InsightMath Texas, Grade 3

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

The program includes a scope and sequence outlining the Texas Essential Knowledge and Skills (TEKS), English Language Proficiency Standards (ELPS), and concepts taught in the course. The scope and sequence establishes a clear order of instruction that helps educators pace learning effectively. It maps out a comprehensive, yearlong instructional plan that shows when and how students learn each concept. The grade 3 scope and sequence also organizes instruction into units and clusters, providing consistency, coherence, and completeness throughout the program.

The materials incorporate the TEKS and ELPS taught in the course. For example, within the grade 3 Overview, the “Standards” tab outlines the TEKS and ELPS addressed in each unit and lesson. The scope and sequence blueprint 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 grade 3 materials include a suggested pacing to support effective implementation of the program. The grade 3 Overview includes a “Pacing Details” section that outlines the concepts and recommends the number of instructional days for each unit. The materials further support implementation by organizing each unit into clusters and lessons, providing educators with a clear structure for pacing instruction throughout the program.

The materials provide pacing for various instructional calendars. For example, the Grade 3 Program Overview Guide provides pacing suggestions for a range of school-year lengths, including suggestions for 180-day and 165-day calendars. The program organizes the two suggested calendars into units and recommends a range of instructional days to implement the program effectively. The “Pacing Guide” within the Grade 3 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 3 instructional materials include a rationale for unit order. For example, the “Big Ideas and Course Organization” section provides the rationale of unit order, explains how concepts to be learned connect throughout the course, and provides a graphic illustrating the progression of learning, outlining the units, big ideas, and connections across domains and clusters. The materials show how each unit contributes to overarching learning goals.

The materials include an explanation of how the concepts to be learned connect throughout the course. For example, the “Balanced Instruction” section explains the logic underlying unit progressions for conceptual understanding, procedural skills, fluency, and application. The “Coherence” section in 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 guides effectively in connecting content across lessons and highlighting the cluster and unit-level essential understandings and big ideas. Additionally, “Setting Up Your Planning Routine” guides educators on using the recommended protocols to internalize units and lessons in the program.

The Digital Planning Guide contains guidance to support educators in previewing each unit, understanding intended outcomes, and internalizing the sequence of learning within each unit and lesson. For example, 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.

Materials include resources for instructional leaders to support educators in implementing the materials as designed. Located in the Help Center, “Support for School-Level Leaders” contains resources for supporting schools through the first year of implementation of the product. The program outlines suggestions for building its foundation, including creating a shared vision, planning professional learning, and establishing implementation expectations. Furthermore, “Implementation Success Indicators” equip school-level leaders with guidance on classroom environment, instructional practices, assessment, and data collection to support implementation, address challenges, and identify effective solutions.

Materials include guidance for instructional leaders to support educators in implementing the materials as designed. The Help Center’s “School Implementation Timeline and Checklist” includes 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 3 materials include comprehensive unit overviews that provide the background content knowledge necessary to effectively teach unit concepts. At the introduction of each unit, a “Schema Building” section provides background knowledge regarding the growth and development of content within the unit and how students’ schemas will grow and change relative to content in the unit. Additionally, each unit contains a “Math” tab that describes how math knowledge is balanced and connected to previous and future content, providing educator background on the extent of the content within each unit. Furthermore, an “At a Glance” page within each cluster of learning 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 outlining the background knowledge educators need to effectively teach each lesson.

Comprehensive unit overviews provide the academic vocabulary necessary to effectively teach unit concepts. The “At a Glance” page summarizes the big idea driving each distinct unit of instruction. The materials provide an overview of previously taught concepts at the beginning of each unit and describe connections learners will build throughout the clusters and lessons. Furthermore, the materials include a “Glossary” section explicitly defining mathematical terms and indicating the grade level at which each term is introduced and used in instruction. The materials list specific vocabulary terms at cluster and lesson levels within each unit.

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

The “Family Guides –Texas” web page contains support links for families in Spanish, organized by unit, with suggestions on supporting the growth of their students. Each guide outlines key math ideas, tips for home support, and suggestions for at-home practice of skills and concepts. The activities reinforce classroom learning and encourage the at-home use of mathematical vocabulary used in the units. For example, in grade 3, unit 1, the materials include an “If... Try...” support that provides targeted family guidance when students struggle with multiplication or division. The guidance directs families to use concrete manipulatives to model equal groups and prompts students to apply known multiplication facts to solve unfamiliar problems through strategic questioning.

English- and Spanish-language “Family Guides” for each unit help families support their students’ mathematical development at home. Each guide highlights key mathematical concepts, introduces the academic vocabulary used in the unit, and provides practical activities that reinforce classroom learning through everyday experiences. For example, the grade 3, unit 1 “Family Guide” encourages families to connect multiplication and division to real-life situations by identifying equal groups in everyday items, exploring different ways to make equal groups, practicing fair sharing with division, and creating arrays with common household objects to represent multiplication and division equations.

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).

Lesson plans in the materials organize daily instruction through a clear sequence of instructional components that support content and language development. For example, 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, “Discourse Questions” and “Look-Fors” in the lesson notes help educators ensure that each student meets content and language objectives.

The grade 3 materials include lesson resources establishing a consistent instructional framework that guides educators through each day’s instruction. For example, lessons are introduced with lesson and language objectives, key lesson questions, and aligned vocabulary needed for mastery of the content. Additionally, clusters containing materials and formative instructional assessments are integrated into lessons 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 include a lesson overview that lists the educator and student materials needed to deliver the lesson. For example, the “Preparing for This Lesson” section identifies the educator and student materials required for each lesson. Furthermore, “Preparing for This Lesson” includes prep notes, a detailed materials list, game assignments, tools, templates, and practice book pages, providing a comprehensive list and description of student and educator materials.

