HMH Into Math Texas, Grade 7

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 align each module to the TEKS and ELPS and identify the concepts taught throughout the instructional year. Additional program materials further support the TEKS and ELPS alignments. These include the “Correlations by Lesson” documents, which break down the concepts covered in each module. Educators can access an outline of the TEKS, ELPS, and concepts covered in the course by selecting the ”Discover” tab under the program dropdown of the scope and sequence. This outline supports 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, ELPS, and course concepts.

The materials show educators how to extend 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 and explains the conceptual progression across modules. For example, concepts progress from proportional reasoning to percent, probability, and proportional problem-solving; from geometry concepts to circumference and area formulas; and from equations to inequalities.

The materials help educators understand how mathematical concepts connect throughout the course. This support helps educators internalize concepts and make connections. For example, “Algebraic and proportional reasoning developed in modules 2, 3, and 4 is furthered in module 7, where students represent linear relationships.”

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

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

The materials 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 flow charts, and lesson sequencing explanations also support educator preparation.

Additionally, the “Step Through a Module” section of the Implementation Guide provides guidance for internalizing module and lesson components. The “Teacher Background” sections include mathematical rationale, examples, and summaries and explain the importance 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 Professional Learning and Coaching Guide 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 support educator planning and help instructional leaders monitor instruction.

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 “What should I understand about the math in this module?” section in the Teacher’s Guide provides a comprehensive overview and background knowledge for each TEKS covered within the module. For example, this section in module 4 states, “Understanding similarity allows students to use ratios to compare and determine unknown side lengths within and between similar shapes.”

The materials include academic vocabulary support within lesson 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 reinforce learning. For example, module 3 suggests using a takeout menu to calculate the cost of a family meal, the tax, and the total cost to reinforce solving problems with percents.

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 alignments. For example, module 3, lesson 1 aligns with TEKS 7.4.D. In this lesson, students “solve problems involving percent increase and decrease using ratios and percents” through a series of four tasks.

Each lesson plan includes tasks, assessments, and practice sets aligned with the lesson objectives, the TEKS, and the ELPS. The materials include many instructional assessments and tools, including “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 3, lesson 2 requires students to use two-color foam counters during the “Spark Your Learning” activity to determine which team packs bags of canned goods at a faster rate.

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 component of the lesson also includes a suggested timing. For example, module 10, lesson 5, task 2 should take approximately 18 minutes.

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

The “Differentiation and Practice,” “Homework,” “Extension,” “Collaborative Groups,” and “Teacher-Led Small-Group Activities” sections include guidance on the effective use of lesson materials for extended practice. These 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 completing the “Almost There,” “On Track,” and “Ready for More” activities. 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. “HMH Waggle supports instruction with auto-assigned, skill-based practice tailored by its AI engine.” The guidance report allows educators to use 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. These formative 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 and 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, the module 4 test includes multiple-choice and open-ended response questions.

The materials use “Benchmark Assessments” and other diagnostic assessments to “determine progress at strategic points in the school year.” The three “Benchmark Assessments” contain a variety of question formats, such as drag-and-drop, graph, multi-select, and multiple-choice, and help gauge mastery of the skills taught during the year.

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

The Implementation Guide provides a clear explanation of the intended 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, plan instruction, and measure student mastery. For example, the “Quick Check” assessment “provides educators with 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 each assessment measures, why it is important, and how to administer the assessment. 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.” 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?” tasks align to the lesson TEKS and daily learning objectives. For example, the “Practice on Your Own” answer key identifies the TEKS and task alignments for each question.

The answer keys for the Module Test and other summative assessments indicate the TEKS alignment and lesson source for each question. For example, module 7, question 2 requires students to write a linear equation based on a verbal description, which aligns with TEKS 7.7.A and lesson 2, “Graph Linear Equations from Situations.”

Diagnostic assessments, such as the “Benchmark Assessments,” include answer keys with a TEKS correlation table. This table aligns each test item to the TEKS and source 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 alignment and Depth of Knowledge (DOK) level for each item. For example, the module 7 test includes multiple-choice and free-response questions that vary in complexity from DOK 1 to 2.

