HMH Math 180 Texas Grade 6

Evaluation for 1.1a
Materials include an alignment guide outlining the TEKS, ELPS, and concepts covered, with a rationale for learning paths across grade levels (vertical alignment) and within the same grade level (horizontal alignment) as designed in the materials.

The grade 6 Alignment Guide includes the Texas Essential Knowledge and Skills (TEKS) and the English Language Proficiency Standards (ELPS), though not all are covered, as the Math 180 Program is a supplemental math product focused on rebuilding the foundational math skills needed for algebra readiness; each listed standard has at least one resource. These standards are presented sequentially, without explicit horizontal or vertical alignment. However, the Resources for Differentiated Instruction Guide addresses both alignments through scaffolding and enrichment tools—like Connect, Boost, Focus, Stretch, and Step-Up lessons—focused on concepts not tied directly to the TEKS or ELPS. The grade 6 "Fractions Teaching Guide" uses visual graphics to clearly show horizontal alignment within the unit, breaking down concepts into interconnected lessons. Each topic includes a "Professional Learning" page outlining prior knowledge and future skill connections, supporting horizontal alignment. The Alignment Guide shows how key mathematical concepts and skills progress across grade levels, supporting algebra readiness. The materials outline the progression of content from one grade to the next, demonstrating how earlier concepts build into more advanced topics.

Evaluation for 1.1b
Materials include an implementation guide with usage recommendations and strategies for effective educator use, such as just-in-time supports, advanced learning, or as a course.

The grade 6 materials include an implementation guide that outlines how to structure classes in various formats, including shortened, multi-block, and double periods, with guidance on whole-class and rotational models. The "Grouping Students for Differentiation" tool helps teachers use data to form student groups and determine intervention points. The Program Guide includes instructional routines and targeted lessons—Boost for students needing support and Stretch for those showing proficiency—along with guidance for multilingual learners, special education, behavioral support, and responsive teaching. "Teacher's Success Pathway" offers structured video training on classroom setup, instructional planning, and data use. The "Teaching Guide" provides in-lesson prompts and scaffolds for teachers to use at different points throughout the lesson. In Lesson 5: "Problem Solving: Solve Problems with Fractions," there are designated points where teachers are prompted to facilitate Turn and Talks and "High-Leverage Practice" as well as provide guidance on how to help students if they have a misconception. The guide provides prompts to ask, with possible student responses, and has "if/then" scenarios to help guide students through misconceptions.

Evaluation for 1.1c
Materials include a TEKS correlation guide with recommended skill entry points based on diagnostic assessment results.

The materials include a dashboard where educators can search the TEKS from kindergarten through Algebra II. This search tool also provides a list of resources that are aligned to each of the TEKS. The grade 6 Program Guide provides guidance that helps educators to manually view and adjust skill entry points, when needed, based on diagnostic assessment results and individual student needs. The materials recommend using "Baseline Scan 1" and "Baseline Scan 2" as a manual diagnostic tool. The materials also include an "Assessment, Progress, Monitoring, and Data" chart, which lists the suggested entry point for students based on individual Rasch Unit (RIT) scores and also explains how to create small groups in class based on RIT scores. Utilizing the "Baseline Scans" as a diagnostic provides a rationale of student misconceptions based on how students responded. This tool will help educators quickly identify what skill to focus on based on how students responded.

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

The grade 6 "Fractions Teaching Guide" starts with a lesson overview that includes an objective (or more than one objective), language goals, an instructional focus, a mathematical thinking focus, grade-level content connections, a materials list, and a statement explaining to teachers why the lesson matters. Teachers are provided with explicit instructions regarding what to say, what to ask, and what to show in order to facilitate the lesson instruction. Anticipated or sample student responses are provided for all questions. Images of the accompanying "Teacher Display Tool" and student mSpace pages are provided. Additionally, "High-Leverage Practice" notes prepare teachers to respond to common patterns of student thinking, elicit student thinking, and modify tasks. This serves as a lesson internalization guide for educators. In grade 6, the materials include a "Block at a Glance" section for each unit of instruction. The "Block at a Glance" lists each lesson in the unit side by side, allowing for unit internalization and helping teachers to thoroughly understand the sequence of learning. It also provides a CheckPoint for differentiation.

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

In the professional learning resources, there are a variety of tools for administrators to use to support educators in implementing the program. The materials include resources and guidance for instructional leaders. Included are videos and resources that allow instructional leaders to connect with Math 180 teachers, including live events to help recognize success, preparation for teacher conferences, and family engagement. The materials include a "What to Look For" guide for administrators and other school leaders. The guide includes a description of what administrators should see when they walk into the classroom. It provides an outline of how a visit to the Math 180 class should be handled, as well as a reflection guide for after the visit.

Evaluation for 1.2a
If designed to be static, materials include detailed lesson plans with learning objectives, teacher and student materials, lesson components with suggested timeframes, and assessment resources aligned with the TEKS and ELPS.

This guidance is not applicable because the program is not designed to be static.

Evaluation for 1.2b
If designed to be adaptive, materials include detailed lesson overviews with learning objectives, lesson components with suggested timeframes, and assessment resources aligned with the TEKS and ELPS.

The grade 6 "Fractions Teaching Guide" includes content objectives and instructional focus statements. Teachers can use the Alignment Guide to see the TEKS aligned with lessons. The materials include overviews with learning objectives aligned to the ELPS, as outlined in the "Language Support at a Glance" document for each instructional block. These documents offer educators guidance and suggested tasks to support emergent bilingual students. The materials include a program overview that displays a suggested time frame for each lesson component and includes a full description of the lesson structure. The Math 180 Program Guide provides an overview of multiple implementation models to meet the needs of each classroom's schedule and needs. The guide provides a breakdown of each component of the lesson and how it is used. The Math 180 Program provides an mSkills assessment for students to take at the end of a teacher-facilitated block of instruction. The assessment is not adaptive. The assessment provides the aligned TEKS and ELPS for each question.

Evaluation for 1.2c
Materials contain support for families in Spanish and English for each unit, with suggestions on supporting the progress of their student(s).

