HMH Into Math Texas, Grade 6

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

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

The scope and sequence charts include the TEKS and ELPS alignment for each module and lesson and identify the concepts taught throughout the instructional year. Additional program materials further support this alignment through TEKS and ELPS correlations, as well as “Correlations by Lesson” documents that break down concepts taught by module. Within the “Discover” tab under the program dropdown, the scope and sequence also outlines the TEKS, ELPS, and lesson concepts to support instructional planning and pacing.

Evaluation for 1.1b
Materials include suggested pacing (pacing guide/calendar) to support effective implementation for various instructional calendars (e.g., varying numbers of instructional days - 165, 180, 210).

The materials provide a “Scope and Sequence with Yearly Pacing” for 165-day and 210-day instructional calendars. The guidance provided in the calendar “moves step by step through each module and shows how each module covers the instructional sequence and standards, and then lists each Module Review and Module Test.” These options support effective implementation while remaining aligned with the TEKS, the ELPS, and course concepts.

The materials provide guidance on extending the 165-day pacing calendar to 180 days by adding “one extra day to each lesson where a Readiness Standard is first taught.” Educators can use the extra day to provide targeted reinforcement, practice, or challenges based on formative assessments, “Quick Checks,” and observations.

Evaluation for 1.1c
Materials include an explanation for the rationale of unit order as well as how concepts to be learned connect throughout the course.

The Teacher’s Guide provides a rationale for the module order, explaining that the program builds concepts by connecting prior learning to new content. For example, students first develop an understanding of ratios and rates. In later modules, they apply these concepts to percents and algebraic relationships. This order ensures that conceptual understanding supports and strengthens application.

The materials support educators in understanding how concepts connect throughout the course. This structure helps educators internalize concepts and make connections. For example, “Students apply their understanding of rational numbers from Module 1 in Module 11 to graph rational numbers and polygons in the coordinate plane and find distance on the coordinate plane.”

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

The program materials include guidance that supports educators with unit and lesson internalization through comprehensive planning supports, structured instructional routines, and embedded educator guidance. The Teacher’s Guide reviews the standards, outlines what students will learn in each module, explains the module flow, identifies the TEKS and ELPS, and includes background information to support instructional preparation and lesson internalization.

The materials also include resources that help educators understand the sequence of learning within each module and prepare for daily instruction. The “Before You Teach” sections outline the mathematical understanding needed for each lesson and explain what students will learn. Planning tools such as the “Editable Lesson Plan,” pacing guidance, module flowcharts, and lesson sequencing explanations support educator preparation.

Additionally, the “Step Through a Module” section of the Implementation Guide provides guidance for internalizing module and lesson components, while “Teacher Background” sections include mathematical rationale, examples, summaries, and explanations of concepts to deepen educator understanding before instruction. The materials also include “Internalization Tools” to support both lesson and unit internalization through guiding questions such as “What do the lesson and language objectives expect from students?” and “What concepts, strategies, or procedures will students learn?” Educators can use the tools to internalize lessons and units, either individually or in a group.

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

The program materials include resources and guidance documents that help instructional leaders support educators in implementing the program as designed. The materials provide implementation supports through resources such as the Professional Learning and Coaching Guide, which includes instructional support, implementation guidance, pacing recommendations, and professional learning resources to assist leaders in supporting effective program use.

The materials also include tools that support classroom observations, reflection, and coaching conversations. For example, the Look-Fors and Reflection Guide provides classroom observation indicators, implementation expectations, reflection questions, and suggested discussion topics to help instructional leaders monitor instruction and support educator planning.

Additionally, the materials include look-for checklists designed for the first 30 days of instruction, along with reflection tools and guiding questions to support classroom visits, targeted feedback, and ongoing instructional implementation conversations with educators.

Evaluation for 1.2a
Materials include comprehensive unit overviews that provide the background content knowledge and academic vocabulary necessary to effectively teach the concepts in the unit.

The Teacher’s Guide includes a “What Should I Understand About the Math in this Module?” section that provides background knowledge about the TEKS covered in the module. For example, module 4 states, “Knowing how to convert units within a measurement system by using proportions and unit rates can be helpful in solving mathematical and real-world problems involving topics such as weight, length, capacity, and time.”

The materials include academic vocabulary support within lesson-planning and module-planning materials, including a vocabulary list embedded in lesson overviews, mathematical language supports, and ELPS-aligned language development guidance to support effective instruction of unit concepts.

The materials also provide an educator’s glossary to help educators teach the mathematical concepts effectively. The glossary includes not only definitions but also pictorial examples when appropriate.

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.

Each module includes family resources in English and Spanish, delivered through a “Family Letter” that explains module objectives, academic vocabulary, and online supports aligned to each lesson. The letters help foster family involvement in supporting students’ progress outside the classroom.

Each “Family Letter” also includes a home activity families can complete together to further reinforce learning. For example, module 2 suggests a string measuring activity to reinforce the concept of division of rational numbers.

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 Teacher’s Guide includes lesson plans with clearly defined lesson objectives, TEKS correlations, and ELPS correlations within lesson overviews and planning materials. For example, module 7, lesson 2 aligns with TEKS 6.6.C, which expects students to “represent real-world situations using verbal descriptions, tables, and graphs” through a series of four tasks presented in a variety of formats.

Each lesson plan includes tasks, assessments, and practice sets aligned with the learning and language objectives, directly correlated to the TEKS and ELPS. Materials include many instructional assessments and tools, such as “Spark Your Learning,” “Task” routines, “Quick Checks,” and “Differentiation and Practice” sections.

Evaluation for 1.3b
Materials include a lesson overview listing the teacher and student materials necessary to effectively deliver the lesson, and the suggested timing for each lesson component.

The Teacher’s Guide includes detailed lesson plans that provide the manipulatives and materials needed for each lesson. For example, module 2, lesson 1 requires 20 two-color counters per group and print or digital number lines to model adding and subtracting integers.

In addition, the Teacher’s Guide includes guidance and recommendations for the timing of each lesson component. The “What Does This Look Like in My Classroom?” section illustrates how to structure the lesson over two 45-minute sessions. Each lesson component includes suggested timing; for example, module 8, lesson 3, task 3 should take approximately 13 minutes.

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

Sections such as “Differentiation and Practice,” “Homework,” “Extension,” “Collaborative Groups,” and “Teacher-Led Small-Group Activities” include guidance on the effective use of lesson materials for extended practice. The resources support educators in assigning additional practice, enrichment, intervention, and adaptive learning opportunities based on student performance data.