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

The “Practice on Your Own” tasks are formative assessments that include scoring information, sample answers, and educator guidance for evaluating student responses. The materials also reference “Assessment Reports on Ed,” which supports 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 3, the table indicates that students who miss item 9 can benefit from a reteach activity on solving multistep rate and ratio problems.

Additionally, Module Projects include scoring rubrics and exemplar responses for interpreting student performance. Guidance also suggests, “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. “Almost There,” “On Track,” and “Ready for More” are small-group educator-led activities that address student learning needs and misconceptions. In addition, multiple levels of independent practice activities meet the needs of students who are not 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. HMH Ed™ provides recommended reteaching resources based on various skills. Waggle’s skill-driven AI engine provides adaptive skill development and targeted support to 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. Educators can use the printable “Whole Class Proficiency and Growth Tracker” and digital reports 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 materials also provide a printable 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. This routine allows students to track their own growth and educators to track student progress throughout the course. For example, the learning goal for module 9, lesson 5 is “I can find and use the volumes of rectangular and triangular prisms and pyramids to solve problems.” 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” 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 9, lesson 5, the activity provides diagrams to help students understand how to compare the volumes of 3D figures by making an educated guess and then doing the calculations. The educator guidance states, “Elicit from students the understanding that you can’t estimate volume by looking at the length of just one edge.”

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 27 skills, including “Order of Operations,” “Solve and Graph Inequalities,” and “Graph Ordered Pairs” 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 “Words to Learn (WTL)” routine and WTL vocabulary cards provide pre-teaching supports that guide educators to introduce key mathematical terms and unfamiliar vocabulary. The supports incorporate strategies such as “Say it” and “Define it” before students engage with lesson content. The guidance for the “Words to Learn (WTL)” routine states, “This routine provides each student with an opportunity to practice and internalize each new term.”

The “Three Reads,” “Turn and Talk,” and “Collect and Display” activities include embedded vocabulary and language supports to help students understand unfamiliar academic language and references in text. For example, in module 8, lesson 2, 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.”

The ELPS Teaching Strategies and other embedded educator supports provide activities and prompts to help students understand unfamiliar references and contextual language in mathematical tasks. For example, the educator support in module 10, lesson 6 states, “Explain that figurative language is often used to make comparisons between abstract concepts and real-world situations. Help students see that the three angles of a triangle can be cut out and placed side-by-side to form a straight line.”

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 based on 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 10 lesson 1 activity, students create two-step equations, develop real-world situations, and modify mathematical relationships to deepen their understanding of grade-level concepts.

Additionally, each module provides leveled practice, including challenge activities for students who have demonstrated proficiency in grade-level content. For example, in the module 1 challenge activity, “Operate on Integers to Solve Problems,” students apply their understanding of integer operations to the melting points of various elements.

The materials also include a module project that engages students in DOK Level 4 tasks “that apply and extend the mathematics found within the modules.” For example, in the “Analyzing Hurricane Frequency” project, students analyze hurricane data, including the measures of center and spread, to determine whether hurricanes have become more frequent in recent years.

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 Teacher’s Guide includes a series of explicit “Ask” prompts to support educators in modeling and explaining mathematical concepts. For example, in module 7, lesson 2, task 1, students create a table, a graph, and an equation to model a linear relationship. The materials state, “ASK” What is the problem about?” and “ASK: What numbers are important? Why are they important?” and offer exemplary responses to guide instruction.

In addition, the materials provide mathematical modeling supports and mathematical language routines. For example, in module 8, lesson 2, task 4, guidance states, “Use the Discussion Supports routine to help students discuss their thinking. Have students think aloud about the relationship between the volumes of prisms and pyramids while solving Part E.”

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 such as “ELPS Support” and common-error correction address the needs of all learners.


The Teacher’s Guide provides educator guidance and recommendations through Universal Design for Learning (UDL) strategies. These strategies promote effective lesson delivery through multiple instructional approaches, including visual, verbal, collaborative, and hands-on learning opportunities.  For example, in module 1, lesson 3, task 3, the UDL Support states, “Provide a partially labeled number line with 0 and -1 marked; students complete ticks every 0.1 to standardize intervals.”

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

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 at varying language proficiency levels. For example, module 1, lesson 6 covers adding and subtracting fractions with unequal denominators. The guidance for pre-production and beginner-level students states, “Provide students with a list or cards showing key phrases before discussion begins,” including terms such as positive number, negative number, and equal denominator. For intermediate students, the guidance states, “Pair students and have them practice explaining their strategy” so they can identify important phrases on their own.