The Math 180 program provides family letters in English and Spanish at the beginning of each concept. The letters include an overview of what students will be learning within a topic, learning objectives, and quick overviews of the activities within the topic. The letters provide information on what students are learning, how support can be provided at home, and progress updates to track proficiency and understanding.

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

The materials include a "Math 180 Assessment Roadmap" in the Math 180 Program Guide. The materials include a suggested screening and placement assessment, formative assessments, interim assessments, and summative assessments. Each of the assessment tools includes a description and purpose for the identified assessment type and information about what each assessment tool assesses. The materials include a section titled "Introducing mSkills Assessments." This section discusses the mSkills assessment and identifies the definition and purpose of the assessment.

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

The materials include a "Teaching Guide" to monitor student progress in the mSpace portion of the program. This guide provides clear guidance for teachers on how to assess student performance and understanding and allows teachers to modify tasks to elicit responses from students. The guide also provides a general rubric for Exit Tickets. The Math 180 Program Guide provides guidance for teachers on the mSkills assessment. The guide provides an overview of the assessment, its purpose, and when it is used. The guide provides tips for students and teachers to use before and during the assessment. Guidance on how to administer the assessment, track progress, and grade the assessment is also included. The Math 180 Program Guide provides best practices for both the teacher and student experience for each of the assessment types. For example, it suggests that teachers remind students not to spend longer than five minutes on a single question and describes how to use test-taking tools.

Evaluation for 2.1c
Digital assessments include printable versions and accommodations, including text-to-speech, content and language supports, and calculators, that educators can enable or disable to support individual students.

The mSkills assessments in Math 180 are accessible in both digital and printable formats. The "Success Zone" within the student application includes a standard calculator feature that can be enabled or disabled to accommodate individual student needs. Teachers have complete control over calculator access and may turn it on or off at the class level or for specific students. By default, the calculator is disabled. Math 180 includes text-to-speech functionality for assessments, but it does not provide built-in content or language supports for digital assessments. Teachers can enable and disable the text-to-speech for individual students. Students have access to read-aloud buttons, which can be used to have questions or answer choices read aloud to them in English or Spanish.

Evaluation for 2.1d
Materials include diagnostic assessments with TEKS-aligned tasks or questions, including interactive item types with varying complexity levels.

The materials include two diagnostic assessments—Baseline Scan I and Baseline Scan II—administered at the beginning of the year. These assessments are composed of multiple-choice questions aligned to a range of the TEKS. The assessments reflect multiple levels of complexity. For example, Baseline Scan II includes Depth of Knowledge (DOK) 1: "Identifying equivalent ratios," DOK 2: "Solving application problems involving proportions," and DOK 3: "Analyzing and solving scenarios related to proportional reasoning." mSpace contains adaptive, step-wise problems with equation editing and graphing that enable students to enter expressions, fractions, and equations using an interactive editor. While the "Baseline Scan" assessments themselves are limited to multiple-choice formats, the mSpace platform offers interactive diagnostic tools and demonstrates alignment to the TEKS with tasks spanning multiple DOK levels. Students engage with math through step-by-step problem-solving, equation editors, graphing tools, and adaptive feedback that support both conceptual understanding and procedural fluency. The mSkills assessments have various question types, such as multiple-choice items, hot text items, gap match items (drag and drop), text entry, and composite items (a combination of item types).

Evaluation for 2.1e
Materials include a variety of formative assessments with TEKS-aligned tasks or questions, including interactive item types with varying complexity levels.

At the conclusion of each block within each unit, an assessment is provided that features a variety of question types. The Program Guide offers detailed descriptions of each question type included in the assessments. Across the various unit assessments, question types include fill in the blank, graphing on the coordinate plane, drag and drop, and multi-select. Performance Tasks are provided at the end of each instructional block, where students encounter various levels of complexity while engaging with the problem-solving model, which includes the stages of "Explore," "Apply," "Analyze," "Evaluate," and "Extend." The materials include a variety of formal assessments within mSpace, including Exit Tickets, Performance Tasks, and mSkills assessments. The mSkills assessments have a variety of questions given at the end of each instructional block and include varying levels of complexity and item types. The materials include a formative assessment called the "Success Zone." The "Success Zone" includes interactive methods to check students' understanding of the material, including games with drag-and-drop, ordering, and multiple-choice questions. The "Success Zone" also has varying levels of questions, including basic recall, skills application, and critical thinking. At the end of every Math 180 lesson, there is an Exit Ticket to assess student mastery of the topic. The Exit Tickets have a range of question types and complexity, including fill in the blanks, error analysis, and writing prompts.

Evaluation for 2.2a
Instructional assessments include scoring information and guidance for interpreting student performance, including rationale for each correct and incorrect response.

The materials include "Assessment Reports" for each mSkills assessment taken within mSpace that gives guidance to teachers on how to read each report and interpret individual student scores and whole-class performance. General advice is also given to teachers about how to use the report in a classroom setting. The Math 180 Program Guide includes detailed information on how to access assessment reports, interpret assessment data, and use the data to drive instruction. mSkills assessments display class and individual student performance, standard performance, and student proficiency. For each mSkills assessment given, the materials include a PDF assessment key. The assessment key includes the correct answer, the aligned TEKS, a rationale for each correct and incorrect answer, and possible student misconceptions. For open-ended questions, a rationale is provided for the correct answer only.

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

The materials include built-in CheckPoint days where students are grouped with targeted lessons based on their progress, performance, and assessment data. These CheckPoint days allow for differentiated instruction for improving targeted areas. The materials provide a Resources for Differentiated Instruction Guide for teachers to reference after an assessment, which provides guidance on next steps for students. Students can work on a Boost or Stretch activity. Each activity type has a description of its intended use. The guide also gives an example of how to group students for instruction using assessment data. Within the online HMH Ed dashboard, teachers can access assessment reports that include student and whole-class performance. In this area, the program can recommend groups for the CheckPoint days based on the data from a specific assessment and then assign each group lessons, Stretch activities, or Boost activities to meet the needs of different target areas. At the end of each block, the materials contain a CheckPoint. This CheckPoint serves as a way to analyze and review student data and plan differentiated instruction.