The Teacher’s Guide includes guidance on the effective use of differentiation and practice activities for students who are “Almost There,” “On Track,” and “Ready for More.” Students work through one to three rotations per lesson, focusing on independent practice, collaborative groups, and educator-led small-group activities.

Additionally, the materials support effective use of the lesson materials through ongoing, leveled practice on Waggle, an adaptive digital learning platform. The materials note, “HMH Waggle supports instruction with auto-assigned, skill-based practice tailored by its AI engine.” When educators actively use the guidance report, they access guidance on using student data to meet the needs of all learners.

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.

Each module includes a variety of formative assessments through “Quick Checks,” “Are You Ready?” tasks, “Mid-Module Checks,” and “Module Reviews.” The assessments include multiple item types such as procedural fluency, reasoning, application, modeling, and open-response tasks.

Each module provides a variety of summative assessments to determine “whether students have mastered skills taught in each module.” The assessments include a Module Test available in digital and printable options, as well as a Module Project that requires students to “apply and extend the mathematics found within the modules.” The Module Test offers a variety of item types; for example, module 7 includes multiple-choice, open-ended response, graphing, and multi-select item types.

The materials use diagnostic assessments such as “Benchmark Assessments” to “determine progress at strategic points in the school year.” The materials include three “Benchmark Assessments,” and each test includes questions in various formats, such as drag-and-drop, graph, multi-select, and multiple-choice. This type of assessment helps gauge mastery of the skills taught in the year.

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

The Implementation Guide gives a clear overview of the purpose and types of instructional assessments that support educators in making data-driven instructional decisions throughout the year. The materials define each type of assessment, assign a specific use, and allocate a time limit.

The Program Assessments at a Glance chart explains how each assessment can help educators determine student readiness, monitor progress, adapt instruction, and measure student mastery. For example, the “Quick Check” assessment gives educators “data that helps them identify students who need support, are ready to practice the relevant skill, or could benefit from a challenge.”

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

The Implementation Guide provides guidance to ensure consistent, accurate administration across all assessment types by outlining what it measures, why it’s important, and how to administer it. For example, the Module Test measures “how well your students have understood the TEKS and process standards covered in the module.”

The materials include guidance on consistently administering assessments to ensure that all students receive the same instructions. For example, guidance for the Module Project states that “students can work on the project after whole-group instruction, or you can devote a specific instructional day to completing the project.” At the same time, the included rubrics ensure that outcomes accurately reflect student learning.

The materials also include suggested timing for each assessment to help maintain consistent administration across classrooms. For example, the “Quick Checks” should be used daily, with a suggested duration of five to ten minutes.

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

Formative assessments including “Quick Checks,” “Practice on Your Own,” and “Are You Ready?” are aligned to the lesson TEKS and daily learning objectives identified within lesson planning materials. For example, the “Practice on Your Own” answer key includes the TEKS assessed and which task the question aligns to within the lesson.

Summative assessments, such as the Module Test, include answer keys that align questions with the TEKS assessed and the corresponding lesson source. For example, in module 7, question 4 requires students to write a linear equation given a table of values, which aligns with TEKS 6.6.B and lesson 1, “Identify Relationships from Tables and Graphs.”

Diagnostic assessments, such as the “Benchmark Assessments,” include answer keys with a TEKS correlation table that aligns each test item to the TEKS and specific lessons.

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

The materials include TEKS-aligned formative and summative assessment tasks of varying complexity, including procedural tasks, open-response questions, mathematical modeling tasks, multistep application problems, and performance-based activities.

All Module Tests include TEKS-aligned questions that vary in item type and complexity. The “Module Test Answer Key” identifies the TEKS assessed and Depth of Knowledge (DOK) level for each item. For example, the module 6 test includes multiple-choice, free-response, and match-table-grid questions that vary in complexity from DOK 1 to 3.

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

The materials include formative assessment opportunities such as “Practice on Your Own” tasks that provide scoring information, sample answers, and educator guidance for evaluating student responses. The materials also reference “Assessment Reports on Ed,” which support educators in interpreting student performance and identifying strengths, misconceptions, and instructional needs.

Each Module Review provides guidance for scoring correct responses and a “Data-Driven Support” table with intervention activities to address skill gaps. For example, in module 1, students who miss item 8 would benefit from a reteach activity on applying absolute value in a real-world situation.

Additionally, Module Projects include scoring rubrics and exemplar responses for interpreting student performance. Guidance also suggests that educators “Have students use the project rubric to set a goal for how they will perform on the activity.”

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

Every lesson includes a “Differentiation and Practice” section that suggests how to respond to trends in students’ “Quick Check” performance. Small-group educator-led activities are available to address learning needs and misconceptions for students who are “Almost There,” “On Track,” and “Ready for More.” In addition, to meet the needs of all learners, materials provide multiple levels of independent practice activities for students who are not currently participating in educator-led small-group activities.

Each module includes “Data-Driven Supports” to respond to student trends on the “Prerequisite Check” and Module Review. Guidance includes recommended reteaching resources based on various skills available on Ed. Adaptive skill development is available through Waggle, “with its skill-driven AI engine, to provide targeted support to your students.”

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 include tools for educators to track student progress and growth through assessment reports, progress-monitoring resources, and data-analysis supports connected to lesson and module assessments. A printable “Whole Class Proficiency and Growth Tracker” and digital reports are available to monitor student proficiency and progress throughout the school year.

The materials include student-facing progress-monitoring opportunities such as self-check routines, progress checks, and reflection opportunities embedded within lesson and assessment structures. The program also provides a printable student tracker to help students “set goals and track their scores for Module Tests throughout the year.”

Each lesson incorporates a “Learning Goal” routine for students to “assess their content knowledge based on the I Can statement” at the beginning and end of the lesson, which allows students and educators to track their growth. For example, the learning goal for module 12, lesson 1 is “I can identify statistical questions, describe the nature of attributes under investigation, and report the number of observations.” Students can rate themselves as “I don’t understand,” “I need more practice,” or “I’ve got it.”

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.

Each lesson includes educator guidance for differentiated instruction and scaffolded small-group activities for students who have not yet reached proficiency based on the “Quick Check.” The “Almost There” educator-led small-group activity provides explicit reteaching guidance, guided questioning, visual models, and structured practice to help students master grade-level content and skills. For example, in module 4, lesson 3, a proportional reasoning diagram is used to help students convert between centimeters and millimeters. Guidance also suggests that students check their conversions by measuring in both units with a ruler.