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 5 includes an ELPS teaching strategy that states, “To support students’ pre-reading skills, have them predict what the problem will ask them to do. These strategies help to build reading fluency.”

Additionally, at the beginning of each module, a “Mathematical Language & Emergent Bilingual” page gives educators tools to plan for language development in the upcoming lessons. Guidance includes vocabulary support and mathematical language routines and highlights one of Dr. Kate Kinsella’s seven key routines that “support teachers and students with best practices for language development, such as ‘Building Fluency,’ ‘Partnering,’ ‘Assigning Discussion Tasks,’ ‘Eliciting Responses,’ ‘Using Response Scaffolds,’ ‘Words to Learn,’ and ‘Vocabulary Quick Teach.’”

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. This section helps educators effectively use the program with emergent bilingual students in bilingual and ESL instructional settings. Guidance states, “You’ll find that Into Math® Texas provides you with 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 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 (WTL)” 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. For example, the guidance in module 4, lesson 2, task 1 suggests using the routine for the academic words dimension, scale, drawing, and scale.

The materials also include embedded emergent bilingual and ELPS teaching strategies to increase comprehension and build background knowledge. For example, in module 1, lesson 6, the guidance states, “Allowing students to compare and make connections among different representations will help build their understanding. Invite students who used different models to share them with the class. Guide students to see similarities between the representations and how each might be useful in different situations.”

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 7, lesson 1, task 1, the guidance states, “Pair beginning students with same-language peers with more English experience. Encourage them to talk through their ideas in their home language before working together to write a response in English.”

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 with the TEKS through representations, mathematical reasoning, and explanations in grade-level tasks. Students apply concepts, proportional relationships, percent reasoning, linear relationships, and geometric formulas. For example, the lesson 2.3 “Quick Check” requires students to apply proportional reasoning and determine constants of proportionality using visual models, tables, verbal descriptions, ordered pairs, and equations. Students justify their reasoning and connect multiple mathematical representations, as required by TEKS 7.4.B.

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 DOK Level 4 task 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 9, lesson 2, students calculate the area of composite figures. The lesson begins with scaffolds to model how to break a shape into smaller components to find the total area. The tasks progress to more challenging shapes and require subtracting a cutout. The final task encourages a variety of approaches as students decompose the shape independently.

Each task uses guiding questions that increase in complexity and rigor, leading to grade-level proficiency. The tasks provide access points for students to build on prior knowledge and deepen their mathematical understanding. In lesson 7.1, task 1, students describe linear relationships. The task begins with sentence stems to describe the relationship, such as “The number of kits increases by ____ as the number of hours increases by ____.” The task then asks, “How could you use the information in the table to find the rate of change?”

Additionally, Module Tests progress from procedural fluency to application and mathematical reasoning through a variety of question types. For example, the module 4 test progressively builds from proportional reasoning concepts to geometric problem-solving and application, increasing complexity while supporting grade-level proficiency in the 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 “begins with foundational knowledge of solving percent change problems. Students then apply this understanding to solve multistep rate and ratio problems. With these skills in place, they are equipped to solve financial literacy problems meaningfully.”

The lessons include “Turn and Talk” routines designed to explicitly connect to prior learning, big ideas, patterns, and relationships between mathematical concepts. For example, lesson 4.1 says, “Recall that a proportion is an equation that states that two ratios are equivalent. Why is it important to match side lengths accurately when writing a proportion?” The materials explicitly connect prior learning about proportions and equivalent ratios to new learning about similarity. Students use previously learned proportional reasoning to compare within-shape and between-shape ratios of rectangles to determine whether shapes are similar. Successful completion of these comparisons demonstrates coherence across units.

Additionally, the “Turn and Talk” routine in lesson 6.1, task 3 states, “Using what you know about adding and subtracting fractions, what are some important steps to remember when subtracting fractions with unequal denominators?” Students make connections between fraction operations with like denominators and unlike denominators.

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 5, students look at probability and statistics. Previously, students learned that “proportional reasoning can be used to make inferences about a population from a random sample.” In the future, students will “apply counting principles, permutations, and combinations to analyze compound probability, larger sample spaces, and binomial situations.”

