 1, lesson 5 provides sentence frames such as “First, I decomposed ____ into ____ and ____. Then, I ____. And then, I ____. I found the product by ____. The horizontal partial products algorithm is helpful because _____” to support the application of mathematical language.

The materials encourage collaborative mathematical discussions in which students listen to, build on, and strengthen their use of mathematical language through ongoing peer interactions. During a unit 1 lesson on representing patterns with input and output tables, the materials instruct the educator to first let students process the table informally: “Ask, ‘What do you notice about this table?’” Once students can express the concept in their own words, the educator defines the terms: “After students have used their own language to explain what they notice, introduce the vocabulary words input (the starting value to which a rule is applied) and output (the value after a rule is applied to an input).” Rather than just lecturing, the educator is directed to “Use the ‘Discourse Questions’” to facilitate a discussion about the rule.” This structure provides student opportunities to hear, refine, and use the new vocabulary with their peers as they discuss how the values relate to one another.

The materials provide educators with exemplar responses that illustrate expected mathematical thinking and support effective questioning and feedback during instruction. Each cluster of study within a unit contains a “Common Errors and Misconceptions” support section for educators. In unit 2, cluster 1, the educator guidance addresses ways to correct misunderstandings about area concepts. Embedded feedback for sample student misconceptions such as “The shape is longer, so it has more area” or “This shape is taller, so it has more area” provides educator scaffolding and support.

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

Grade 4 materials appropriately integrate the TEKS mathematical process standards within content instruction, describing how students engage in mathematical practices throughout the unit. Unit 1 materials identify the pertinent mathematical process standards and provide instructional narratives explaining how students: apply mathematics in authentic contexts; use structured problem-solving processes; analyze information; formulate solution strategies; justify mathematical reasoning; and evaluate the reasonableness of solutions. The materials also identify the lessons in which each process standard is addressed, demonstrating that the mathematical process standards are intentionally integrated into instruction rather than presented as stand-alone skills.

The materials embed the TEKS mathematical process standards within lessons and activities, allowing students to apply reasoning, problem-solving, communication, and representation while learning grade-level mathematics. In unit 9, lesson 1, students engage with TEKS 4.1D as they use several representations of decimals, such as place-value tokens, base 10 blocks, and expressions to reason about decimal addition and subtraction as well as the implications of using visual supports to recognize and explain place value in each digit in an expression and its resulting sum or difference.

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

The materials explain how the mathematical process standards support instruction across lessons and learning experiences throughout the course. Unit 1, lesson 1 identifies process standards 4.1B and 4.1F alongside the content TEKS and explains how students analyze multiplicative comparisons, formulate and justify solution strategies, evaluate reasoning, and communicate mathematical relationships. This lesson-level implementation supports the program-level documentation that process standards are integrated across lessons and units.

The materials describe the relationships among the mathematical process standards and their continuity across the course, reflecting a clear, intentional design in which process standards are not taught in isolation. Instead, they are integrated and repeated across various lessons to build mathematical fluency and good math habits. Rather than limiting a skill to one lesson, multiple process standards coalesce in one activity, ensuring, for example, that a single financial-literacy activity is never just about computing a number. Students select a calculation tool or technique, analyze how income and expenses affect profit, and justify their financial choices to their classmates. This overlapping design helps the process standards translate into everyday math habits across the whole course.

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

The materials explain how the TEKS process standards support instruction and learning experiences within each unit. Process standard 4.1C is integrated in lessons in unit 9, for example. In lessons 2, 3, and 5, “Students develop flexibility in selecting appropriate tools and techniques to solve problems involving decimal and financial planning. They choose virtual manipulatives such as base 10 blocks and place value tokens to visualize decimal addition and subtraction. Students also choose mental math, estimation, and number sense techniques when working with money, when determining reasonable totals and differences, and when checking the accuracy of their work. They choose when to use standard algorithms or alternative strategies, such as adding dollars and then cents separately or ungrouping and regrouping based on place value. By selecting tools and techniques strategically according to the problem context, students strengthen both their conceptual understanding and procedural fluency in decimal computation and financial reasoning.”