Additionally, the materials include guidance within the “Data-Driven Report” to “address specific learning gaps identified in the Prerequisite Check.” The materials provide intervention activities on 35 skills, including “Multiplication Facts,” “Decimal Operations,” and “Evaluating Expressions,” to prepare for grade-level content.

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 include preteaching supports for unfamiliar academic and mathematical vocabulary through the “Words to Learn (WTL)” routine and “WTL Vocabulary Cards,” which guide educators to introduce key mathematical terms using strategies such as “Say It” and “Define It” before students engage with lesson content. Guidance states, “This routine provides each student with an opportunity to practice and internalize each new term.”

The materials also include embedded vocabulary and language supports to help students understand unfamiliar academic language and references in text, through language routines such as “Three Reads,” “Turn and Talk,” and “Collect and Discuss.” For example, in module 7, lesson 3, the “Collect and Display” routine suggests, “During pair work, circulate and listen to student discussion. Write common or important words, phrases, sketches, or diagrams…on a visual display for students to see.”

Additionally, the materials include embedded educator support through “ELPS Teaching Strategies” to help students understand unfamiliar references and contextual language encountered in mathematical tasks. For example, module 7, lesson 3 states, “Review examples of figurative language and discuss how they might add to writing. Then read students’ examples and support them in rewriting the problem to use different forms of figurative language.”

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.

Each lesson provides differentiated instruction, including enrichment and extension activities, for students who have demonstrated grade-level proficiency in the “Quick Check.” Students who are ready for a challenge will benefit from the “Ready for More” small-group activity. For example, in the module 2, lesson 2 activity, students apply integer operations in new situations, create their own mathematical examples, and engage in deeper mathematical reasoning.

Additionally, each module provides leveled practice, including “Challenge” activities for students who have demonstrated proficiency in grade-level content. For example, in module 11, students’ understanding of graphing on the coordinate plane is extended through three open-ended questions in the “Challenge” activity “Graph Polygons on the Coordinate Plane.”

The materials also include a Module Project that “engages students in Depth of Knowledge (DOK) Level 4 tasks that apply and extend the mathematics found within the modules.” For example, in the “Peaks and Valleys” project, students visualize and interpret integers in a geographical context by comparing the elevations of different locations in California.

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 materials provide explicit prompts to support the educator in modeling and explaining the mathematical concepts. The Teacher’s Guide includes a series of “Ask” prompts for each lesson task. For example, in module 6, lesson 2, task 1, students use concrete models to find the part given the whole. The materials state, “ASK: What does 40% mean compared to the whole?” and “ASK: How will you group 60 to model 40% with counters?” along with exemplary responses to guide instruction.

In addition, the materials provide guidance for modeling and explaining concepts through mathematical modeling supports and mathematical language routines. For example, in module 2, lesson 3, task 4 guidance directs educators to “have students use the Turn & Talk routine. Support students by pointing out that if the divisor is multiplied by a power of 10, then the dividend must be multiplied by the same power of 10.”

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

The Teacher’s Guide provides detailed lesson plans for effective lesson delivery and facilitation using a variety of instructional approaches. Each lesson begins with a “Spark Your Learning” activity to engage students and encourage discussion of mathematical concepts. The materials provide whole-group instruction through a series of tasks with a variety of instruction strategies such as “Turn and Talk,” hands-on manipulatives, and real-world connections. Teaching strategies are embedded throughout each lesson to address the needs of all learners, including “ELPS Support” and correction of common errors.

The materials also provide educator guidance and recommendations through Universal Design for Learning (UDL) strategies in the Teacher’s Guide, promoting effective lesson delivery through multiple instructional approaches, including visual, verbal, collaborative, and hands-on learning opportunities. For example, in module 11, lesson 2, task 1, “UDL Support” states, “Allow students to share their thinking by drawing figures with different numbers of sides that are and are not polygons. Have students compare and share their drawings with other students.”

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.

Each lesson provides multiple types of practice to support implementation within the “Differentiation and Practice” section. The materials include independent practice, educator-led small-group activities, and collaborative group activities tailored to students’ needs. Guidance suggests that collaborative group activities be completed in pairs, while a variety of independent practices allow students the opportunity to reinforce concepts and skills from the lesson individually.

The materials include guidance and recommended structures, such as whole-group instruction, small-group intervention, partner work, and independent learning opportunities to support effective implementation. For example, each lesson has a “What Does This Look Like in My Classroom?” section, which includes guidance on presenting the lesson tasks to the whole group and differentiating instruction using one to three small-group rotations.

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 “Spark Your Learning” opening activity for each lesson includes teaching strategies for emergent bilinguals (emergent bilingual) at varying language proficiency levels. For example, in module 2, lesson 3, on multiplying and dividing rational numbers, guidance for pre-production and beginner-level students states, “Consider using visual aids to help students fill in the blanks with the correct numbers.” For intermediate students, educators are guided to provide a sentence starter such as “To find out how many cups of pecans Sara needs . . .” to help students use increasingly more academic language.

The materials also include embedded educator guidance for linguistic accommodations aligned with the ELPS, including sentence stems, academic vocabulary supports, discussion routines, and scaffolded language-development activities. For example, module 5, lesson 2 includes an ELPS teaching strategy that states, “Explain that when we write to describe, the purpose is to help the reader ‘see’ what is being described, whether it is a place, a person, or a process. A good description includes evidence or detail to help the reader ‘see’ more clearly.”

Additionally, at the beginning of each module, there is a “Mathematical Language & Emergent Bilingual” page that provides the educator with tools to plan for language development in the upcoming lessons. Guidance includes vocabulary support and mathematical language routines.

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

The “Language Growth for All Learners” section of the Implementation Guide describes how each lesson aligns with the ELPS, includes observable and measurable language objectives, and provides teaching strategies that support mathematical communication, helping educators effectively use the program with emergent bilingual students in bilingual and ESL instructional settings. Guidance describes the program as providing “opportunities to help your students develop their command of mathematical language and content simultaneously.”

In addition, the materials include a Language Development Resource Guide designed to “offer a structured approach to supporting students’ language development through professional development for teachers.” The guide provides math language routines, teaching strategies, student support resources for academic vocabulary and cognate support, and a description of the UDL principles. The guide helps ensure that students receive the targeted support that promotes language development.