Additionally, each lesson explicitly connects the content and language from previous grade levels to the current lesson and explains how these concepts extend to future learning. For example, lesson 10.2 connects prior learning on solving one-step equations to solving two-step real-world problems. The lesson prepares students for solving quadratic equations with square roots in future courses.

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 new mathematical skills. The 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, module 9, lesson 2 begins with students investigating a real-world problem. They need to determine the area of a rectangular garden with a smaller rectangle taken out. Students apply previously learned knowledge of rectangles to find the area of the garden before introducing the area of composite figures. Students use the provided grid to check their thinking.

The materials also include a “Prerequisite Check” for each module to connect prior concepts and procedures from current and previous grades to new learning. For example, module 4 activates earlier skills, such as multiplying decimals, solving proportions, and equivalent ratios, and connects these skills to solving geometric problems using proportional reasoning. 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 9, lesson 5, the practice includes three review questions from modules 3, 6, and 8. Students review converting feet to meters and the concepts of volume relationships between prisms and pyramids. They also make inferences from a random sample.

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 8 provides opportunities for spaced retrieval practice focused on determining the area of rectangles, triangles, and parallelograms. This “Prerequisite Check” prepares students for explaining geometric formulas in upcoming lessons.

The materials also include a Module Project that offers opportunities for students to apply previously learned skills and concepts. “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 provides interleaved practice by requiring students to apply previously learned skills and concepts. For example, in module 9, lesson 4, students revisit content from earlier lessons and units, including slope-intercept form (lesson 7.3), sampling and populations (lesson 6.1), percent change (lesson 3.1), and equation solving fluency. As students revisit this content, they also engage with current geometry concepts involving nets, lateral area, and surface area. The practice intentionally mixes multiple mathematical domains and representations, requiring students to select appropriate strategies and connect prior learning across lessons and units rather than work on a single isolated skill. This structure promotes flexible problem-solving and strengthens retention of previously learned concepts and procedures.

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” activities provides a mixed set of problems on the lesson concepts, allowing students to choose 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 includes a Module Review that offers interleaved practice opportunities with previously learned skills and concepts across lessons. This review allows students to practice and review the TEKS taught in the module and includes 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. Students also select appropriate methods for finding solutions in unfamiliar contexts, which helps them develop flexible thinking skills. For example, in lesson 4.3, task 2, students use a problem-solving model to analyze, plan, solve, justify, and evaluate a problem. Given the sequence, students must analyze what 2.25 inches on the map represents and then interpret specific locations on the map, evaluate the process, and check the reasonableness of their answers.

Additionally, in module 5, lesson 7, students create and analyze a tree diagram for a compound event and evaluate whether the diagram represents the complete sample space before connecting the representation to probability.

The materials also provide low-floor, high-ceiling “Spark Your Learning” activities to help students interpret, analyze, and evaluate representations. These activities enhance students’ critical thinking skills and enable them to transfer their learning to new contexts. For example, in lesson 9.2, students must interpret the pieces needed to use a formula so they can find the composite area of a figure. They discuss their answers in a “Turn and Talk” activity and determine whether there is another way to calculate the area.

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

Throughout the materials, students create a wide variety of mathematical models to represent and solve real-world situations, including visual representations, equations, tables, and diagrams. For example, in module 5, lesson 7, students create a tree diagram to represent the sample space for a compound event, making their reasoning visible before using probability notation.

Additionally, in module 7, lesson 2, students create a table and graph to represent the remaining solution in an IV bag over a specific period. The lesson says, “Use your table and graph to determine when the IV bag will be empty.” The task requires students to create and use their own mathematical representation to help them solve.

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

Each lesson gives students opportunities to apply conceptual understanding to new problem situations and contexts through the lesson tasks. “Turn and Talk” activities within the lesson also provide structure to language routines. For example, in lesson 6.2, task 1, students calculate the lateral surface area of a triangular prism. The materials state, “How would the lateral surface area change if the height of the lampshade doubled? How do you know without calculating?” Through discussions, students go beyond computations and develop a conceptual understanding of how changes in dimension affect each surface.