Furthermore, the materials describe the relationships among the mathematical process standards and their continuity throughout each unit. The materials include an article titled “InsightMath Texas—Connecting the Process Standards.” InsightMath Texas intentionally incorporates the seven TEKS mathematical process standards throughout its curriculum using a progressive system of “Student Strengths” that build in complexity across grade levels. Instead of treating these standards as isolated skills, the curriculum combines multiple process standards within the same lesson, which ultimately continue throughout the course.

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

The materials identify the mathematical process standards addressed within individual lessons to support instructional planning and implementation, such as the lesson-level overview of the TEKS mathematical process standards incorporated into lesson 7. Lesson 7 materials identify the applicable process standards (4.1E and 4.1G) and explain how students organize mathematical information using tables, communicate mathematical ideas, and justify financial decisions using precise mathematical language.

Additionally, the materials include educator guidance for each mathematical process standard that is incorporated into a lesson. For example, unit 9, lesson 8 addresses TEKS 4.1.F as “Students calculate weekly expenses and income for a car wash business and then analyze the relationship between these amounts to determine profit. They connect the relationship by subtracting expenses from income to show how profit is calculated, and they explain how to increase profit (e.g., spend less, wash more cars). Students also reason that the business may not have the same expenses each week because some supplies can be reused, and they use this understanding to predict how lower expenses could lead to a higher profit. Finally, students connect spending to earnings by discussing how the initial costs of supplies make it possible to generate income and profit.”

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

Unit 0 introduces students to the program through activities focused on developing mathematical thinking, perseverance through problem-solving, and making sense of mathematics. These activities provide students and educators with the language needed to explicitly use, build, and discuss these skills throughout the grade level. In addition to the activities themselves, the TEKS mathematical process standards highlight these skills throughout the course. The lessons in unit 0 introduce students to open-ended, creative mathematical challenges with low floors and high ceilings while developing the mathematical mindsets, language, and skills students need to approach creative mathematical thinking throughout the year.

The materials require students to persevere through problem-solving. Unit 2, lesson 2 provides students with multiple opportunities to think mathematically by analyzing comparison situations, identifying known and unknown quantities, representing unknowns with variables, creating equations, and justifying their reasoning. Students persevere through problem-solving by predicting solutions, testing strategies, analyzing incorrect responses, revising their thinking, and solving increasingly complex comparison situations in which the unknown appears in different positions. Students make sense of mathematics in the lesson as they explain what each quantity represents, justify variable selection, interpret multiplicative comparison language, connect equations to contextual situations, and communicate their reasoning through structured discourse.

Students make sense of mathematics throughout the program. In the unit 4, lesson 11 “Launch,” students engage in a “Notice and Wonder” routine in which they compare an area model side by side with a vertical math problem. The routine pushes students to recognize that the expressions are recorded vertically to match the partial products from the model, helping them build structural reasoning. This lesson helps students transition to formal algorithms by encouraging them to organize the partial products vertically or horizontally and justify the layout they prefer. Students focus on deeply understanding the mathematics rather than simply memorizing procedures.

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

The materials guide students to understand multiple ways to represent and solve problems. For example, in unit 2, lesson 13, students solve addition and subtraction problems involving customary units by representing quantities with equivalent measurements, regrouping when necessary, and converting between larger and smaller units such as pounds and ounces, feet and inches, gallons and quarts, and yards and feet. The “Look-Fors” direct educators to observe students as they explain how they combine or subtract like units, determine when regrouping or converting is needed, and use relationships between customary units to write equivalent measurements. Students identify known and unknown quantities and explain how equivalent measurements support accurate solutions. “Discourse Questions” such as “How did you determine the total number of pounds and ounces?”, “What numbers did you add?”, and “What equivalent measurement did you make?” require students to explain, compare, and justify their reasoning while selecting appropriate conversion and solution strategies.

Students explain and justify multiple ways to represent and solve mathematical tasks through mathematical reasoning, discussion, and comparison of solution strategies. For example, in the unit 2, lesson 1 “Explore,” students examine the same comparison situation using two mathematical approaches by drawing pictures and writing equations with addition comparison language such as longer, and multiplication comparison language such as times as long. Students compare the representations to understand the relationship between additive and multiplicative comparisons. Throughout the materials, built-in student exemplars called “Argumenteers” further support this work by presenting multiple solution strategies for the same problem, prompting students to explain, compare, and justify why different approaches can accurately represent and solve mathematical situations.