Lessons include the suggested timing for each lesson component in the program. “Understanding the Structure of InsightMath” in the Help Center outlines a consistent four-part lesson structure. The program lists an allotted time and guidance for the lesson launch, explore, reflect and 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 educator lesson support to extend student learning beyond core instruction. In each lesson’s “Differentiation” section, extension challenges provide details to support educators in collecting evidence of progress toward mastery. Additionally, within each lesson, a “Workshop Time” section contains game assignments that give students opportunities to investigate and practice a concept learned in the unit.

The educator resources explain how to implement additional learning opportunities that reinforce and extend student understanding. For example, the article “Understanding the Structure of Insight Math” provides specific educator guidance 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.

Assessments using various question formats and task types measure student understanding at multiple points throughout each unit. 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 each unit evaluates 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 lessons provide frequent opportunities to monitor student learning through varied assessment activities. For example, each cluster highlights formative assessment opportunities and identifies when educators implement them. These embedded assessment opportunities 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 3 materials describe how each assessment type supports instruction and student learning throughout the program. For example, 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.” 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 assessments provide “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 assessment opportunities 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 materials and resources give clear definitions and purposes of the types of assessments to support educators with 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 assessment administration procedures that promote consistent implementation across classrooms. For example, the “Diagnostic Assessment Guide” for each unit includes explicit implementation instructions, materials, an item map aligned with the TEKS, and suggestions for supporting students. The materials provide a script to ensure the administration of assessments is standard across examiners.

“Making Assessments Accessible for All Students” guides educators in determining how to accommodate students with special needs during assessments while still ensuring the content and rigor of an assessment remains the same. Considerations to support all learners during formative, diagnostic, and summative assessments are outlined. The recommendations support accurate and reliable results for diverse learners.

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

The formative assessments measure student progress throughout instruction by targeting the knowledge and skills taught within each lesson. For example, within each cluster, lesson-level formative assessments align with the TEKS and objectives of the lesson, which are clearly labeled. “Look-Fors” and “Discourse Questions” in lesson notes contain activities, prompts, and questions aligned to the lesson objectives and the TEKS.

The diagnostic assessments identify students’ prerequisite knowledge and provide information to guide instruction at the beginning of each unit. For example, the “Diagnostic Assessment Guide” correlates each item number with a specific Texas standard, suggests activities to help students build prerequisite skills, and provides educator guidance to monitor emerging skills that will develop over the course of the unit.

Summative assessments in the materials measure student learning at the end of each unit by evaluating mastery of the unit’s objectives. For example, an item map in the “Summative Assessment Guide” identifies the specific TEKS aligned to each assessment item.

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

The instructional assessments use multiple question formats to measure students’ understanding of mathematical concepts and skills. 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.

The assessments require students to demonstrate learning through a range of cognitive demands and mathematical tasks. 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. The “Summative Assessment Guide” within each unit provides information on each item’s alignment to Webb’s Depth of Knowledge 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.

The InsightMath Texas Grade 3 formative assessment resources help educators analyze student understanding and identify next instructional steps. For example, each formative assessment opportunity guides educators in interpreting student performance to determine lesson mastery. This guidance is followed by suggestions for supporting students and occasional extension suggestions. The materials provide a “Formative Assessment Recording Log” to record student performance.

The grade 3 assessment guides include scoring support and sample responses to help educators evaluate student work consistently. For example, the assessment guides provide detailed examples of student responses, particularly when there is more than one possible answer. The “Diagnostic Assessment Guide” for unit 10 includes the following guidance: “Possible answers: 3 quarters; 7 dimes and 1 nickel; 6 dimes and 3 nickels or other combinations of coins with a sum of 75 cents.” The “Summative Assessment Guide” for unit 3 offers “Accept any answer that has a vertical or horizontal line splitting the larger rectangle into two smaller rectangles, has an accurate equation for each smaller rectangle, and shows that the whole rectangle is 6 × 9 = 54.”

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” 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 3 materials contain educator guidance to support students whose summative assessment performance indicates “areas of struggle.” 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 materials provide documentation resources to help educators monitor student learning throughout each unit, such as the formative assessment opportunities at each cluster level within every unit. The “Formative Assessment Recording Log” enables 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.

Structured reflection opportunities encourage students to monitor their own learning throughout the year. The grade 3 Playbook provides multiple opportunities throughout a unit to assess their own learning of the unit’s content in the “My Thinking Path” section and their development of math process strengths in the “My Goals” section. For example, students complete a “My Thinking Path” activity midway through and at the end of each unit. Students also complete a “My Goals” activity at the beginning, middle, and end of each unit. The materials revisit the same math process strengths throughout the year, enabling students to reflect on their growth relative to those strengths and monitor their progress across the school year. For example, “I learn from my mistakes” appears in units 1, 5, and 8; “I notice patterns and try to understand them” appears in units 1, 3, and 7.

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 to help educators address unfinished learning and strengthen grade-level understanding. The “After this Unit” page in each unit includes ways to address areas of struggle, providing educator guidance to support students who have not yet reached proficiency on grade-level content and skills. For example, when learners struggle to explain or use multiplication representations in unit 1, the program prompts educators to “Continue to model various multiplication and division representations (equal groups, skip counting, repeated addition and subtraction, and array models) with explicit discussion of what the numbers mean and how they model the problem.”

Each grade 3 lesson includes instructional supports that help educators adjust instruction to meet students’ learning needs. For example, in unit 1, the “Differentiation” component of lesson 8 suggests providing manipulatives such as cups or paper; screenshots or drawings; explicitly written sentence frames, and visual cues. It also recommends reviewing the two types of division problems from lesson 7 and using color and annotations to support students not yet reaching proficiency in the grade-level standards of interpreting division situations.

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 supports that help students understand unfamiliar language encountered during instruction. For example, the “Differentiation” section of each lesson provides educator guidance on supporting language during instruction. These supports include sentence frames and key lesson vocabulary support. Additionally, this section contains support for in-text references (e.g., figurative language, idioms, words with mathematical meanings that differ from colloquial meanings) that may need additional explanation or support.