The materials also include “Practice on Your Own” assessments that provide opportunities for students to apply conceptual understanding to new contexts. For example, in lesson 2.4, students communicate ideas of proportionality in a real-world context. Questions require students to apply conceptual understanding to answer “What is the meaning of the point (1, 16) on the graph?” Students then apply their understanding to a new context when they describe “how the graph would be different if Yazmin’s jogging rate were a different constant.”

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. Independent practice reinforces skills and helps develop automaticity.

The “Practice on Your Own” section builds students’ automaticity and fluency to help them complete grade-level tasks. For example, in module 1, lesson 6, students move from basic algorithm-type fraction problems to real-world problems. The new problems are the same but have a less-supported structure, so students build automaticity and fluency. Repetitive tasks strengthen automaticity and support fluency by asking students to apply a new idea to each prior problem.  

Additionally, the materials provide fluency practice with a variety of concepts within the “Differentiation and Practice” portion of the lessons. Educator guidance states, “Give students Fluency practice as it is available to help promote automaticity.” The grade 7 “Fluency Practice” includes skills such as multiplying two- and three-digit numbers and adding and subtracting fractions.

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 and accurate mathematical procedures. For example, in lesson 7.1, task 2, students complete a table to show the linear relationship between the batches of muffins and the total number of muffins baked. Questions prompt students to show the relationship in another way by writing a rule and an equation that represents it. The materials demonstrate flexibility with multiple representations of linear relationships while maintaining accuracy.

Additionally, in module 9, lesson 1, students calculate the area and circumference of a circle and discuss “Which measurement is easier to use to find circumference and area, radius or diameter? Why?” This helps students understand different situations in which the radius versus diameter leads to more efficient calculations. The lesson tasks reinforce accuracy while encouraging the flexible selection of strategies to solve problems efficiently.

“Practice on Your Own,” “Practice Plus,” and Waggle provide continued opportunities for students to apply efficient, flexible, and accurate procedures independently after the lesson. For example, in lesson 10.2, students build solving efficiency through repeated practice with two-step equations. Students use flexible procedures to write equations from varied real-world situations, interpret solutions in context, and practice accurate procedures through repeated equation solving, application problems, cumulative review, 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 throughout the materials provides opportunities for students to evaluate their processes for efficiency, flexibility, and accuracy. For example, in module 4, lesson 3, students use a scale to determine the distance between two locations on a map. The prompt “Explain why your answer in part C makes sense,” provides students an opportunity to evaluate solutions for accuracy. Questions such as “How effective was your strategy to solve this problem? What might you do differently?” provide opportunities for students to reflect on the efficiency and flexibility of their approach.

Additionally, in lesson 10.6, task 1, students engage in an “Evaluate Reasonableness” question that requires them to critique mathematical procedures, explain their reasoning, and determine the validity of solutions. The materials state, “How can you check that the measure of the third angle is correct? Check that your answer is correct.” Through discussions, students evaluate alternative approaches and consider the effectiveness of different solution methods, addressing efficiency, flexibility, and accuracy.

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 that help students refine solution methods and develop increasingly efficient mathematical approaches. For example, in lesson 1.2, students perform operations on positive decimals. In task 3, the educator guidance states, “Remind students that mental math is a technique they can use to solve problems efficiently. Have students volunteer a few mental math strategies that they find helpful.” Discussions lead students to understand that decomposing numbers can lead to more efficient processes.

The Teacher’s Guide for lesson 4.2, task 3 includes embedded questions and instructional guidance that help educators move students from visual and proportional reasoning toward increasingly efficient use of scale factors and proportional relationships. The guidance supports educators in prompting students to compare strategies and recognize more efficient approaches for solving scale and similarity problems.

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 the procedural fluency required by the TEKS. For example, the module 6 guidance states, “Conceptually, students will understand how data from random samples can be used to represent and make inferences about a population. They will learn why randomness, sample size, and clear data displays affect the reliability of conclusions drawn from data.”

Additionally, in module 10, the “Teacher Background” section identifies the module concept, which focuses on understanding similarity, proportional reasoning, and scale relationships. The procedural emphasis explains how students apply ratios, proportions, equations, and scale factors to solve geometric and real-world problems involving similar figures and scale drawings.