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 include a variety of “Mathematical Language Routines” to support emergent bilingual students in developing academic vocabulary, increasing comprehension, and building background knowledge through oral and written discourse. For example, the “Words to Learn” routine supports students as they learn and internalize the academic vocabulary introduced in lessons. The routine involves saying, defining, discussing, and using the new academic vocabulary. In module 2, lesson 1, task 1, the guidance suggests using the routine for the academic words addend and sum.

The materials also include embedded “Emergent Bilingual” and “ELPS” teaching strategies to further increase comprehension and build background knowledge. For example, in module 2, lesson 3, the guidance states, “Encourage students to discuss and collectively write down what each label means in their own words, using precise vocabulary to explain how the area model visually represents the value of each digit.”

In addition, the materials include embedded guidance to help students make cross-linguistic connections through oral and written discourse, connecting their home language to English. For example, in module 10, lesson 4, the task 5 guidance states, “Invite students to first describe their scenario in their home language, then present a concise English statement . . . . This strengthens accurate spoken math language tied to the context.”

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.

Lesson practice provides opportunities for students to demonstrate depth of understanding aligned to the TEKS through representations, mathematical reasoning, and explanations in grade-level tasks such as proportional relationships, integer reasoning, and algebraic relationships. For example, the lesson 6.2 “Quick Check” requires students to demonstrate understanding of percent concepts through multiple representations, including concrete models, bar models, equivalent fractions, decimals, and percents. Students apply percent reasoning to determine parts of a whole and connect visual, numeric, and symbolic representations as required by TEKS 6.5.B.

Instructional assessments over the course of a module, such as Module Reviews and Module Tests, assess the same grade-level concepts and require students to apply procedural skill, conceptual understanding, and mathematical reasoning, as required by the TEKS. Both assessments include educator guidance that directly correlates each question with the assessed TEKS.

Additionally, each module includes a Module Project that requires the application of mathematical concepts in a real-world context. Guidance states, “Through real-life explorations, students synthesize concepts and apply understanding to complex tasks.” The project contains a DOK Level 4 task, which asks students to analyze information, select an appropriate strategy, solve the problem, and explain or justify their reasoning using mathematical representations and written responses, as required by the process standards.

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

Each lesson provides a series of tasks that progressively increase in rigor and complexity, leading to grade-level proficiency. For example, in module 2, lesson 1, students are expected to add and subtract integers. The lesson begins with a task that uses concrete models, such as counters, to demonstrate how to create zero pairs. Students move to using number lines to model adding and subtracting integers. The final task has students make predictions and write equations to represent addition and subtraction within a real-world problem.

Each task uses guiding questions that increase in complexity and rigor, leading to grade-level proficiency by providing access points for students to build on prior knowledge and deepen their mathematical understanding. In task 2 of lesson 9.1, students order the angle measures of a triangle. The task begins with guiding questions such as “Which angle has the greatest measure?” and “Which angle has the least measure?” It progresses to “Why is the angle opposite AC the greatest in triangle ABC?”

Additionally, Module Tests progress from procedural fluency to application and mathematical reasoning through a variety of question types. For example, the module 4 test progresses from foundational ratio and rate reasoning to multistep application and problem-solving, requiring students to demonstrate increasing rigor and conceptual understanding aligned with the grade-level TEKS.

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

The materials include module-level and course-level rationales that explicitly connect mathematical ideas across lessons and modules. For example, the rationale for module 3 states, “It begins with foundational knowledge of comparing additive and multiplicative relationships, which is essential for representing ratios and fractions. Students then apply this understanding to representing percents. In the next module, students will learn to solve ratios and rate problems.”

The lessons include “Turn and Talk” routines designed to connect to prior learning by explicitly connecting big ideas, patterns, and relationships between mathematical concepts. For example, lesson 9.2 asks, “How did you use what you already learned about the order of operations to generate equivalent numerical expressions?” The materials explicitly connect prior learning about equivalent expressions and order of operations from module 8 to the development and application of area formulas for parallelograms in module 9, demonstrating coherence across units and mathematical concepts.

Additionally, the “Turn and Talk” routine in task 3 of lesson 12.4 prompts students, “Use what you know about place value to explain how reading the stem-and-leaf key can help you avoid mistakes when finding the median and mean.” The discussion allows students to apply previous knowledge to a new context, building connections between 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 Teacher’s Guide for each module includes a “What Will Students Learn in This Module?” section that connects the current content to prior learning and future connections. For example, in module 4, students look at proportional and nonproportional relationships. Previously, students “represented relationships, points, and lines on the coordinate plane.” In future modules, students will “model and solve multistep problems involving proportions, including the use of function notation in their relationships.”

Additionally, each lesson explicitly connects the content and language learned in previous grade levels to the current lesson and how it extends to future learning. For example, lesson 8.2 connects prior mathematical knowledge and academic language related to numerical expressions and the order of operations to the current learning on generating equivalent expressions. Guidance also identifies future learning connections, including solving equations, simplifying expressions, and analyzing linear relationships, demonstrating coherent progression of content and language across grade levels while preparing students for future mathematics 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..

Each lesson begins with a “Spark Your Learning” activity designed to connect students’ prior knowledge of concepts and procedures to the new mathematical skills. Educator guidance states, “Resist the temptation to teach the content needed to solve the Spark problem; instead, let students use their prior knowledge.” For example, in module 9, lesson 2 begins with students investigating a real-world problem to determine if a parallelogram-shaped table is the same size as a rectangular table. Students must connect prior knowledge of the area of rectangles to explore the area of the parallelogram before being introduced to the formula in the lesson.

The materials also include a “Prerequisite Check” for each module to connect prior concepts and procedures to new learning. For example, module 2 activates prior knowledge of fraction and decimal operations, connecting them to operations with integers, rational numbers, and mixed fractions. The “Data-Driven Support” table helps educators identify intervention activities to help prepare students for the upcoming lessons.

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

Each lesson includes a “Train Your Memory” section on the independent practice handout that offers spaced retrieval opportunities for previously learned skills and concepts across lessons and units. For example, in module 10, lesson 2, the practice includes three review questions from modules 2, 7, and 8. Students review division skills with mixed numbers, as well as the concepts of equivalent expressions and rate of change.