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 a printable tracker—available in English and Spanish—for students to put a check mark on each completed lesson within the instructional blocks. The materials include a student dashboard where students can track key performance indicators, such as overall progress through the program, learning segments (units) completed, session counts, performance levels (e.g., "Explore Zone," "Learn Zone," and "Success Zone"), and session duration. The materials include a "Program Activity Report" that provides tools for educators to monitor student progress. The report displays results from the student application and the "Mindset Scan," which provides students with an opportunity to reflect on their own learning strategies, attitudes, and behaviors. The Program Guide provides instructions on how to read and interpret the report. The materials provide a "Summary Reports" section for each class for teachers to track student assessments. Reports include student results on assessments, progress over time, and student usage. The materials include an educator dashboard that automatically compiles real-time student assessment data into tables and reports, highlighting areas of strength and weakness by color in the "Program Activity Report."

Evaluation for 2.2d
If designed to be static, materials provide prompts and guidance to support educators in conducting frequent checks for understanding at key points throughout each lesson or activity.

This guidance is not applicable because the program is not designed to be static.

Evaluation for 2.2e
If designed to be adaptive, materials provide frequent checks for understanding at key points throughout each lesson or activity.

The mSpace materials include sections for students to practice a skill independently before completing their Exit Ticket. The materials include a "Program Activity Report." This report provides educators with real-time reports on student progress and understanding, which allows educators to identify students who need additional support and provide more targeted instruction. In the adaptive platform, understanding is assessed in two sections: the "Learn Zone," which targets basic application, and the "Success Zone," which measures higher-level understanding. The "Learn Zone" includes three parts—Try, Practice, and Master and Fast Track—each offering different levels of support and feedback. Students answer questions based on their current block and receive immediate feedback. Incorrect responses prompt either a retry, a hint, or a display of the correct answer with a brief explanation.

Evaluation for 3.1a
Materials include explicit educator guidance for lessons or activities scaffolded for students who have not yet reached proficiency in prerequisite or grade-level concepts and skills.

Within each unit, the Math 180 materials contain guidance on Boost lessons that target students who have not demonstrated proficiency in a block of content. Boost lessons allow students to solve scaffolded problems that introduce key concepts, and students are explicitly taught how to use familiar strategies to solve a range of problems. The materials include a CheckPoint day at the end of each topic. The purpose of the CheckPoint is to provide differentiated instruction by grouping students based on their progress and performance. Instruction can then be planned and scaffolded for students who have not yet met grade-level proficiency. The CheckPoint directs educators on how to reinforce concepts for these students or how to challenge students who have already met grade-level requirements. The Resources for Differentiated Instruction Guide provides teachers with guidance for lessons or activities for students who have not yet reached proficiency after an assessment. It includes three types of Boost lessons, each designed for a specific instructional purpose. Focus lessons reinforce foundational skills before moving on to a new topic. The teacher key in the Focus lesson provides instructions for teacher implementation, scaffolded questions, and a strategy to focus on when problem-solving.

Evaluation for 3.1b
Materials include explicit educator guidance for language supports, including pre-teaching and embedded supports for developing academic vocabulary and unfamiliar references in text.

The "Topic at a Glance" includes math terms and academic language. The "Topic Tracker" provides language goals. Throughout the notes, vocabulary "breakouts" notify teachers to display and provide support throughout the lesson. The materials include a "Teaching Guide" at the beginning of each instructional block, with guidance on different aspects of the lesson, including vocabulary, language goals, math terms, and academic language. The "Language Goals" section includes pre-teaching supports for developing the vocabulary across the lesson. Additionally, the math terms include pre-teaching supports for developing new or unfamiliar math vocabulary words that are introduced within the block. The materials include short instructional videos within each lesson that provide context for the new concept, skill, or strategy. The videos include a step-by-step procedural strategy using visual models and important math vocabulary. Key math terms and properties are defined and used in the videos to support students' development of academic vocabulary. These videos are embedded within the student program and target both academic vocabulary and unfamiliar math terms and language. Each lesson contains a language support lesson for the teacher to use when planning. These lessons provide explicit guidance for educators on how to integrate language development into math instruction for students at varying levels of English proficiency. They model strategies for pre-teaching essential academic vocabulary, clarifying unfamiliar cultural or contextual references, and using scaffolds, such as visuals, sentence frames, and structured discussion routines. The materials include vocabulary prompts within each lesson. These embedded supports allow educators to productively facilitate discussions related to the material and help students to better understand and become familiar with the academic vocabulary and unfamiliar real-world vocabulary.

Evaluation for 3.1c
Materials include explicit educator guidance for enrichment and extension activities for students who have demonstrated proficiency in grade-level and above grade-level content and skills.

At the end of each block, students have the opportunity to apply their understanding of the concept in a Performance Task. The "Teaching Guide" provides mathematical thinking that should be seen and includes rubric guidelines for where a student may be within the extension. The materials include "High-Leverage Practices" with "breakout" notes for teachers. These notes include ways for teachers to extend students' thinking with questions to ask and ways to take the practice one step further. The materials include Step-Up questions built into each lesson, intended to challenge students to connect concepts to Algebra I and written for pairs or small groups to work through together. The materials include a "Differentiation Guide" that includes a Stretch section, which gives educators guidance on modifying and extending the lesson for students who have already met grade-level proficiency so that they can challenge themselves and deepen their knowledge. Stretch and Step-Up lessons are used for students who have demonstrated proficiency in content and skills. These lessons provide nonroutine activities and extend students' understanding of the content. Each lesson has a teacher key with guidance on how to facilitate it and guided questions to ask students.

Evaluation for 3.1d
Digital materials include accommodations, including text-to-speech, content and language supports, and calculators that educators can enable or disable to support individual students.