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, lesson 1.2, task 2 requires students to use multiple representations while solving problems with rational numbers. Students model mathematics with visual representations, interpret pictorial models, and connect those models to symbolic calculations and numerical reasoning. In module 5, lesson 7, students use a tree diagram to represent compound events before using probability notation. These tasks require students to explain their thinking as they transition from visual models to abstract procedures.

Additionally, the “Teacher Background” emphasizes the importance of using concrete models and manipulatives, pictorial representations, and abstract representations to meet the standards. For example, module 10 states, ”Using equations to represent geometric relationships connects algebraic reasoning with geometric understanding. This integration supports students in modeling mathematical structures, justifying solutions, and applying equations across different areas of mathematics.” The materials ensure that students engage in meaningful mathematics by actively constructing their own understanding through various representations instead of just memorizing rules and procedures.

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 10.2, task 1, students use algebra tiles to create a two-step equation model. Students explain their model by answering questions such as “How can you work with the algebra tiles on the equation mat so one side of the mat has only variables?” Then students solve the same type of equation algebraically and explain the connection between the concrete model and algebraic representation.

The materials also support students in creating, defining, connecting, and explaining representational models to abstract concepts. For example, in lesson 5.7, task 1, students create a tree diagram for a compound event, define possible outcomes, and connect the representation to symbolic probability notation. The diagram helps students build connections to the symbolic notation used in probability. The “Turn and Talk” requires students to explain “Which technique for representing a sample space—drawing a tree diagram or making a list—is more efficient? Why?”

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 1.3, students interpret and operate with rational numbers using multiple visual representations and structured discourse routines. Students use visual models, including number lines and other mathematical representations, to explain relationships among rational numbers during “Turn and Talk” discussions. “Math Language Routines” within the lesson require students to communicate mathematical reasoning using precise academic vocabulary and justify solutions with peers. Educator-guided questioning, language objectives, and structured discussion prompts support students in connecting mathematical vocabulary to visual models. Students also increasingly use precise mathematical language during collaborative conversations.

Additionally, in module 8, lesson 1, students develop academic mathematical language related to volume through manipulatives and peer discussions. The materials state, “Use unit cubes, isometric dot paper, or graph paper to find how many 1-inch cubes could fit into a box with edge lengths as shown. Describe how you found your answer.” Students use visuals and manipulatives to navigate the problem and gain a deeper understanding of volume. The “Turn and Talk” guidance states, “Encourage students to think about work they have done previously with finding the area of plane figures and how they applied similar procedures in this problem,” which helps students connect the concrete objects to prior knowledge.

The Implementation Guide 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 and scaffold academic conversations. The section also provides multiple opportunities for students to use precise mathematical language during instruction to explain and justify their thinking.

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 students’ use and development of academic vocabulary through the language routines. For example, in lesson 11.2, the “Turn and Talk” routine guidance states, “Encourage students to share their thoughts about how the interquartile range (IQR) and median values reflect the consistency in the biking distances...Using a number line or graphing the data points can help visualize the relationship between the median, range, and consistency in the context of biking distances.”

Additionally, in module 4, lesson 2, the educator guidance scaffolds precise mathematical vocabulary within the context of scale drawings by directing educators to “Provide a word bank of lesson-specific academic vocabulary for students to construct precise explanations connecting the model to a proportion or equation.” The embedded word bank includes the terms ratio, proportion, corresponding, actual, drawing, units, and equation, supporting students in using academic terms to explain the relationship between a scale model and proportional reasoning.

The materials also include a Language Development Resource Guide that provides scaffolding and supports students’ development of academic mathematical language. The materials state, “Deliberately teaching academic vocabulary plays a crucial role in fostering student success both in the classroom and in life. Here are some key advantages of building and reinforcing academic vocabulary: enhanced comprehension, critical thinking, improved communication, academic achievement, lifelong learning, and confidence building.” 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.

Additionally, each module incorporates a “Stronger and Clearer Each Time” language routine that allows students to use, hear, and refine mathematical language. The routine asks students to share their thoughts with a partner, ask thoughtful questions, and revise their response. The materials include embedded educator guidance to support the routine. For example, lesson 8.2 says, “Remind students to ask questions of each other that focus on describing their thinking, especially related to determining volume, 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, in lesson 2.1, students analyze real-world proportional situations and solve problems using tables, graphs, equations, and verbal reasoning. They also participate in “Three Reads” and “Turn and Talk” routines, justify their solutions, and communicate mathematical thinking using precise mathematical language. The educator guidance intentionally embeds the process standards throughout instruction rather than presenting them as isolated expectations.