Additionally, each module begins with a “Prerequisite Check” on previously learned skills and concepts, providing “insight into students’ mastery of prerequisite concepts that are required to succeed with the new learning in the module.” For example, module 9 provides opportunities for spaced retrieval practice focused on classifying triangles by angle and determining the area of rectangles to prepare students for representing and solving area and volume problems in the upcoming lessons.

The materials also include a Module Project that offers opportunities for students to apply previously learned skills and concepts. The materials state, “Each Module Project gives students essential and extended opportunities to practice engaging with content within the modules, and to do so at a Depth of Knowledge level 4.”

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

The “Train Your Memory” section of the independent practice provides interleaved practice by requiring students to apply previously learned skills and concepts. For example, in module 8, lesson 2, students revisit prior lesson content on calculating percents (lesson 6.1), qualitative rate problems (lesson 4.1), and the application of absolute value (lesson 1.3) while simultaneously applying new learning involving the distributive property and equivalent numerical expressions. This structure promotes flexible problem-solving and reinforces previously learned mathematical relationships as students learn new content.

The materials include a variety of practice- and application-based tasks that require students to use previously learned skills and concepts within the same problem set, such as multiple representations, calculations, mathematical reasoning, and real-world interpretation. For example, the “Practice on Your Own” provides a mixed set of problems on the lesson concepts, giving students a choice in how to solve. The questions align with the lesson tasks in random order, which promotes flexible thinking as students learn to switch between different types of problems and strategies.

Additionally, each module provides a Module Review that provides interleaved practice opportunities with previously learned skills and concepts across lessons. The review is designed to allow students to practice and review the TEKS taught in the module and include a variety of questions that promote flexible thinking to solve different types of problems.

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

Lesson tasks regularly require students to interpret, analyze, and evaluate representations for mathematical concepts and situations. These tasks enable students to select appropriate methods for finding solutions in unfamiliar contexts and to develop flexible thinking skills. For example, in lesson 1.4, task 2 requires students to locate rational numbers on a number line and interpret their meaning. Furthermore, students evaluate numbers by comparing fractions using inequalities and, lastly, order rational numbers to analyze their values and placement from least to greatest.

Additionally, in lesson 2.2, task 3, students use two-color counters to interpret integer division, analyze what the model shows, write a matching division equation, and generalize the sign rule for quotients. The task requires students to interpret and analyze a representation rather than only computing.

The materials also provide low-floor, high-ceiling “Spark Your Learning” activities to help students interpret, analyze, and evaluate representations, enhancing their critical thinking skills and enabling them to transfer their learning to new contexts. For example, in lesson 1.2, students must interpret thermometer readings, evaluate specific temperatures within a given range, and determine whether they can draw additional temperatures on the thermometer to represent temperatures higher and lower than those shown.

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

Throughout the materials, students create mathematical models to represent and solve real-world situations by constructing visual representations, equations, tables, and diagrams that model mathematical relationships. For example, in module 3, lesson 3, students create a strip diagram and shade a grid to represent 75 percent in different ways. Questions ask, “How can you use a concrete model to represent this percent based on the fraction?” The task requires students to generate and explain their own mathematical representation to aid in the solving process.

Additionally, the “Practice on Your Own” assessments provide students with opportunities to communicate their mathematical thinking through tangible or physical representations, figures, or drawings. For example, lesson 9.2 states, “Model and explain how a parallelogram can be decomposed and rearranged to find its area.”

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

Each lesson provides opportunities to apply conceptual understanding to new problem situations and contexts through the lesson tasks and structured language routines such as “Turn and Talk.” For example, in lesson 6.2, task 2, students estimate, draw a diagram, and calculate 35 percent of 120. The materials ask, “How does the calculation using an equation match your model?” Through discussions, students develop a conceptual understanding of how the model supports the calculations.

The materials also include “Practice on Your Own” assessments that provide students with opportunities to apply their conceptual understanding to new contexts. For example, in lesson 10.6, students must apply their conceptual understanding of linear equations to a new context by creating their own real-world story that matches the equation 2x = 56. They must then justify why the story fits the equation by explaining the meaning of each number and operation, algebraically transferring their mathematical understanding to a new context. The problem moves beyond procedural fluency because students connect symbolic notation to a novel real-world situation and explain the underlying relationships.

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

Throughout the materials, students engage in repeated practice that builds automaticity and fluency with grade-level mathematical concepts before applying these skills to more complex tasks. The Implementation Guide lists independent practice resources, such as “Practice Plus,” “Practice on Your Own,” and Waggle, and explains that independent practice reinforces skills and helps develop automaticity.

The “Practice on Your Own” section is designed to build the automaticity and fluency necessary to complete grade-level tasks. For example, in module 2, lesson 6, the problems involve dividing fractions in different formats and allow grade-level tasks to be performed through repetition and by building new division problems by upscaling the next problem’s format. Repetitive tasks strengthen automaticity and support fluency by applying a small new idea to each prior problem.  

Additionally, the materials provide “Fluency Practice” on a variety of concepts within the “Differentiate and Practice” portion of the lesson. Educator guidance states, “Give students Fluency Practice as it is available to help promote automaticity.” Grade 6 “Fluency Practice” includes skills such as comparing and ordering decimals and converting fractions and decimals to percents.

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 lesson tasks provide opportunities for students to apply flexible, efficient, and accurate mathematical procedures. For example, in lesson 4.3, task 2, students explore different ways to set up a proportion. Questions prompt them to expand their thinking: “Are there any other ways to write a proportion than the one shown? If so, provide an example.” The materials demonstrate flexibility in setting up proportions while maintaining accuracy.

Additionally, in module 8, lesson 5, students generate equivalent expressions by distributing and combining like terms. Tasks begin with algebraic tiles and progress to algebraic representations, demonstrating flexibility. The “Turn and Talk” asks students, “How do reordering and regrouping help you add like terms more efficiently?” The lesson tasks reinforce accuracy while encouraging the flexible selection of strategies to solve problems efficiently.

The materials also provide continued opportunities to apply the efficient, flexible, and accurate procedures independently after the lesson through practice, such as “Practice on Your Own,” “Practice Plus,” and Waggle. For example, in lesson 8.3, students build factoring efficiency by using factor trees and exponent notation. Students use flexible procedures to represent prime factorizations in multiple equivalent forms, and practice accurate procedures through repeated factorization, classification, and fluency practice.