Math 180 digital materials offer built-in supports for diverse learners. These supports are available throughout the student application, including the student dashboard. A calculator is accessible within the student application in both the "Learn Zone" and "Success Zone" in Math 180. Teachers have full control over calculator accessibility and can enable or disable it at both the class and individual student levels. The materials provide a text-to-speech option to enable or disable audio instructions for individual students. The materials also allow educators to pick English or Spanish audio for students or allow students to select their preference for English or Spanish. While the materials allow for text-to-speech, they do not provide content and language supports for students. However, students have access to read-aloud buttons, which they can use to have questions and answer choices read aloud to them in English or Spanish.

Evaluation for 3.1e
Materials include educator guidance on offering options and supports for students to demonstrate understanding of mathematical concepts in various ways, such as perform, express, and represent.

The materials include "High-Leverage Practices" within each lesson of the "Teaching Guide." These practices provide teachers with strategies to promote flexible thinking and problem-solving. These include "if/then" guidance (e.g., "if the student answers in this way, then do this") and suggestions for using various models and diagrams to help students represent or explain their thinking. The materials include several problems throughout the curriculum that allow students to answer or explain their work in various ways, including numerical answers, justification statements, models, and diagrams. The materials include Performance Tasks that give students opportunities to demonstrate understanding in various ways. Educators are directed to add pointed questions to elicit responses from students. Performance Tasks also include detailed instructions for educators to help guide students through the process.

Evaluation for 3.2a
Materials include explicit (direct) prompts and guidance for educators to build knowledge by activating prior knowledge, anchoring big ideas, and highlighting and connecting key patterns, features, and relationships through multiple means of representation.

The materials include Do Now and Connect activities that activate prior learning related to the day's topic. Educator guidance is given for both of these types of questions in the unit's "Teaching Guide." The online materials include training videos for educators for each instructional block that demonstrate instructional routines, strategies, and "High-Leverage Practices." The training videos assist teachers in developing a conceptual understanding and anchoring key ideas to Math 180 strategies and interactive visual models. The materials include Boost and Stretch lessons that provide additional practice for students to see the big ideas and importance of what they are learning. These lessons provide prompts and guidance for educators to develop understanding of the concepts. Educators are guided to highlight and connect key patterns, features, and relationships—such as number properties, place value, and operations—through multiple means of representation, including visual models, manipulatives, verbal explanations, and symbolic notation. The materials include a "Teaching Guide" where teachers are given direct prompts and guidance to activate prior knowledge. The "Teaching Guide" also provides scripted questions and prompts that model thinking during the "Model" and "Guided" teaching sections. These questions and prompts are used to highlight key patterns, features, or relationships from the lesson.

Evaluation for 3.2b
If designed to be static, materials include educator guidance for effective lesson delivery and facilitation using various instructional approaches.

This guidance is not applicable because the program is not designed to be static.

Evaluation for 3.2c
Materials include multi-tiered intervention methods for various types of practice and structures and educator guidance to support effective implementation.

mSpace provides guided, collaborative, and independent practice in various stages of the lessons. These tools can be used with the whole group, small groups, or individually. The "Teaching Guide" provides guidance to support when to change structure and effective implementation. The online materials include student access to the "Learn Zone," where students actively and independently practice and master the mathematics of each application lesson. The materials include CheckPoint days during which teachers deliver multitiered, differentiated instruction. These sessions offer various types of practice, review, and lesson extensions to meet students' diverse needs. Boost lessons rebuild key concepts and allow students to make sense of the lesson, and Stretch lessons challenge students with nonroutine problems. These lessons can be used in small groups, pairs, or individually. The materials include an index of all differentiated instruction lessons. The index explains the different types of differentiated lessons included and the purpose of each, allowing teachers to develop a more individualized approach for each student. The index also includes step-by-step instructions on how to deliver the lessons.

Evaluation for 3.2d
Materials include enrichment and extension methods that support various forms of engagement, and guidance to support educators in effective implementation.

In the "Learn Zone" and "Brain Arcade," activities are available for students to extend and enrich their understanding. While in the "Learn Zone," students can "Fast Track" lessons they already understand to continue working at their level. In the "Brain Arcade," each game has chapters that are leveled for students to work at their appropriate level and continue growing beyond. The materials include "Resources for Differentiation" in each lesson block, where educators are provided with guidance on how to implement the tools to enrich and extend student understanding. The Math 180 Program Guide provides educator guidance on how to effectively implement the online student application alongside the textbook, including both an overview of the entire program and detailed explanations of each of the sections and how to use them for targeted enrichment and practice. The materials include Stretch lessons that provide enrichment for students who have mastered a grade-level topic. The "Teaching Guide" provides educators with detailed strategies and resources to effectively implement the Stretch lessons. The materials include Stretch and Step-Up lessons that are used as extension and enrichment activities. These lessons provide nonroutine activities and extend students' understanding of the content. Each lesson has a teacher key with guidance on how to facilitate these lessons and guided questions to ask students. Students can complete these lessons in small groups, pairs, or individually.

Evaluation for 3.2e
Materials include prompts and guidance to support educators in providing timely feedback during lesson delivery.

At the end of each lesson block, the materials include an Exit Ticket. The question is related to the current lesson and provides educators with a script to introduce the check for understanding. However, it does not provide guidance on how to respond to students' responses. The materials include a "High-Leverage Practices" section in each lesson that provides teachers with questions and prompts to use while assessing student learning, as well as areas of possible misunderstandings. The following is an example from one of the "High-Leverage Practices": "IF students add numerators and denominators, THEN they may be relying on misconceptions or old habits." In the online student platform, students have the opportunity to work in the "Learn Zone." In the "Learn Zone," students work on problems for the current instructional block. If a student misses a step, a hint box pops up. If a student misses the step after the second attempt, an example problem appears. If a student misses the step after a third attempt, the correct answer is shown, and the student must enter it to move to the next step. The materials include structured prompts for educators to ask students throughout the lesson. These prompts ensure timely feedback for students and also help to keep students engaged. They also give educators an opportunity to address student understanding and any misconceptions. The materials include a "Success Zone." As students work through the program, teachers can monitor usage and performance. This allows educators to provide timely feedback to students. However, the program does not provide guidance or prompts to support teachers in providing feedback to students.

Evaluation for 3.3a
If designed to be static, materials include educator guidance on providing and incorporating linguistic accommodations for all 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.