Furthermore, the materials include an article titled “Addressing the Needs of Special Populations in Texas,” which includes guidance for educators to support emergent bilingual (EB) students. For example, the article encourages educators to show central concepts multimodally by using different types of sensory inputs: acting out scenarios or inviting students to do so, showing videos or images, using gestures, and talking about 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 grade 3 materials include opportunities to deepen and extend learning beyond grade-level expectations with lessons containing an “Extension” challenge within the “Differentiation” phase. For example, in unit 1, lesson 1, students count out 12 cubes and find as many ways as possible to put the 12 cubes into equal groups, comparing those ways to the ways they found for 24 cubes. The Teaching Guide suggests providing activities and tasks including higher-order thinking, open-ended questions, and real-world applications.

The grade 3 lesson resources encourage students to apply grade-level concepts in more complex and authentic ways after demonstrating understanding. For example, in the “Differentiation” phase of unit 2, lesson 13, students already measuring area with square meters efficiently engage in the real-world application challenges of creating their own area problem for a peer to solve, and altering the side length of a given rectangle to change how animals in a farm are arranged.

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 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 examples of proficiency from students when responding to the prompts to support learners in consolidating their understanding and restating it in clear mathematical language. Each phase of the lesson plan is summarized concisely and clearly, with models provided to explain 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 3 materials prepare educators to facilitate instruction through a range of routines for use throughout the program. Unit 0 introduces educators to various instructional approaches used in lessons, providing them with guidance to facilitate activities and preparing them for the types of learning interactions that they will facilitate throughout the year. For example, in “Puzzle Talk,” students engage in a whole-class discussion, sharing strategies and analyzing feedback.

Additionally, the grade 3 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, lesson 6 in unit 1 uses “Fair Sharing” puzzles, collaborative exploration, small-group and class discussion, Playbook assignments, and open-ended writing to teach modeling and solving partitive division problems.

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 as to how to implement those activities and facilitate discussions about the underlying mathematics.

The grade 3 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 provide students an opportunity to extend practice at their own pace. “Explore” activities within lessons are suggested for implementation in small-group settings. Lastly, the “Reflect and Connect” phase of each lesson requires individual reflection followed by whole-group discussions, providing an opportunity 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. “Addressing the Needs of Special Populations in Texas” includes educator guidance on providing linguistic accommodations for various levels of language proficiency. This article provides a list of universal language supports for specific lessons, and essential information for educators about the language supports within the Differentiation section. However, ELPS proficiency levels are not explicitly referenced in educator guidance to support EB students.

The materials provide support for EB students, but there are no other linguistic accommodations for additional language proficiency levels. Although materials include 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 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. This resource guide contains structured instructions on how to integrate the materials into ESL programs.

Additionally, Universal Design for Learning (UDL) lessons offer further guidance on how to implement lessons to reach all learners, including EB students. The lessons integrate design elements that make the program particularly accessible to EB students, providing a rationale for and explanation of their 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.

The materials incorporate embedded language supports that help educators strengthen students’ academic language and content understanding during instruction. Each lesson includes embedded guidance for educators to support EB students through the “Supporting Language” category within the “Differentiation” section. However, cross-linguistic oral and written connections do not appear in the materials.

The materials encourage mathematical discussion that strengthens academic language and conceptual understanding. For example, grade 3 lessons include “Discourse Questions” that develop academic vocabulary, increase comprehension, and build background knowledge.

The materials provide opportunities for students to communicate mathematical thinking through writing. 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, each lesson includes a student “Practice Page” with a mix of spiral review to strengthen prior learning, targeted practice aligned to the day’s focus, and real-world word problems for application in varied contexts that require students to demonstrate depth of understanding aligned to the TEKS. The unit 1, lesson 1 “Practice Page” requires students to write an equation to represent a repeated addition equation representing equal groups, define a number as odd or even, represent two different ways to create equal groups from the number 12, and solve a real-world problem involving division.

The materials include instructional assessments that allow students to demonstrate their understanding of grade-level mathematical concepts and skills aligned to the TEKS. Formative assessments embedded throughout the units require students to represent multiplication and division concepts using equal groups, grouping and splitting situations, arrays, and equations. The unit summative assessment requires students to apply these understandings to solve problems and demonstrate mathematical reasoning. These assessments require students to demonstrate depth of understanding and grade-level knowledge aligned to the TEKS.

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

The materials sequence learning experiences to build students’ mathematical understanding from concrete exploration to increasingly complex application of grade-level concepts. For example, when addressing TEKS 3.4H—determine the number of objects in each group when a set of objects is partitioned into equal shares or a set of objects is shared equally—students progress through increasingly sophisticated tasks. In unit 1, students begin by using physical manipulatives to explore equal groups and recognize when numbers cannot be divided evenly, then transition to technology-based manipulatives, visual models, and division equations. They also explore partitive and quotitive division and use visual representations to strengthen conceptual understanding.

Students then apply these concepts in more complex contexts. In unit 1, lesson 10, they model real-world division situations and investigate divisibility with the number 23. In unit 3, students solve division word problems using strip models, equations, and known multiplication facts, then connect array models to division and missing-factor multiplication equations. These experiences demonstrate mastery of TEKS 3.4H and prepare students to extend their understanding to TEKS 3.4F, 3.4I, and 3.4K in units 3 and 5.

In grade 3, educator-guided questions increase in complexity by prompting students to move from identifying equal groups to explaining relationships, representing situations symbolically, and connecting multiplication concepts to problem-solving situations. These scaffolded questions build on prior understanding and support grade-level proficiency aligned to the TEKS.

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 “InsightMath - Course Organization Grade 3” web page explicitly details how patterns, big ideas, and relationships between mathematical concepts connect throughout the grade level. The grade 3 materials demonstrate coherence across units by connecting patterns, big ideas, and relationships. For example, the concept of arrays in multiplication found in unit 1 is connected to finding the area of rectangles in unit 2.