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.

Each unit of the program includes two lessons with a “My Thinking Path” activity for Workshop Time.” In unit 2, lesson 6, students reflect on and make sense of the mathematics they have explored throughout the cluster by writing about their thinking and discussing their ideas with their educator and peers. In the “My Thinking Path” pages, students reflect in writing on their mathematical thinking for key topics across the unit.

The materials give students opportunities to write about mathematics and develop their understanding through interactions with their educator and peers. For example, in unit 2, lesson 6, students communicate mathematical thinking through writing, drawing, speaking, and listening. Students independently select a prompt related to the unit’s big idea and record their thinking in their Playbook math journal using writing and/or drawings. Then the materials direct students to share their journal entries with a partner, ask questions about each other’s thinking, and participate in a whole-class discussion facilitated by the educator’s “Discourse Questions.” Students also reflect on their progress toward their mathematical goals using a “Goal Page” and independently complete a “Practice Page” while the educator monitors student strategies and uses “Discourse Questions” to support mathematical reasoning.

Discussion activities require students to make sense of mathematics with their educator and peers. For example, in unit 2, lesson 11, students first explore and develop an understanding of customary units of volume through direct experiences as they estimate and pour liquids between containers. Students then discuss and make sense of a new tool: a conversion chart for customary volume, solving conversion problems involving mixed units using equations or strip diagrams of their choice. The “Details,” “Look-Fors,” and “Discourse Questions” prompt students to show their thinking using models, equations, and words, then discuss their strategies and reasoning with peers.

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 program supports educators in encouraging students to share explanations, arguments, and justifications. The lesson notes provide educators with “Details,” “Look-Fors,” and “Discourse Questions” to guide students in sharing and reflecting on their problem-solving approaches through activities that require analyzing various strategies and justifying why one strategy may be preferred over another. For example, in unit 4, lesson 11, students multiply a two-digit number by a two-digit number using an area model and record the partial products. Students reflect on their problem-solving choices and justify their decisions to their peers by explaining how they decompose each factor to make multiplication more efficient.

The materials also prompt educators to support student reflection on problem-solving approaches, including explanations, arguments, and justifications. In unit 1, lesson 1, for example, students identify and compare factor pairs for rectangular arrays by first solving independently, then participating in Share with Class discussions using structured “Discourse Questions.” Educator guidance and “Look-Fors” prompt students to explain how they determine factor pairs, justify why reversing factors creates the same rectangle and product, explain why certain side lengths do or do not form rectangles, and use academic vocabulary such as factor pair to communicate their reasoning.

Lastly, “Discourse Questions” prompt students to defend and reflect on their mathematical reasoning through questions such as “How do you know this is a factor pair?”, “If the factor pairs were switched, would that change the rectangle? Why or why not?”, and “Do all numbers have the same number of factor pairs?” These questions require students to explain their reasoning, justify mathematical claims with evidence, compare strategies, and reflect on the reasoning of others during whole-class discussions.

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

Unit 1, lesson 1 includes prompts that support educator feedback based on student responses and anticipated misconceptions. As students sort factor pairs into two distinct categories, educators guide a discussion that focuses on how students determine which factor pairs belong together and the properties they share. Educators ask questions such as “How did you know which number the factor pairs represented?”, “What did you title the categories? Why?”, and “What is similar or different about the factors and factor pairs of 12 and 24?” This questioning sequence allows educators to identify sorting misconceptions in real time. When a student incorrectly sorts a factor pair, educators encourage the student to explain the shared attributes of the category, helping the student reflect on and self-correct their factor-pair sorting.

Additionally, for each unit and cluster, educators receive guidance on providing explanatory feedback based on student responses and anticipated misconceptions. For example, “Common Errors and Misconceptions” guidance for unit 5, cluster 2 offers suggestions for addressing the misconception that multiplication always results in a greater number and division always results in a lesser number. Students may use faulty estimation to judge the reasonableness of answers by expecting quotients to always be less than dividends, which may be true for some whole-number situations but does not apply universally. To address this misconception, educators might emphasize that dividing by one results in the same number, and that dividing by a number less than one can result in a number greater than the starting number.