This guidance is not applicable because the program is not designed to be static.

Evaluation for 3.3b
If designed to be adaptive, materials include embedded linguistic accommodations for all levels of language proficiency [as defined by the English Language Proficiency Standards (ELPS)], which are designed to engage students in using increasingly more academic language.

The materials include comprehensive supports to address four ELPS proficiency levels—Entering, Emerging, Expanding, and Bridging—throughout lessons and units. At the start of each unit, a clear language objective is provided, listing key math terms and academic vocabulary in both English and Spanish to support foundational understanding for all learners. For Entering (Pre-production and Beginning) students, the materials guide teachers to introduce vocabulary with modified sentence stems and choral responses, helping students engage with new terms through repetition and modeling. The use of bilingual supports, including a language toggle and closed captioning on videos, along with text-to-speech options, further facilitates comprehension at this level. At the Emerging (Intermediate and High Intermediate) level, students build on vocabulary by practicing answers using sentence stems and engaging in choral repetition before progressing to more independent use of academic language. Teachers are provided with specific guidance in the "Language Support at a Glance" document to scaffold this development effectively. For Expanding and Bridging (Advanced) learners, minimal teacher guidance is provided. This encourages students to independently use sentence stems and participate in verbal discussions, such as Turn and Talks, to share their reasoning and explanations, promoting higher-order academic discourse. Additionally, throughout lessons, students have access to an interactive glossary in the "Learn Zone," where they can independently look up unfamiliar terms in English or Spanish, supported by definitions and visual representations. This tool promotes ongoing vocabulary development and supports students across all proficiency levels as they engage with mathematical concepts.

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

The materials include a focus language expectation outlining the ELPS that are addressed and provide strategies and scaffolds for educators to use for a specific block. The materials include a "Language Support at a Glance" document at the beginning of every instructional block that includes suggested sentence stems and suggested differentiation. The materials include a "Language Development" guide, which provides information for teachers on how to implement language development in class. The guide explains the different inclusions in the program for language development, such as vocabulary routines, language goals, sentence frames, and partner talk. The materials include a "Language Support" section in the Program Guide. This section discusses teacher implementation of language supports for each learning block. It also explains how to implement the purpose of each task and how to make sure that students are able to grasp and understand the necessary academic language. The Math 180 Program Guide includes a language development one-pager that describes the importance of language development in the classroom and how the Math 180 program supports language development. The materials provide guidance on strategies to promote discourse that, in turn, supports language development in the classroom, like whole-class discussion and choral response. The "Teaching Guide" provides examples of where language supports can be found in a lesson and their intended use.

Evaluation for 3.3d
Materials include embedded guidance to support emergent bilingual students in developing academic vocabulary, increasing comprehension, building background knowledge, and making cross-linguistic connections through oral and written discourse.

Lessons include introductory videos emphasizing key vocabulary (e.g., coefficient, expression, etc.), Think-Pair-Share routines, and "Math Talk" discussions. Students compare strategies, explain reasoning, and connect concepts, like integer operations, to real-world contexts, building academic vocabulary, comprehension, and background knowledge orally. "Success Zone" activities, Exit Tickets, Guided Practice, and practice journals, require students to define key terms, justify solutions, and explain problem-solving processes in writing. Graphic organizers and contextual prompts (e.g., temperature changes and elevation) support comprehension and background knowledge through written tasks. "Language Support at a Glance" guides teachers to leverage Spanish cognates (e.g., evidencia [evidence] and fracción [fraction]), highlight phrasing differences across languages, and encourage students to compare solutions using their home language. Supports include opportunities for students to share responses both orally and in writing, addressing crosslinguistic connections in a structured way.

Evaluation for 3.3e
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 throughout learning pathways (including instructional assessments) require students to demonstrate depth of understanding aligned to the TEKS.

Throughout each block of the unit, the materials prompt students to practice problems that encourage the use of multiple representations to demonstrate their understanding. After completing these practice problems, students take a CheckPoint that provides additional just-in-time support for their learning. Within each learning block, the concepts are broken down into lessons that include several opportunities for students to work through mSpace and answer questions. Each lesson ends with an Exit Ticket, which assesses students' knowledge learned within each lesson and varies in both complexity and item types. Each learning block ends with an mSkills assessment that includes 20 questions of varying complexity and item types. The materials include a "Brain Arcade," which includes interactive games and activities for students to practice and demonstrate their skills and depth of knowledge across multiple topics. The materials include Performance Tasks for students to apply their depth of understanding by solving real-world problems. The Performance Tasks include analyzing data, answering prompts, and evaluating completed work.

Evaluation for 4.1b
Questions and tasks, including enrichment and extension materials, increase in rigor and complexity, leading to grade-level and above grade-level proficiency in the mathematics TEKS.

Within the mSpace materials, each instructional block includes Performance Task enrichment opportunities that increase in rigor and complexity, leading to grade-level proficiency in the math TEKS. These tasks follow a problem-solving model, which enables tasks to be extended, allowing for a comprehensive understanding of the standard. The materials include Stretch lessons for students who have demonstrated grade-level proficiency in a particular topic. Stretch lessons allow students to demonstrate learned skills and engage with above-grade-level work in the "Challenge" section of the lesson. The materials include the "Success Zone," which offers a review of the topic learned to test student knowledge of the material through a Jeopardy-style game. The questions asked in the review increase in rigor and complexity as the point value increases.

Evaluation for 4.2a
Materials demonstrate coherence across concepts horizontally within the grade level by connecting patterns, big ideas, and relationships.

The materials include a "Block at a Glance," which provides an overview of how the different lessons progress throughout the unit. The materials include a "Learning Progressions" section at the beginning of each unit that states the identified learning target for the unit. The learning target is then broken down into prerequisite, current, and upcoming objects of skills that horizontally build across the program and target the progression of the skills. The materials include a "Program Overview" in the Math 180 Program Guide that lists each instructional focus statement that is then broken down into blocks, topics, and lessons, with attached procedural and conceptual focus statements listed for each lesson. This visual tool allows teachers to see both the horizontal and vertical progression of skills across the materials. The materials include Do Now to engage students, activate prior knowledge, and review previously learned skills. Do Now is also used to prepare students for new learning. Students then connect previously learned concepts and build on those skills during "Concept Lessons" and "Problem-Solving Lessons."