In grade 3, the materials demonstrate coherence by connecting multiplication concepts to equation writing. Students first use multiplication to find the area of rectangles in lesson 8, then write equations to represent area relationships in lesson 9. The materials state, “These connections help students link numerical operations to mathematical representations and deepen conceptual understanding across mathematical concepts.”

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

The grade 3 materials connect content and academic language learned in previous grade levels to current grade-level learning. The “Schema Building” section states that students enter the unit with established place-value understanding from grade 2, including composing and decomposing numbers and using addition and subtraction strategies. Students build on previously learned vocabulary and concepts, such as place value and multiplicative relationships between place values, to extend their understanding of numbers up to 100,000.

The materials build on students’ prior mathematical language by reinforcing familiar vocabulary while introducing new terminology in context. For example, in unit 5, students expand their knowledge of multiplication by discovering how properties and flexible strategies can make calculations more efficient, particularly as they work with larger numbers and multistep problems. This deepened understanding of multiplicative relationships prepares students for the multi-digit multiplication and division work in grades 4 and 5, in which they will apply these same properties and strategies to increasingly complex numbers and real-world contexts.

The materials identify how current learning serves as a foundation for mathematical concepts and skills that students will encounter in future grade levels by explicitly stating in the Grade 3 Program Overview Guide that “Students’ deepened understanding of place value will support their work with multi-digit multiplication and division in grade 4. These connections show students how current concepts serve as a foundation for future mathematical learning.”

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

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. For example, in unit 1, lesson 4, students connect what they learned about representing equal groups as repeated addition in grade 2 (and reviewed in lesson 3) with a new concept of representing equal groups with multiplication. In unit 1, lesson 6, students connect their informal experience of decomposing numbers into equal groups with the new concept of division equations.

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. Each lesson begins with lesson descriptions under the timing indicators in the Digital Planning Guide. Lesson descriptions connect the lesson’s content to students’ previous learning and preview the future learning students will experience. “Discourse Questions” on each slide support students in connecting prior learning and new skills. For example, 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.

Units and lessons provide spaced retrieval opportunities with previously learned skills. Units and clusters end with one or more lessons that provide a mixed review of content from across the unit, providing spaced retrieval that allows students to determine which operations or strategies are appropriate for each task, supporting students in identifying distinguishing features of tasks that let them choose relevant approaches. For example, in three lessons at the end of unit 6, students review addition and subtraction strategies from across the unit, supporting students in noticing key components of a situation that enable them to choose an appropriate operation and solving strategy based upon the context or the numbers involved.

The lesson resources integrate ongoing review into daily instruction to strengthen students’ recall of previously learned concepts. Each lesson includes a student “Practice Page” with spaced, spiral review problems. For example, in unit 1, lesson 7, students review two grade 2 concepts, finding a missing addend to make an equation true and using an open number line to add, before completing three problems related to the current lesson, in which they determine the number of objects in each group in a division situation.

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. For example, 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 unit 1, lesson 1 “Practice Page,” students review one concept from grade 2 (telling time), then a concept from earlier in the unit (multiplication using equal groups using a geometry context), then solve mixed division problems from the current lesson.

The materials revisit mathematical concepts throughout the course to strengthen connections across lessons and units. Within unit 1, lessons address multiplication and division concepts. Then, unit 3 revisits unit 1 lesson 1 concepts to build more flexible models and strategies for multiplication and division. The lesson “Practice Pages” provide interleaved practice; for example, in the unit 1, lesson 7 “Practice Page,” learners write the missing part of an equation, create equal groups, and interpret remainders.

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

The questions and tasks require students to interpret models and representations for mathematical concepts and situations. Across a cluster, unit, or group of related units, students begin with making sense of concepts through manipulatives and visual models, then progress toward flexibly using numerical or symbolic representations and strategies. For example, in unit 6, lesson 1, “Representing Numbers to 100,000 with Base Ten Block Relationships,” students interpret, analyze, and evaluate a range of models and make connections between various models and strategies through “Discourse Questions” tied to an interactive animation. The materials ask students, “What do you see on the screen? What do you notice or wonder?” “What is this puzzle asking you to do?” (interpret) “What do you think is going to happen when you use the Go button?” and “What have you tried?” “Why did it work or not work?” (analyze) The “Discourse Question” “What did you learn from the animation after you used the Go button?” (evaluate) requires students to evaluate how the representation supported their understanding of the mathematical concept.

The questions and tasks require students to analyze models and representations for mathematical concepts and situations. In unit 6, lesson 10, students consider multiple strategies for solving a problem and develop their reasoning and communication skills by explaining why they chose a certain strategy to add and subtract three-digit numbers. In the lesson, students subtract on an open number line to find out which expression has a greater difference. Students analyze and share their strategies, deciding on the most efficient sequential strategies for the number-line model.

The questions and tasks require students to evaluate models and representations for mathematical concepts and situations. In unit 6, lesson 3, students interpret their strategy for solving a mental math problem, then record their work visually on a number-line model. During the strategy-sharing part of the lesson, students analyze multiple representation pathways, such as transitioning from a marked number line to an open number line. They also evaluate which sequential strategies are the most efficient for the given problem, such as evaluating how getting to the nearest hundred makes the model more efficient. Students also use an open-number-line representation to subtract, evaluating and comparing the results of different expressions to determine which one produces a greater difference.

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. Unit 1, lesson 1 requires students to create their own equal-group models using connecting cubes to represent multiplication situations. Students construct multiple representations, analyze whether equal-group arrangements are possible or impossible, and use the models they create to explain and justify their conclusions.

Furthermore, the 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 6, lesson 5, students create number-line models to understand relative sizes of numbers using place value.

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, the materials use simple examples to introduce concepts to students, who then have the opportunity to transfer and reinforce their understanding through additional tasks with less scaffolding and/or greater challenge. Students begin unit 6, lesson 3 by representing multi-digit numbers in place-value charts using place-value blocks, then build on this understanding to represent the number with place-value language, expanded form, and expanded notation. Students then apply their new skills to represent the heights of different mountains in expanded notation and translate from various forms to standard notation without scaffolds or visual models.