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 problem-solving model used throughout the materials provides students with opportunities to evaluate their processes for efficiency, flexibility, and accuracy. For example, in module 5, lesson 3, students use the model to graphically represent a unit rate for a real-world problem. Prompts such as “Explain why your answer makes sense using the graph” and “How can you use the unit rate to explain how you know your answer is reasonable?” provide opportunities to evaluate solutions for accuracy. Demonstrating flexibility within concepts, the “Turn and Talk” then asks, “What is another point on your graph? How does it show the same unit rate?”

Additionally, in lesson 10.6, task 5, students analyze, plan, and solve a real-world problem by writing and solving an inequality. The materials include specific questions that help students evaluate the accuracy of their solutions by explaining why their solutions make sense. Then, the materials ask, “How effective was your strategy to solve this problem? What might you do differently?” These questions provide students with an opportunity to reflect on the efficiency and flexibility of their approach.

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

Embedded educator guidance provides instructional prompts, questioning strategies, and scaffolds to help students refine solution methods and develop increasingly efficient mathematical approaches. For example, in lesson 4.2, students create two equivalent ratios to compare two delivery teams. The “Turn and Talk” asks, “How is comparing ratios using equivalent ratios in fraction form similar to or different from using a table or double number line?” to guide students in understanding that multiplying to find a common denominator is more efficient than drawing models.

Additionally, in lesson 12.5, the Teacher’s Guide provides embedded instructional supports that help educators guide students from constructing and interpreting box plots toward more efficient analysis of data distributions. Educator questioning, discussion prompts, and facilitation notes encourage students to compare representations, recognize meaningful patterns, and select efficient strategies for interpreting data rather than rely on isolated calculations.

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

The “Teacher Background” in each module explicitly states how the materials balance conceptual understanding with procedural fluency required by the TEKS. For example, in module 1, guidance states, “Conceptually, students will understand the relative size and position of rational numbers. They will learn why numbers can be compared, ordered, and represented on a number line to make sense of quantities in math and real-world situations. Then, students will use procedural understanding to locate, compare, and order rational numbers.”

Additionally, in module 8, the “Teacher Background” explicitly describes how the conceptual emphasis develops students’ understanding of representing, interpreting, and analyzing data distributions and selecting appropriate measures of center and spread. The procedural emphasis explains how students construct and interpret dot plots, stem-and-leaf plots, histograms, box plots, and numerical summaries to solve problems and justify conclusions.

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.

The questions and tasks incorporate concrete models and representations alongside standard algorithms to help students build connections. For example, in lesson 2.2, task 3, the materials guide students in modeling 24 divided by 6 using two-color counters. Students then move to write a division equation to represent the model and state “a general rule to predict the sign of the quotient when dividing integers.” Later, in lesson 6.2, students use strip diagrams to represent percent relationships before solving symbolically by connecting pictorial and abstract representations. The progression from concrete to abstract helps students build conceptual understanding.

Additionally, the “Teacher Background” section emphasizes the importance of using concrete models and manipulatives, pictorial representations, and abstract representations to meet the standards. For example, module 8 states, “Students will use concrete, pictorial, and algebraic representations to determine whether two expressions are equivalent. This helps them understand the meaning of equivalence, build flexible problem-solving strategies, and connect visual and symbolic mathematics.” The materials ensure that students engage in meaningful mathematics, not just memorizing rules and procedures, by actively constructing their own understanding through various 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 tasks include support to help students create and connect concrete models to abstract concepts. In lesson 2.1, task 1, students create a model using two-color counters to represent the addition of integers. The materials include questions such as “What counters are left over and what value do they represent?” to require students to explain how the concrete model relates to the abstract concept. Students also define additive inverses and zero pairs while justifying how the concrete model corresponds to the abstract computation.

The materials also support students in creating, defining, connecting, and explaining representational models to abstract concepts. For example, in module 12, lesson 2, students create dot plots and stem-and-leaf plots to represent data. Students use the models to answer abstract questions about the center, clusters, and gaps and how they relate to the data in context. The materials ask students to explain how a dot plot and a stem-and-leaf plot are similar and different and support their statements with evidence from plots in the lesson.

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

The materials intentionally develop students’ academic mathematical language by integrating multiple visual representations, hands-on manipulatives, and structured language routines. In lesson 7.1, students analyze tables and graphs to identify independent and dependent quantities while using foam two-color counters to support their conceptual understanding. The lesson embeds the “Words to Learn” vocabulary routine to introduce and reinforce mathematical terminology and incorporates multiple “Mathematical Language Routines,” including “Three Reads,” “Discussion Supports,” “Collect and Display,” “Compare and Connect,” and “Critique, Correct, and Clarify.” The routines require students to engage in collaborative discussions, explain their reasoning using precise mathematical vocabulary, and connect visual representations with mathematical language throughout the lesson. 

Additionally, in module 8, lesson 5, students use an area model to explain the distributive property and connect visual partitions to precise mathematical language. Guidance directs educators to provide a visual glossary with labeled partitions and arrows for distribute, expand, and equivalent and then use “Turn and Talk” to have students explain how the area model shows the distributive property. If students need additional support, educators encourage them to trace parts of the model while naming the terms aloud. The tasks develop academic mathematical language through visuals, explicit connections between vocabulary and diagrams, and structured oral discourse.

The materials also provide educator guidance through the Implementation Guide, which explains how educators can support students’ development of academic mathematical language through intentional instructional routines and language supports. For example, the “Language Growth for All Learners” section describes instructional strategies that help educators build mathematical vocabulary, scaffold academic conversations, and provide multiple opportunities for students to explain and justify their mathematical thinking using precise mathematical language during instruction.

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 include embedded educator guidance to support the implementation and development of academic vocabulary through the language routines. For example, in lesson 12.1, the “Turn and Talk” routine includes guidance to extend student conversations by “having students write a set of statistical questions and a set of questions that are not statistical questions to ensure they are making the appropriate connections and distinctions.”

Additionally, in module 8, lesson 5, educator guidance scaffolds students’ vocabulary use as they reason about equivalent expressions using an area model. Guidance suggests that educators provide a visual glossary with labeled partitions and arrows for the terms distribute, expand, and equivalent so students can connect vocabulary to the diagram. Students then discuss how the area model shows the distributive property, and additional support directs students to trace parts of the model while naming the terms aloud. Instead of having educators teach vocabulary with isolated definitions, the embedded guidance helps students develop and use vocabulary in the immediate mathematical context of interpreting and explaining equivalent expressions.