Evaluation for 4.2b
Materials demonstrate coherence vertically across concepts and grade bands, including connections from grades 3–12, by connecting patterns, big ideas, and relationships.

The materials include a "Progression to Algebra" that outlines what students will do in the current unit and what skills will follow. The materials include a "Program Overview" in the Program Guide that lists color-coded concepts to show relationships across grade levels. The materials include a "Program Matrix" that shows a well-structured progression of mathematical concepts and breaks each concept down into different blocks and lessons. The Math 180 Program Guide includes an outline of vertical alignment across grade levels. The guide provides a summary of how skills build and evolve from one grade level to the next.

Evaluation for 4.2c
Materials demonstrate coherence across lessons or activities by connecting students’ prior knowledge of concepts and procedures to the mathematical concepts to be learned in the current grade level and future grade levels.

The materials include a "Progression to Algebra" section that outlines prerequisite skills students are expected to have mastered prior to beginning the unit. Following the progression is "Topic at a Glance," which shows what topics will be taught in the unit. The materials do not explicitly indicate when a skill progresses into the next grade-level TEKS within a unit. The materials include a lesson breakdown in each "Teaching Guide" that gives teachers information about what they are teaching, prompts, and more. Many of the lessons include a Connect question that is intended to help students make connections between prior learning and what the current learning objective is for the lesson. The Connect questions vary across lessons and address both conceptual and procedural learning depending on the question given. Lessons are designed to activate prior knowledge connected to prior learning through the daily "Do Now." As the lesson progresses, multiple opportunities are provided to practice the skill designed to be on grade level. As students continue through the blocks, the lesson proceeds to above-grade-level understanding. The materials include a Stretch lesson after each instructional block to challenge thinking beyond the targeted focus concept. In the teacher key of a Stretch lesson, suggestions are given to teachers to prompt prior knowledge of the current or previous units so that students can apply their knowledge to the more challenging problem to solve. Additionally, language or vocabulary prompts are given to access prior knowledge, as well as a "Listen Strategy Bank" and additional extension opportunities. These address both conceptual and procedural learning within the focus concept, depending on the question asked.

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

The materials include a Do Now question at the beginning of each lesson, which are designed to engage students at the start of each lesson. These activities involve quick, focused tasks that help students review previous concepts and prepare for new learning. They serve as a warm-up to activate prior knowledge and set the stage for the day's instruction. The materials include a "Concept and Problem Solving" section in each unit. These sections contain problems to allow for continual assessment of progress and allow students to make connections to previous learning. In the online student platform, students can work in the "Learn Zone," "Success Zone," and "Brain Arcade" to practice what has previously been taught or what the diagnostic determined that they should practice. The materials include a "Game Lesson" two to three times within each instructional block. In "Game Lessons," students engage in collaborative practice to help build fluency and flexibility with learning objectives from "Concept Lessons." These games often review previously taught concepts while also including new instructional focus concepts. The end of each block includes a Card Sort and a Sum It Up activity, each of which allows for review of key concepts and vocabulary learned throughout the block.

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

The online student application includes a "Brain Arcade" with access to 11 different engaging games for students to play at any point. The games are designed to target several instructional blocks and chapters, with many different concepts included within each game. The Math 180 Program Guide has a description of each game and a list of the skills that are targeted for each game. The materials provide students with interleaved practice in the "Success Zone," where students can review information they have learned in each topic. The "Success Zone" is a Jeopardy-style game where students earn points for each problem answered correctly. The materials include Performance Tasks at the end of every instructional block that measure students' ability to integrate knowledge and skills across multiple standards. The tasks require mathematical expertise, strategic thinking, reasoning, collaboration, and writing. These Performance Tasks often require the use of multiple mathematical skills from several different prior lessons in order to complete the entire task proficiently. The "Learn Zone" provides students with opportunities to practice newly learned skills and concepts. Students practice scaffolded problems based on performance. Students are then moved to the "Master" level to demonstrate proficiency of the skill learned.

Evaluation for 5.1a
Questions and tasks provide opportunities for students to interpret, analyze, and evaluate mathematical concepts and complex, real-world situations.

The materials include several problems throughout the curriculum that allow students to use multiple strategies and provide opportunities to demonstrate learning in a variety of ways, including modeling answers, explaining or justifying answers, using numbers to solve, interpreting information, and evaluating their own learning. The materials include different instructional routines, including Turn and Talk, Question Chains, Answers Up, and Think-Pair-Share. These routines allow students to analyze and evaluate, enhancing their critical-thinking skills. The materials include simulation Performance Tasks in the "Explore Zone" of some blocks, where students perform a simulation, such as designing an aquarium, using the skills they learned in that block. This provides students with the opportunity to interpret, analyze, and evaluate a model using a real-world situation. The Math 180 Program Guide describes the use of the "Explore Zone" within the Math 180 program. The "Explore Zone" is used for students to engage with a simulation before a topic is introduced. In the simulation, students are given real-world problems and plan, create, and execute their plan to meet designated simulation goals.

Evaluation for 5.1b
Questions and tasks provide opportunities for students to create concrete models and representations of mathematical situations.

The materials include opportunities for students to use concrete models of mathematical situations. For example, in the "Fractions Series," students use a fraction number cube and fraction pieces to play a partner game of creating fractions to cover a one-whole fraction strip. The materials include the "Learn Zone" in the student application, which includes questions and problems to solve that direct students to create and manipulate model representations. Students have the ability to actively build math models, such as creating a fraction bar to find equivalent fractions. The materials include practice problems and examples that allow students to use and create pictorial representations and concrete models. Students can draw and build models to show a visual representation of their thinking. In the "Fractions Series," students play a game in which they use a concrete model to create equivalent expressions. Students use physical fraction pieces (provided in the Game Box) to create an equivalent expression to one whole.