The materials provide opportunities for the application of mathematical understanding to new contexts and situations. Clusters and units contain culminating lessons that support students in choosing from a mix of strategies that they have learned over time. In the two culminating lessons for unit 6, students apply multiple strategies for adding and subtracting that they have learned from across the unit to new real-life situations (lesson 16) and numeric situations (lesson 17), discussing how they can use estimation to support calculations, make connections between strategies, and choose strategies efficiently.

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

The materials reinforce the automaticity students need to complete grade-level tasks. Targeted lessons support developing grade 3 multiplication and division fact fluency, beginning with using known facts to find unknown products or quotients. In unit 3, lesson 7, students explore various strategies for using known multiplication facts to find unknown products. Students first practice multiplication facts with threes, fives, and a bonus question with nines to support moving toward fluency with flexible intermediate strategies such as skip counting and repeated addition. Students then use models to identify patterns in multiplication by zero and by one, followed by modeling and discussing doubling and grouping strategies, such as finding 7 x 7 by finding 7 x 2 = 14, then 14 x 2 = 28, then 28 x 2 = 56, then subtracting one group of seven to get 7 x 7 = 49.

The materials include tasks that promote fluent use of mathematical strategies and procedures to solve grade-level problems accurately and efficiently. In unit 3, lesson 7, students build multiplication fact fluency through a sequence of related tasks. Students first model 2 x 7, then use that model to determine 4 x 7, 6 x 7, 7 x 7, and 9 x 7. Students explain how a known multiplication fact helps solve increasingly complex facts, strengthening automaticity through repeated reasoning. The lesson concludes with independent practice that provides additional opportunities to accurately and efficiently apply multiplication facts in multiple contexts.

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. In unit 3, lesson 15, students practice multiplication through multiple learning experiences within the lesson. Students begin with a “Notice and Wonder” routine to analyze equal groups, solve multiplication situations involving groups of objects, complete guided and independent practice pages, compare and discuss two different solution strategies, and reflect on how their strategies are alike and different. The lesson concludes with a Thinking Path, Goal Reflection, and “Practice Page” that reinforce multiplication concepts. Students work through the Playbook page, using known facts to complete the pictographs and related equations, and solving the word problem in two ways. As students share their strategies, the discussion focuses on efficient methods of computation involving composing and decomposing numbers in various ways.

The materials include opportunities for students to use and compare flexible solution strategies while applying mathematical procedures throughout instruction. Throughout the grade level, students practice flexible strategies through specific focus on individual skills and opportunities to immediately practice and reinforce them. In unit 3, lesson 8, students discuss and compare flexible grouping strategies for using known multiplication facts to find unknown products. For example, students compare finding 12 x 3 = 36 by grouping six groups of six; 10 threes and two threes; five threes, five threes, and two threes; and other student-discovered grouping strategies.

The materials include opportunities for students to reinforce procedural accuracy through repeated application of mathematical procedures within lessons and across the unit. Unit 3, lesson 15 tasks students with solving a word problem in two ways. During the strategy-sharing phase of the lesson, the focus shifts to flexible methods of computation. Students practice composing and decomposing numbers in various ways using their knowledge of facts. Then they apply these flexible procedures to accurately complete pictographs and their equations.

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.

The lessons and units give students opportunities to evaluate the efficiency of procedures, processes, and solutions. In unit 3, lesson 11, each student uses two partitioning strategies to find the same product with an area model, such as finding 8 x 7 by finding 4 x 7 and doubling or by finding 5 x 8 and adding 2 x 8). Students compare the efficiency of various strategies across the class, then practice using partitioning strategies independently and discussing which strategies would be more or less efficient for finding the product.

In addition, unit 2, lesson 7 provides students with multiple opportunities to select and apply different procedures for determining area. Students compare areas visually, verify their reasoning using square unit grids, estimate the areas of irregular figures, justify how they determined area, and create multiple shapes of specified areas. These experiences encourage students to choose efficient approaches, apply flexible measurement strategies, and verify the accuracy of their solutions.

Lastly, in unit 3, lesson 12, students explore compensation strategies for multiplication by using 10 facts to solve nine facts by taking one group away. Flexible thinking strategies support students in understanding and applying properties of operations when multiplying. In the “Explore” lesson phase, students determine how many party favors need to be ordered for a quinceañera. Students explore strategies such as doubling, grouping, or compensating for solving 9 x 8. During class reflection, students evaluate the efficiency and accuracy of problem-solving methods.

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

The program provides embedded support that helps educators guide students toward efficient approaches. In lessons, “Details,” “Look-Fors,” and “Discourse Questions” support the educators in guiding students toward a more efficient strategy in a learning trajectory that progresses across each cluster, unit, or group of related units. Unit 3, lesson 7 “Discourse Questions” and “Look-Fors” support educators in noticing how grouping and doubling strategies are more efficient than repeated addition, and guide students toward using these strategies.

Furthermore, unit 3, lesson 8 embeds supports that guide educators toward increasingly efficient strategies for determining totals of equal groups. Students begin with concrete representations, determine totals of repeated equal groups, represent quantities in multiple ways, compare strategies, and apply their understanding independently. The “Show it another way” prompt encourages educators to facilitate discussion about multiple solution strategies, supporting students in developing more efficient approaches to multiplication.

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

The program directly states how the conceptual and procedural emphases of the TEKS are addressed 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 7, the “Conceptual Understanding” section states, “Building from students’ grade 2 work with partitioning shapes into halves, fourths, and eighths, this unit develops a deep understanding of fractions as numbers that represent equal parts of a whole. Students explore the critical concept that equal parts can have different appearances while maintaining the same area, and they use various models, discrete sets, and number lines to visualize that all fractions are composed of unit fractions.”

The materials communicate how students develop procedural knowledge and apply the mathematical skills required by the grade-level TEKS. In the “Exploring Area” unit, students learn that area is the amount of flat space a 2D shape covers, measured by tiling square units without any gaps or overlaps (conceptual emphasis). Students move from counting individual squares to breaking down irregular shapes into rectangles, ultimately learning to measure side lengths and use multiplication as a faster procedure to find total area.