The materials also include a Language Development Resource Guide that provides scaffolding and supports students’ development of academic mathematical language. The guide provides strategies for teaching academic vocabulary and for using the “Words to Learn” routine, high-utility words, and vocabulary cards.

Evaluation for 5.4c
Materials include embedded teacher guidance to support the application of appropriate mathematical language to include vocabulary, syntax, and discourse to include guidance to support mathematical conversations that provide opportunities for students to hear, refine, and use math language with peers and develop their math language toolkit over time as well as guide teachers to support student responses using exemplar responses to questions and tasks.

The materials include educator guidance to support students’ application of mathematical language throughout instruction. Each lesson incorporates multiple “Mathematical Language Routines” to structure mathematical discourse. Guidance provides scripted questions, anticipated student responses, and discussion prompts that encourage students to explain their reasoning using precise mathematical vocabulary. Students listen to classmates’ explanations, compare mathematical representations, refine their thinking through peer discussions, and communicate mathematical ideas using appropriate vocabulary and syntax. The materials also provide educator guidance for addressing misconceptions and extending student responses, helping students strengthen their mathematical language over time.

The materials embed language supports in the Teacher’s Guide for each lesson. For example, module 5, lesson 1 includes the “Words to Learn” routine to introduce new vocabulary. The lesson also includes guidance suggesting that educators “support students with writing probabilities by providing sentence frames” and “provide frequent opportunities for them to practice pronouncing new mathematical terms.” The embedded supports provide educators with tools to develop students’ vocabulary through oral and written discourse.

Additionally, each module incorporates a “Stronger and Clearer Each Time” language routine that allows students to use, hear, and refine mathematical language. The routine involves sharing thoughts with a partner, asking thoughtful questions, and revising responses. The materials include embedded educator guidance to support the routine, such as this from lesson 10.1: “Remind students to ask questions of each other that focus on describing their thinking, especially related to the formula for area, the equation they used, and why 7 meters couldn’t be the length, and to then use insights from the discussion to refine their answers or reasoning.” The materials also include exemplar responses to all guiding questions.

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

Lesson materials integrate the TEKS process standards by embedding problem-solving, mathematical communication, reasoning, representation, and tool selection throughout instruction and student tasks. For example, lesson 5.1 immediately implements the process standards by engaging students in the “Three Reads” routine, requiring them to analyze a real-world ratio problem; represent their thinking with tables, double number lines, equations, and mathematical language; justify proportional reasoning; and communicate solutions during structured discussions and “Turn and Talk” activities. Throughout the lesson, students explain their reasoning, defend their solutions, evaluate representations, and use multiple mathematical models to solve authentic ratio and rate problems.

Additionally, each “Practice on Your Own” assessment integrates the process standards by identifying questions labeled “PS.” For example, in lesson 7.1, questions require students to “analyze relationships” represented in graphs and tables to determine the independent and dependent variables and to write an equation to represent the situation.

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

The “Mathematical Connections” page in the Teacher’s Guide provides a module-mapping table that explicitly identifies connections between mathematical topics and mathematical processes (“MT to MP”) across the grade 6 course. For modules 4–6 and 9, the materials state that students “apply a problem-solving model and apply mathematics to problems in everyday life” as they solve ratio, rate, percent, area, and volume problems. For module 10, students “apply mathematics to problems arising in everyday life; communicate mathematical ideas using multiple representations, including symbols; explain and justify mathematical ideas and arguments; and use a problem-solving model.” For module 12, students “explain and justify mathematical ideas and arguments when displaying and analyzing data.” The materials explicitly map recurring mathematical-process practices to specific modules and content domains across the grade 6 sequence.

Additionally, the Implementation Guide provides a “Correlation by Standard” table that directly identifies where each process standard is incorporated throughout the course. For example, lessons 2.5, 7.1, 8.1, 9.1, 12.4, and 12.7 incorporate process standard 6.1F.

The materials also include course-level “Process Standards Anchor Charts” guidance that describes how students use the process standards throughout instruction: “To support students’ understanding of the TEKS process standards, have them use the anchor charts in the front of the Student Edition as they work through the lessons.” The student-facing chart then operationalizes the standards through recurring prompts, including “What situation does the problem describe?” “What plan or strategy will you use?” “How do you know the solution answers the question?” and “How reasonable is the solution?”

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

The Teacher’s Guide includes a dedicated “Module Planning” section that describes how the grade 6 TEKS process standards are incorporated throughout each module and connected across the unit. For example, in module 5, the planning narrative explains that students develop the problem-solving model (TEKS process standard 6.1B) throughout the module and apply all steps together in the culminating lesson. It also identifies where students use multiple representations to communicate mathematical ideas (TEKS process standard 6.1D) and precise mathematical language (TEKS process standard 6.1G) within specific lessons. In addition, the module explains the instructional progression from representing ratios and rates using scale factors to proportional relationships, tables, graphs, and percent applications, demonstrating how the process standards support learning throughout the unit rather than in isolated lessons.

The planning pages for module 9 explain how students learn the steps of the problem-solving model (TEKS process standard 1.B) and then use all the steps together in lessons 2 and 3 to solve a problem related to finding the area of kites shaped like parallelograms and finding the areas of the triangular bases of a triangular prism, respectively. The lessons incorporate other process standards throughout the module content. For example, lesson 1 has students select tools (TEKS process standard 1.C) to demonstrate their understanding of triangle properties and analyze relationships (TEKS process standard 1.F) between the angles and sides of triangles. Lesson 3 has students apply areas of triangles to problems arising in society (TEKS process standard 1.A). Lesson 5 asks students to use precise language (TEKS process standard 1.G) when solving problems with rectangular prisms.

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

At the beginning of each lesson, the Teacher’s Guide provides a comprehensive lesson overview that identifies the mathematical content standards, learning objective, language objective, prior learning, future connections, and the specific TEKS process standards incorporated into the lesson. For example, in module 3, lesson 1, the overview explicitly identifies TEKS process standards 6.1D and 6.1E, explaining that students will communicate mathematical ideas using multiple representations and create and use representations to organize, record, and communicate mathematical ideas while comparing additive and multiplicative relationships. This lesson-level planning information provides educators with a clear overview of the process standards that are intentionally embedded in instruction before the lesson begins.