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

Through the Worked Example, Try It, Guided Learning, and Practice problems, students have the opportunity to explain their thinking, model the problem in various ways, and connect ideas using estimation. The materials include the "Brain Arcade," which allows students to apply learned skills in a fun and engaging game. The "Brain Arcade" is a series of math games designed to help students become fluid, fluent, and flexible with important skills within and extending beyond Math 180 lessons. The "Brain Arcade" is the destination for meeting fluency standards and offering practice with facts, multi-digit operations, inverse relationships, unknowns, properties of numbers, integers, and more. The materials contain a Performance Task at the end of each block. The Performance Task gives students the opportunity to use what they have learned in a real-world application, allowing them to develop their conceptual understanding of the skills they have learned. The materials include simulations in the "Explore Zone." Each simulation presents students with a real-world problem or task to complete. Students use the concepts they have learned to complete the simulation. Students can transfer their mathematical knowledge to build critical-thinking skills and make real-world connections.

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

Within mSpace, students work on practice problems, which include a series of steps to complete the question, providing students with an opportunity to show their understanding and thinking. Students develop fluency in their skills by thinking through the problems in various ways and by using different visuals. The materials include access to the "Brain Arcade" in the student platform. The "Brain Arcade" allows for both fluency and automaticity practice in 11 different games that target facts, multi-digit operations, inverse relationships, unknowns, properties of numbers, and integers. Each instructional block ends with a "Game Lesson" that allows students to play math-based games related to the current topic. Students build automaticity through the repetition of solving the problems in the games. The games also help make learning more fun and interesting, increasing student engagement.

Evaluation for 5.2b
Materials provide opportunities for students to practice the application of efficient, flexible, and accurate mathematical procedures throughout learning pathways.

The materials provide students in grade 6 with opportunities to practice the application of efficient, flexible, and accurate mathematical procedures throughout learning pathways. The "Learn Zone" offers scaffolded practice that supports efficiency and accuracy through step-by-step guiding questions. For example, in "Proportional and Linear Relationships," Block 1, Lesson 1, students solve percent problems using double number lines, estimation, and part-to-whole ratios. While these methods are modeled within the lesson, students also encounter different representations across multiple problems, such as tables and tape diagrams, encouraging flexible thinking as they select appropriate strategies to solve similar types of problems. Additionally, the "Brain Arcade" offers games that require students to apply efficient and accurate mathematical procedures. Although the games have structured rules, students must make independent decisions about strategy use—such as whether to apply estimation, proportional reasoning, or standard algorithms—depending on the problem context.

Evaluation for 5.2c
Materials provide opportunities for students to evaluate mathematical representations, models, strategies, and solutions for efficiency, flexibility, and accuracy throughout learning pathways.

Math 180 includes "Find or Fix" and "Who's Right?" questions in the "Success Zone." These questions specifically prompt students to review solved problems, identify errors, and determine which strategy or solution is correct, allowing them to evaluate both the accuracy and efficiency of different solution methods. Throughout lessons, students engage with various mathematical models and strategies, including double number lines, tape diagrams, tables, and equations. For example, in the "Proportional and Linear Relationships" Topic, students are asked to compare different ways of solving the same ratio or percent problem, supporting both flexibility and efficiency. Stretch and Step-Up lessons ask students to analyze another person's reasoning or solution to a problem. Students must express agreement or disagreement and justify their thinking, reinforcing evaluation of accuracy and encouraging consideration of flexibility and efficiency in approach.

Evaluation for 5.2d
Materials contain guidance to support students in selecting the most efficient approaches when solving mathematics problems.

The materials include a Program Guide that outlines a conceptual and procedural focus for each topic. The Program Guide includes the singular strategy that will be used during the lesson but does not provide educator guidance on supporting students with other strategies. The materials include an adaptive student application where students have access to the "Explore Zone," "Fast Track," the "Learn Zone," and the "Success Zone." While students have choice in the pathway they work on within the online application, they are limited to what they have been assigned and must show mastery before advancing. The tools that are built into the application are limited to demonstrating one way to solve the skill. The materials include guidance and prompts for teachers to show students how to use a specific method for solving problems involving practice. However, multiple methods are not provided for students to choose from in any given question. The materials include the "Learn Zone," which provides instant feedback. When a question is answered incorrectly, prompts guide students toward the correct solution. However, students are required to use a specific method and are not permitted to use their own problem-solving strategies. The "Teaching Guide" provides step-by-step instructions for teachers to help students with solving math problems by breaking them down into smaller, easier-to-understand steps. It provides guidance for educators on teaching students different strategies to solve the problems. However, the materials do not help students determine the most efficient way to solve the problems.

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

In the Math 180 Program Guide, the procedural and conceptual focus is named for all the topics in each series. The Math 180 Program Guide includes a "Learning Matrix," which breaks down each instructional block into the conceptual and procedural focus areas of each lesson. The materials include a TEKS Alignment Guide, which includes a listing of all the TEKS covered and the lessons in which they are covered. The Alignment Guide also provides questions or activities within the program that align with each specific grade-level TEKS. The materials provide "Math 180 Progress Updates" for families that highlight students' conceptual and procedural understanding and alignment with the conceptual and procedural emphasis of the TEKS. The components work together to support how the conceptual and procedural empahsis of the TEKS are addressed.

Evaluation for 5.3b
Questions and tasks provide opportunities for students to use concrete models, pictorial representations, and abstract models as required by the TEKS.

The materials include frequent use of pictorial representations, such as double number lines, graphs, and tables, to represent information aligned to the TEKS. The materials include opportunities for students to digitally manipulate abstract visuals that align with their understanding of pictorial representations. The digital component also shows concrete models being manipulated, but it does not have students use the tools. In the instructional blocks of the "Fractions Series," students have opportunities to use concrete models, such as fraction strips and fraction bars; pictorial representations, such as digital fraction pieces, number lines, and fraction strips; and abstract models, such as less-than and greater-than symbols. In the online student dashboard, students have access to mTools, which include digital manipulatives, such as number lines and fraction pieces. The materials include the "Learn Zone," which uses interactive models and pictorial representations, such as fraction tiles, decimal grids, and bar models, to represent mathematical ideas.