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 3, questions and tasks include the use of concrete models and manipulatives, pictorial representations, and abstract representations. In lessons, units, and clusters, students begin with more concrete representations and models, then transition to more abstract representations. In unit 7, lesson 1, students use pattern blocks and grid drawings as manipulatives to partition whole shapes into equal parts as an exploratory introduction to fractions, for example.

In unit 7, lesson 1, students use pattern blocks and grid drawings to partition whole shapes into equal parts as an exploratory introduction to fractions. Students then discuss and compare flexible grouping strategies for using known multiplication facts to find unknown products. For example, students compare finding 12 x 3 = 36 by grouping six groups of six; 10 threes and two threes; five threes, five threes, and two threes; and other student-discovered grouping strategies. Next, in unit 7, lesson 2, students iterate fractions by shading in pictorial models, choosing and arranging virtual fraction bars (virtual concrete manipulatives), then labeling pictorial models with the abstract notation for fractions using numerators and denominators.

Additionally, in unit 7, lesson 5, students engage in concrete, pictorial, and abstract representations of fractions. Students build fractional models using manipulatives, interpret and draw area models representing fractions and wholes, record fractions using symbolic notation such as 1/4 and 3/4, justify why models represent a whole, and complete independent practice applying all three representations.

Evaluation for 5.3c
Materials include supports for students in connecting, creating, defining, and explaining concrete and representational models to abstract (symbolic/numeric/algorithmic) concepts, as required by the TEKS.

The materials include supports that help students connect concrete and representational models to abstract mathematical concepts, strengthening their understanding of mathematical relationships and procedures. Unit 7, lesson 9 slides and “Discourse Questions” prompt students to articulate explicit relationships between partitioning pictorial set models and writing fractions in abstract notation with a numerator and denominator, showing and explaining that if three people share six pupusas equally, each person will get 2/6 of the pupusas, for example. The “Differentiation” section provides additional strategies to support students in connecting models to abstract representations.

The materials include supports that guide students in constructing and creating concrete and representational models to demonstrate and communicate abstract mathematical concepts. In unit 7, lesson 9, each student uses two partitioning strategies to find the same product with an area model, such as finding 8 x 7 by finding 4 x 7 and doubling, or by finding 5 x 8 and adding 2 x 8. Then students compare the efficiency of various strategies across the class, practice using partitioning strategies independently, and discuss whether certain strategies would be more or less efficient for finding the product.

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. Each unit provides specific ways to support students with key unit or cluster concepts. For example, unit 7 “After This Unit” suggestions support students who are struggling with the abstract skill of interpreting the meaning of the numerator and denominator. Materials guide educators to “Emphasize the meaning of the numerator as the count of equal parts and the denominator as the number of equal parts in one whole. While this concept is revisited, the meaning established now serves as the basis for all future work with fractions. Provide regular opportunities for students to explain in their own words what each number in a fraction represents. Highlight a variety of models and ask students to identify the numerator and denominator in each model.”

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

The materials support mathematical communication by connecting visual models to academic vocabulary and conceptual understanding. The program supports students as they engage with new mathematical language using manipulatives. In unit 7, lesson 1, students fold and cut sheets of copy paper to identify one-half, one-fourth, and one-eighth. They learn vocabulary terms unit fraction and denominator to describe how the size of the parts decreases as the number of parts increases. The materials use this concrete model to help students visualize the mathematical terms they use.

The materials promote the development of mathematical vocabulary through structured opportunities to discuss, explain, read, and write about mathematical ideas while encouraging students to use precise mathematical language during hands-on exploration of mathematical concepts. For example, in unit 7, lesson 5, students develop academic mathematical language through visual fraction models while identifying and describing fractions. Students use area models to represent fractions, explain how a model represents one whole, label and sort fraction models using mathematical vocabulary, identify the fractional value of each square in a partitioned whole, and apply their understanding on a “Practice Page.” This sequenced approach supports students’ use of terms such as whole, fraction, numerator, denominator, one-fourth, three-fourths, equal parts, and partition while connecting visual representations to symbolic notation.

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 provide instructional supports that help educators build students’ understanding and use of mathematical vocabulary during instruction. During a unit 7 lesson on exploring fractions involving discrete sets, the educator scaffolds new vocabulary by prompting students to compare and contrast familiar and unfamiliar models. Students compare a continuous-area model such as a fraction bar to a discrete-set model such as a group of individual counters. The “Discourse Question” Is the whole always a shape? prompts students to reconsider what “the whole” means. The educator guidance uses this comparison to help students attach the formal word set to a concrete visual collection.

The materials embed educator prompts and instructional routines that encourage students to develop and apply precise mathematical terminology within mathematical contexts. In unit 7, lesson 2, embedded educator guidance intentionally develops students’ academic mathematical vocabulary through multiple language supports. Rather than assuming students already know the language of fractions, the materials provide explicit scaffolds for receptive and expressive language. The “Supporting Language” section includes sentence stems such as “The model shows the fraction ____” and sentence frames such as “In the fraction ____, the number ____ represents ____,” and “The model shows the fraction ____ because ____.” These supports help students apply precise mathematical vocabulary while explaining their reasoning. The educator guidance also identifies vocabulary that should be explicitly taught and reinforced, including half, halves, equal share, area, perimeter, and split. The materials further direct educators to ensure students understand that split means “to break apart or divide,” connecting everyday language to its mathematical meaning. The program encourages educators to connect multiple representations with fractional notation, such as 1/2, helping students consistently use mathematical language across visual models, symbols, and classroom discussions.