Additionally, throughout each lesson, a “PS” appears next to specific items where the process standards are applicable. For example, lesson 12.4, task 2, requires students to select tools, such as a calculator or statistical software, to calculate measures of center for a dot plot, as required by 6.1.C.

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

Each lesson opens with a “Spark Your Learning” activity that presents an authentic scenario before formal instruction and asks students to identify multiple ways to represent and solve the problem. For example, in lesson 4.1, students engage in productive struggle through the task by making a prediction and comparing two rates before learning a formal procedure. Rather than calculating exact unit rates, students determine which volunteer is working faster, explain their reasoning, and justify which person will fill more recycling bins first. The task concludes with a “Turn and Talk” discussion where students share and compare strategies, encouraging perseverance, mathematical reasoning, and reflection before formal instruction.

The materials also incorporate a “Problem-Solving Model” throughout each module, providing opportunities for students to think mathematically, persevere, and make sense of mathematics in real-world contexts. For example, in lesson 11.3, students use the problem-solving model to determine the distance between two post-office drop boxes using the coordinate plane. Students analyze the problem, create a plan, solve the problem, and justify their work. To help students persevere through the solving process, educator guidance includes prompts such as “ASK: How could you show two parts on your coordinate plane to find the distance?” The “Turn and Talk” allows students to make sense of the mathematics by adjusting the problem, asking, “How would the distance change if you needed to find the distance between (−0.2, 1) and (1.8, 1)?”

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 support students in understanding, explaining, and justifying that there can be multiple ways to solve mathematical problems. For example, in module 1, lesson 2, students first use a number line to compare and order scores and explain their reasoning. Then they must produce a different representation in the “Show Another Way” routine: “Show how you can use a diagram other than a number line to communicate your reasoning when ordering the scores.” The educator guidance explains the instructional purpose: “Using a representation other than a number line allows students to show another way to support a productive struggle.” This approach directly supports students in understanding and explaining that the same problem can be represented and reasoned through in more than one way.

Additionally, in module 6, lesson 3, students use base 10 blocks and strip diagrams to determine the total number of plants in a garden, given a percentage and the number of pepper plants. The “Turn and Talk” supports students in explaining and justifying multiple approaches by asking, “Which model made it easier to solve the problem? Why?”

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 lesson includes a series of tasks that allow students to make sense of mathematics. Students complete tasks that provide opportunities to do, write about, and discuss math with peers and educators. For example, in lesson 3.1, students complete five tasks to compare additive and multiplicative relationships using tables and graphs. All five tasks provide real-world problems to help students make sense of the mathematics. Students are encouraged to discuss the math through “Turn and Talk” routines. A sample prompt reads, “Look at both lines on the graphs. How do they show the difference in how Devin and Kwan’s page counts change each day? Listen to a classmate’s answer, then respond. Do you agree with your classmate’s answer?” The materials also require students to provide written explanations using precise mathematical language.

The materials provide additional opportunities for students to communicate mathematical thinking through writing and discussion. For example, in module 11, lesson 3, task 1, students explain their reasoning in writing, justify conclusions with mathematical evidence, and compare solution strategies during whole-class discussion. Educators guide students with purposeful questions that encourage reflection, mathematical communication, and revision of thinking before independent practice.

The materials also provide prompts and guidance for educators to help students share and reflect on their problem-solving methods through justifications, explanations, and arguments. For example, in lesson 10.6, educator guidance states, “Have students write down their reasoning for how they determined the inequality that models the situation and any questions about it. Then, in pairs, have students share their thinking.” Students ask one another questions about the operations and the inequality symbol used and then “use insights from the discussion to refine their answers or reasoning.” These prompts require students to engage in grade-level mathematics, articulate their reasoning, discuss their reasoning with peers, and revise their recorded response.

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 grade 6 materials support educators in guiding students to share and reflect on their problem-solving approaches through structured mathematical discourse. For example, in module 2, lesson 4, task 2, students solve a rich mathematical task and explain how they selected their solution strategy using mathematical evidence. Educators facilitate partner and whole-class discussions by prompting students to compare approaches, justify why their strategy is effective, and evaluate whether another method could be more efficient. After listening to peers, students reflect on their own reasoning and then complete independent practice, reinforcing explanations, arguments, and justifications.

Additionally, in lesson 6.2, educator guidance suggests a variety of language routines and direct questioning prompts to help students share and reflect. In task 1, the “Turn and Talk” routine asks students, “How did your prediction help you choose a technique to find 40% of 60?” The guidance prompts educators to have students “describe how they have solved percent problems, such as using counters grouped into tenths or using a fraction of the whole.” In task 3, students provide an argument to counter the claim that their answer is unreasonable. Educator guidance states, “Have students revisit their justification to think about the terms they used to justify their solution.” In task 5, the materials prompt students to justify their technique and explain why it is efficient for solving the problem, allowing students to reflect on their process.

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

The Teacher’s Guide provides explicit guidance for educators to monitor student understanding throughout the lesson using the “Learning Goal” routine, “Quick Checks,” and real-time student responses. Rather than simply confirm answers, educators circulate, observe student strategies, identify misconceptions, and use purposeful questions to help students explain and justify their reasoning. The guidance prompts educators to ask students how they know their solution is correct, compare classmates’ approaches, and defend their conclusions with mathematical evidence. Educators are encouraged to build classroom discussions from student thinking, fostering meaningful mathematical discourse and deeper conceptual understanding. This ongoing cycle supports responsive instruction by encouraging educators to adjust support during instruction based on demonstrated understanding.

The materials explicitly direct educators to monitor student responses and provide targeted explanatory feedback throughout each lesson. For example, module 4, lesson 1 anticipates that students may incorrectly compare 3:20 and 5:40 by reasoning that “5 is bigger, so Alex is faster,” without first matching the times. The scripted feedback prompts educators to ask, “What happens to the comparison when you align the time at 40 minutes for both students?” and “How many equal time chunks would it take to reach 12 bins for each student?” This directly supports educators in responding to an anticipated misconception by providing explanatory, concept-focused feedback rather than simply telling students the correct answer.

Additionally, the Teacher’s Guide provides prompts and guidance throughout each lesson to address common errors. For example, in lesson 3.3, students create equivalent fractions to determine the percentage of the book that Diego has read. The materials highlight a common error: changing only the numerator when forming equivalent fractions. Guidance suggests reminding students that “the scale factor must be applied to both parts,” as well as using fraction tiles to help students make sense of the math.