Additionally, each “Practice on Your Own” assessment integrates the process standards by identifying questions labeled “PS.” For example, the questions in lesson 5.6 require students to “analyze relationships” represented in the spinner to determine theoretical probabilities and “use precise language” to justify differences between theoretical and experimental probabilities.

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

The course-level “Mathematical Connections” guidance explicitly describes the role of process standards across grade 7: “Into Math Texas intentionally make[s] mathematical connections across the grade level to help drive the scope and sequence” and “uses these connections, supported by the Texas Mathematical Process Standards, to build deeper understanding, promote transfer of learning, support coherence across topics, and strengthen problem-solving and reasoning.” The accompanying coursewide table then describes process-standard connections across modules, such as “Representations are created to record and communicate proportion, ratio, and rate concepts in Modules 2–4” and “Mathematical ideas are communicated using multiple representations in Modules 5–7 and Modules 11–12.”

Additionally, the Implementation Guide provides a “Correlation by Standard” table that identifies where each process standard is incorporated throughout the course. For example, lessons 2.4, 3.2, 5.6, 5.7, 8.3, 10.3, and 11.2 incorporate process standard 7.1.F.

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 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 explains how the grade 7 TEKS process standards are incorporated throughout each module and connected across the unit. For example, in module 2, the planning pages identify the process standards emphasized within the unit, including the problem-solving model, communication through multiple representations, creation and use of mathematical representations, analysis of mathematical relationships, and justification using precise mathematical language. The module overview explains how these process standards support students as they progress from representing constant rates of change to analyzing proportional relationships and applying proportional reasoning to increasingly complex mathematical situations. This unit-level description demonstrates the intentional integration of the process standards throughout the module, which supports conceptual development.

The planning pages for module 7 explain that “students learn the steps of the problem-solving model (PS 1.B), and then they use all the steps together in Lesson 3 to solve a problem related to converting between representations of linear relationships.” The planning pages note, “Lessons 1 and 2 have students communicating mathematical ideas using multiple representations (PS 1.D),” “Lesson 2 has students apply mathematics to problems arising in everyday life (PS 1.A),” and “Lessons 1 and 3 have students display, explain, and justify mathematical reasoning (PS 1.G)” in connection with representing, graphing, and converting linear relationships.

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, the overview in module 3, lesson 2 explicitly identifies PS 7.1.F, which emphasizes analyzing mathematical relationships to connect and communicate mathematical ideas and prepares students to solve multistep ratio and rate problems using tables, equations, and proportional reasoning.

Additionally, throughout each lesson, a “PS” appears next to specific items that meet the process standards. For example, lesson 10.4, task 3 requires students to use precise language when explaining how to solve a two-step inequality, as required by process standard 7.1.G.

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 before formal instruction begins. The activity presents an authentic scenario and asks students to identify multiple ways to represent and solve the problem. For example, in lesson 4.2, students engage in a scale-drawing problem involving the design of a bicycle shop display. The task asks students to determine dimensions from a scale drawing using various possible solution strategies. Students describe multiple approaches, explain their reasoning, compare strategies during the “Turn and Talk,” and determine when multiplication or division is appropriate. These activities encourage mathematical thinking and sense-making before the establishment of formal procedures.

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 3.3, students calculate the balance in a savings account after it earns interest for 12 months. Students analyze the problem, create a plan, solve the problem, and justify their work. Educator guidance includes prompts such as “ASK: What factors do you need to take into account to calculate the interest?” to help students persevere through the solving process. To help students make sense of the mathematical concepts, the “Turn and Talk” asks, “How can understanding interest help people plan their savings?”

Additionally, in lesson 7.2, task 2, the materials guide students through a set of problems, adding a step to each one. The setup has students look at tables, compare graphs, investigate intercepts, make predictions, and then justify whether the predictions are true. The “Turn and Talk” then asks, “Did your graph in Part F confirm or refute your hypothesis in Part E? Summarize what you now understand about graphs of linear equations.” The task allows students to think mathematically as they persevere through the work, and the “Turn and Talk” helps them make sense of the mathematics from a real-world perspective.