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 mathematical language, including vocabulary, syntax, and discourse. For example, after students analyze equal groups and repeated addition in unit 1, lesson 4, educators introduce and reinforce the academic vocabulary multiply and multiplication, explicitly defining multiplication as “finding the total of equal groups or equal parts.” Educators model appropriate mathematical syntax by reading equations aloud using precise language, such as “3 multiplied by 5 equals 15” and “3 times as much as 5 is 15.” These language models provide students with examples of how to communicate multiplication equations using accurate mathematical terminology. The materials provide prompts that require students to explain and justify reasoning, including “How does the repeated addition/multiplication equation represent the number of shoes?” “How are the equations the same and different?” “Could you write a multiplication equation for 10 + 2 + 5 = 17? Why or why not?” These questions encourage students to compare representations, analyze mathematical structure, justify their reasoning, and communicate using academic language. Embedded “Look-Fors” identify the mathematical language and reasoning educators should expect to hear, such as students explaining that multiplication represents equal groups, identifying what each number in the equation represents, and correctly using the terms multiply and multiplication in their explanations. The materials alert educators to the common student misconception that unequal groups can be represented with multiplication, allowing them to facilitate productive mathematical discussions that clarify students’ understanding.

The materials encourage collaborative mathematical discussions in which students listen to, build on, and strengthen their use of mathematical language through ongoing peer interactions. For example, during the unit 7 lesson on analyzing the meaning of one-half, educators introduce the term fraction after the students have informally processed the concept. The guidance prompts, “After students have used their own language to explain their strategies for solving, introduce the vocabulary word fraction,” and provides a precise, student-friendly definition: “a number representing the number of selected parts out of the number of equal parts of 1 whole.” The educator reviews the “Look-Fors,” actively listening for students to apply the student-friendly definition during discussions.

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 includes a “Common Errors and Misconceptions” support section that helps educators address student misunderstandings. In unit 2, cluster 1, the materials identify strategies for addressing misconceptions about area concepts. Embedded feedback clarifying 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 scaffolding and support.

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

The instructional materials appropriately integrate the TEKS mathematical process standards into grade-level instruction by placing them alongside the content standards within each instructional cluster. For example, in grade 3, cluster 1, the lesson identifies the content TEKS (3.4H and 3.4K) and the mathematical process standards (3.1A, 3.1B, 3.1C, 3.1E, and 3.1G). The materials describe how students apply the process standards throughout the lesson by analyzing problems, developing and justifying solution strategies, selecting appropriate tools, creating visual representations, and communicating mathematical reasoning. The program intentionally integrates the TEKS process standards throughout instruction to support students’ mathematical thinking and problem-solving.

TEKS process standards embedded within lessons and activities allow students to apply reasoning, problem-solving, communication, and representation while learning grade-level mathematics. Unit 9, lesson 2 includes the opportunity for students to practice mathematical process standard 3.1G by drawing models to compare the lengths of different insects represented as fractions with the same numerator or denominator, and explain their strategies for comparing and finding missing lengths based on provided measurements and relationships among the insects. Then they justify their comparisons and reasoning using their models during academic conversations with their peers and educator.

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. Lesson 10 explicitly identifies the applicable mathematical process standard (3.1D) alongside the content TEKS and describes how students communicate mathematical reasoning using area models, diagrams, symbols, equations, and mathematical language. The lesson-level implementation demonstrates how the program integrates process standards 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 that integrates process standards throughout instruction. The program integrates key concepts and revisits them across various lessons to build mathematical fluency and strong math habits. Rather than limiting a skill to one lesson, multiple process standards coalesce in an activity, ensuring that a single measurement activity is never simply about arriving at a number. For example, in a lesson such as lesson 3 or 10, students select a tool, determine how the units relate, and explain their thinking to their classmates. This overlapping design helps process standards become everyday math habits across the entire course.

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

The materials describe how the mathematical process standards support instruction and learning experiences within each unit. For example, in unit 9, several learning experiences incorporate process standard 3.1C. In lessons 1, 3, and 12, “Students select appropriate tools and techniques to solve measurement problems accurately and efficiently throughout the unit. Students determine which tools (e.g., rulers, yardsticks, customary liquid measurement containers) best suit different attributes and levels of precision. Students also select estimation techniques, using visual comparisons and known benchmarks to make and refine predictions before measuring. Through thoughtful selection of both tools and techniques, students develop precision, flexibility, and confidence in solving a variety of problems related to real-world measurement situations.”

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.” The program intentionally incorporates the seven TEKS mathematical process standards throughout its curriculum using a progressive system of “Student Strengths” that builds in complexity across grade levels. As noted previously, the program combines multiple process standards in a single lesson, which continues 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, providing lesson-level overviews of the TEKS mathematical process standards. The materials specify the lessons in which each process standard (3.1A–3.1G) is incorporated and describe how students engage in the process through the lesson activities, including applying mathematics to real-world situations, problem-solving, creating representations, analyzing relationships, and communicating mathematical reasoning.

The materials provide lesson-level information that identifies the mathematical process standards associated with the instruction, including educator guidance for each mathematical process standard that is incorporated into a lesson. For example, unit 9, lesson 10 addresses process standard 3.1A as “Students apply their understanding of liquid volume and measurement to solve problems arising in everyday life (e.g., filling fish tanks, estimating liquid volume of bottles and jugs).”

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

The grade 3 materials provide students with opportunities to engage in mathematical thinking. For example, 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 equip 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 mathematical process standards highlight these traits within each lesson in unit 0 and throughout the course. The lessons in the first unit introduce students to open-ended, creative mathematical challenges while developing the mathematical mindsets, language, and skills students need to engage in creative mathematical thinking throughout the year.

The materials require students to persevere through problem-solving. In unit 5, lesson 2, students think mathematically as they analyze area models, explore multiple ways to partition factors, compare equivalent expressions, and justify efficient strategies for finding products. Students persevere through problem-solving as they predict, test, and refine strategies; analyze incorrect approaches; and revise their thinking across multiple tasks. Students make sense of mathematics through discourse that connects area models, partial products, equivalent expressions, and use of parentheses. Students explain and justify how different representations model the same mathematical relationship.