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 various methods to solve mathematical problems. For example, in module 4, lesson 1, students investigate proportional relationships and learn that there are multiple ways to represent and analyze mathematical relationships. Students compare measurements, organize data, determine whether the relationship is proportional, and represent their reasoning using ratios, tables, equations, and written explanations. Prompts require students to explain how their representation demonstrates proportionality, and they compare their reasoning with classmates. These steps reinforce that students can solve the same mathematical problem using multiple representations and solution methods and give students an opportunity to justify the validity of their approach.

Additionally, the materials incorporate “Show Another Way” questions that help students understand that there are multiple ways to represent and solve problems. For example, in module 5, lesson 7, students determine the probability of a compound event using both a tree diagram and a list of the sample space. The “Turn and Talk” asks, “Which technique for representing a sample space—drawing a tree diagram or making a list—is more efficient? Why?” This supports students in explaining and justifying the use of multiple approaches.

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 follows a series of tasks that allow students to make sense of mathematics. Students complete tasks that provide opportunities to do, write, and discuss mathematical concepts with peers and educators. For example, in lesson 7.1, students complete four tasks involving representing linear relationships verbally and using tables. All four tasks provide real-world problems to help students make sense of mathematics. Students discuss the math through “Turn and Talk” routines and use academic language, including the term variable, “to write a rule summarizing how the values in the linear relationship change.”

The materials provide additional opportunities for students to communicate mathematical understanding through writing and discussion. For example, in module 1, lesson 8, task 2, students explain their mathematical reasoning in writing, justify their conclusions with evidence, and participate in collaborative discussions to evaluate and compare solution strategies. Educators encourage students to critique reasoning and support mathematical claims using appropriate mathematical language.

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 8.2, educator guidance states, “Remind students to ask questions of each other that focus on describing their thinking, especially related to determining volume.” Students then “use insights from the discussion to refine their answers or reasoning.” This requires students to engage in grade-level mathematics, articulate their reasoning, discuss it 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 7 materials guide educators to use structured mathematical discourse to help students share and reflect on their problem-solving approaches. For example, in lesson 1.8, the guidance suggests a variety of language routines and direct questioning prompts to help students share and reflect. In task 1, the “Turn and Talk” requires students to explain how they made a prediction earlier in the problem. Educator guidance states, “Have students detail their approach to solving the equation using the number line or describe and justify their thinking to demonstrate use of mathematical terms such as negative number, positive number, and additive inverse.” In task 4, students develop an argument and must justify whether they agree with a stated claim. The “Review: Spark Your Learning” section asks students, “After solving more problems with rational numbers, how might you approach this problem differently?” This question provides an opportunity for students to reflect on their approach.

Additionally, in lesson 7.3, the problem-solving task directs students to “Show your thinking,” while embedded educator guidance has students “brainstorm possible strategies,” solve the problem, and share their thinking. These tasks help students to communicate and reflect on different problem-solving approaches rather than simply report an answer.

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 by using the “Learning Goal” routine, “Quick Checks,” and real-time student responses. Rather than 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 solutions are correct, have them compare classmates’ approaches, and ask them to defend their conclusions with mathematical evidence. Educators 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 based on demonstrated understanding rather than waiting until the end of instruction.

The materials explicitly direct educators to monitor student responses and provide targeted explanatory feedback throughout each lesson. For example, module 7, lesson 3 states, “As students solve the problem, monitor their responses and use the Spark Discussions table to provide common-error support.” The materials note, “Students might incorrectly add all the quantities rather than multiplying and then adding” and provide the incorrect response “4 + 3 + 5 = 17. The total cost is $17.” Rather than merely correct students’ errors, educators offer explanatory prompts, including “What unit does each quantity involve?” to help students distinguish the starting cost, hourly rate, and number of hours.

Additionally, the Teacher’s Guide provides prompts and guidance throughout each lesson to address common errors. For example, in lesson 10.1, students write two-step equations to represent a real-world problem. The materials provide two incorrect equations that students may write and show how to guide students to the correct equation. Educators ask students, “Which amount repeats per wristband?” After answering this question, students can explain the need to multiply the cost per wristband by the number of wristbands and then add the fixed fee to find the total.