Students make sense of mathematics throughout the program. For example, in grade 3, unit 6, lesson 13, the primary objective is for “Students to explain and justify their strategy,” forcing them to think deeply about why a mathematical strategy works, rather than just following steps. In the “Launch” section, students interpret prewritten solution strategies and determine which ones accurately match the given word problem.

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, explain, and justify multiple ways to represent and solve problems. In unit 5, lesson 12, students independently write an equation while using magnets, the pen tool, or another model to represent their thinking. During the “Share with Class” discussion, preloaded sample student responses called “Argumenteers” expose students to multiple valid representations of the same problem, including strip diagrams, arrays, and equations. The “Look-Fors” prompt students to explain how their array, strip diagram, or equation represents and solves the problem and how each quantity connects to the problem context. Educator questions such as “How did you solve the problem?”, “Which operation did you use?”, “Why did you choose that operation?”, and “How does your equation represent the problem?” require students to explain and justify their reasoning. For example, students justify using multiplication to determine 30 tables (6 × 5) and then 60 signs (30 × 2), explaining how each factor in the equation 6 × 5 × 2 = 60 corresponds to quantities in the situation.

Students explain various ways to represent and complete tasks through numerous opportunities for mathematical reasoning. In the lesson 1 “Launch” section, students use a partial-products strategy to explore multiple ways to partition the same area model. Students evaluate two partitioning strategies rather than simply copying one method. During this routine, students actively compare strategies and explain why they prefer one approach over another. This activity helps students recognize that although a rectangle can be partitioned in different ways, the overall product remains the same.

Students must justify their thinking in representing and solving mathematical problems. Many activities include Argumenteers that show various problem-solving methods and enhance mathematical discourse by helping students explain and justify multiple ways to solve problems and complete tasks. In unit 2, lesson 13, the Argumenteers support students as they understand, explain, and justify multiple approaches or strategies by placing effective target strategies alongside student strategies, which may be less sophisticated or creative in comparison. In this lesson, slides E4, E5a, and E6a include Argumenteers that demonstrate strategies students can use to add mixed customary units, such as adding two lengths given in feet and inches.

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

Students have multiple opportunities to make sense of mathematics through collaboration with peers and educators throughout the materials. For instance, each unit includes two “My Thinking Path” activities. In unit 5, lesson 7, 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 peers and educators. In the “My Thinking Path” pages, students write reflections on their mathematical thinking for key topics across the unit, providing opportunities for students to think about their learning, communicate their understanding, and discuss their mathematical ideas with peers.

The materials provide opportunities for students to do, write, and discuss mathematics with their educator and peers to deepen their mathematical understanding. In unit 5, lesson 7, students complete a Thinking Path journal entry reflecting on the unit’s big mathematical idea, share their thinking with a partner, and contribute to a whole-class chart of student thinking. Educator guidance includes “Discourse Questions” that extend student thinking and encourage students to write their ideas, use manipulatives, or discuss their thinking with a partner when they encounter challenges. Students also engage in reflective goal-setting by sharing their progress with a partner and participating in educator-facilitated discussions on strategies to reach their goals. Throughout the lesson, “Discourse Questions” prompt students to explain their reasoning, reflect on their learning, and describe how they solve problems, providing repeated opportunities to do, write, and discuss mathematics actively.

Discussion activities require students to make sense of mathematics with educators and peers. For example, in unit 5, lesson 16, students deepen their understanding of area models by strategically partitioning one- and two-digit numbers to find products. Students explore visual models through partner and whole-class discussions before drawing area models, writing equations, and explaining their reasoning. A Playbook page extends the learning by prompting students to respond in writing to “How did I find the same product using different strategies?” Throughout the lesson, “Discourse Questions” and “Look-Fors” prompt students to discuss, explain, and justify their mathematical thinking.

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 as they encourage students to share explanations, arguments, and justifications. The lesson notes provide “Details,” “Look-Fors,” and “Discourse Questions” to guide students in sharing and reflecting on their problem-solving approaches through activities that require analyzing different strategies and justifying why one strategy may be more useful than another. In unit 6, lesson 13, students solve word problems involving addition and subtraction of three-digit numbers, reflecting on their choices and justifying their decisions to their peers.

The materials provide explicit educator guidance to support students in sharing and reflecting on their problem-solving approaches through explanations, arguments, and justifications. For example, in unit 1, lesson 1, students collaborate to create equal groups using 20 and then 24 cubes, record multiple solution methods, and share their work with the class. Educators display student work and use “Discourse Questions” to facilitate discussion about strategies for creating equal groups. The “Look-Fors” prompt educators to observe students as they explain their strategies, justify why groups are equal, identify multiple solutions, record the number of groups and objects in each group, and explain why some equal groupings are not possible. “Discourse Questions” such as “How do you know your groups are equal?” and “Is there only one way you cannot make equal groups? How do you know?” require students to explain and justify their reasoning, compare solution methods, defend their conclusions, and revise their thinking through classroom discourse.

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

The materials include prompts that support educator feedback based on student responses and anticipated misconceptions. For example, in unit 1, lesson 1, educators receive guidance for addressing the misconception that any number can be divided into any number of equal groups. Students first work with 24 cubes to determine which numbers will not result in equal groupings. Educators then guide students to identify when groups no longer divide evenly, such as when creating five equal groups with 24 cubes results in a remainder. Rather than simply telling students that five does not work, the guidance encourages educators to have students use concrete tools to model the error and make sense of the mathematics.

In addition, educators receive guidance on providing explanatory feedback based on student responses and anticipated misconceptions for each unit and cluster. The “Common Errors and Misconceptions” guidance for unit 2, cluster 1 provides suggestions for addressing misunderstandings about the concept of area. For example, students may focus on a single dimension of a shape when comparing areas, stating that a shape has more area because it is longer or taller, even when the overall area is smaller. To address this misconception, educators may emphasize that the area represents the total amount of surface within a set boundary. Educators may also provide examples in which a shorter, wider shape has more area than a longer, narrower shape and prompt students to use square tiles to determine the area of each shape.