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

The materials include a digital component where students have the opportunity to watch video representation models connected to abstract concepts. Students then create and apply their understanding through application to similar problems. In the "Fractions Series," Block 1, Topic 2, Lesson 3, students play a game called "Fraction Action." Students use concrete fractions pieces to generate equivalent fractions by rolling a concrete fractions cube. Students use concrete models to connect abstract concepts. Students must use the tiles and a fractions dice to remove or exchange tiles to make an equivalent fraction shown on the dice. Then, students explain how they generated the equivalent fraction. In the Exit Ticket for this lesson, students use a representational model that mimics the game played during the lesson. Students use the model to explain their thinking regarding creating an equivalent fraction from the given question and model. In the online student dashboard, students have access to mTools, which include digital manipulatives, such as number lines and fraction pieces. Students use these tools alongside given models and pictorial representations to help answer questions. The materials include Boost lessons that direct students to solve problems by using models. The lesson starts with a review of the material, using a model as reference, then engages students to use the model to solve. The Boost lesson goes on to direct students to practice the skills by writing their own abstract equation based on the model. The materials include the "Learn Zone," which includes problems for students using concrete and representational models. The "Learn Zone" gives students a concrete model and asks them to create or complete a given problem. In the "Rates and Ratios Series," Block 3, Topic 3, Lesson 5, students are given a problem-solving lesson where they create representational models to express ratios in different forms. Students use the representational models they created to help answer questions about multiple representations of ratios. The representational model helps students with abstract concepts.

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

The materials include a video to introduce the concept of the lesson. The video is rich in academic vocabulary and displays the terms, reads them aloud, and connects the math concept to the terms by replacing the academic language with a problem to solve. The materials provide strategies to engage students in the use of academic language. In the Program Guide, the "Research Foundations" provide guidance for educators using the strategies. The "Teaching Guide" notes the appropriate times to use the strategies. The Think-Pair-Share, Turn and Talk, and "Vocabulary" strategies provide students with an opportunity to share aloud with their classmates and use mathematical language. Each lesson in the "Teaching Guide" includes a vocabulary section that defines new mathematical terms and directs teachers on how to introduce that vocabulary to students. The "Teaching Guide" also includes a language development section in each lesson to clarify the context in which these mathematical terms are used throughout the lesson and in mathematical language. The materials include online student access to the "Learn Zone." One of the tools available to students in the "Learn Zone" is the "Glossary," which is a searchable bank of mathematical terms that students can access at any time while working within the "Learn Zone." When students select a term in the "Glossary," they receive a definition in both English and Spanish, an audio recording of how to pronounce the word, and a visual example of the word. The materials include a "Language Goals" section in each lesson. Each lesson includes a list of mathematical terms that are used in the lesson. Throughout the lesson, the materials direct teachers on when and how to incorporate the vocabulary to ensure student understanding of key mathematical concepts. In the "Decimal and Integer Series," Block 1, Topic 2, Lesson 1, students have opportunities to develop their academic language when writing integers in expanded and word forms. During the lesson, students receive an integer and a visual of each digit in its respective place value. The vocabulary words place value, thousandths, and ten thousandths are highlighted for students to see where the place value is in number form. Teachers prompt students to name the digit in each place value. Students practice identifying place value and writing out the word form of integers in the independent practice and Exit Ticket of this lesson. In the "Linear and Nonlinear Functions Series," Block 1, Topic 2, Lesson 1, students are introduced to lines of symmetry and reflection on a coordinate plane. Students are provided with a visual of a figure of a coordinate plane that has the line of symmetry labeled. The "Teaching Guide" provides teachers with scaffolded questions to ask students, such as the following: "What would a reflection of this figure look like?" "What are the coordinates of point ___?" "What quadrant is the figure located in?" These scaffolded questions provide students with the opportunity to practice and develop academic vocabulary. Later in the lesson, during the guided instruction, students are tasked with filling in the blanks to describe the reflection of a figure. In the independent practice and Exit Ticket of this lesson, students are asked to describe the reflection of a figure using vocabulary from the lesson.

Evaluation for 5.4b
Materials include embedded educator guidance to scaffold, support, and extend students’ use of academic mathematical vocabulary in context when communicating with peers and educators.

The materials include "breakouts" throughout the lessons, providing educator guidance on where key vocabulary should be introduced, opportunities for language development, and how to use visuals to build understanding. The "breakouts" support all learners, connecting academic terms to strengthen the relationship between math terms and concepts. Each instructional block in the "Teaching Guide" includes a "Professional Development" section for educators, which provides guidance on the upcoming block. The "Professional Development" section includes the Math 180 strategy that will be used to solve the given problems within the unit, as well as all mathematical terms that will be used and their definitions and visual examples. Each lesson includes explicit instructions for teachers on how to scaffold and support students' use of mathematical language. Each lesson plan lists vocabulary words for students and explains when and how the supports for these words are to be used in the lesson. The materials include instructional videos that are integrated within each lesson. The videos provide information about the lesson and a demonstration of the types of problems that are being studied. The videos also include a discussion of the vocabulary used in the lesson, which provides an extension of knowledge of mathematical vocabulary by use of visual depictions. The materials include prompts to facilitate Turn and Talks during the lessons. The "Teaching Guide" provides teachers with scaffolded prompts to ask students during Turn and Talks and throughout different parts of each lesson. The "Teaching Guide" provides academic vocabulary for teachers to introduce to students and prompts teachers to provide visuals to students, modeling the use of academic language through scripted responses. The materials include prompts and scaffolded questions to support student use of academic vocabulary. The "Teaching Guide" provides guidance on reviewing key vocabulary and gives scripted responses to model vocabulary use. At the end of each lesson, students have the opportunity to work with a partner and use the academic vocabulary to write responses to explain their answers. The "Teaching Guide" provides scaffolded questions to prompt students' written and verbal responses when answering independent questions.

Evaluation for 5.4c
Materials include embedded guidance to support student application of appropriate mathematical language and academic vocabulary in discourse.

The materials include the instructional strategies "Vocabulary," Turn and Talk, and Think-Pair-Share, which encourage students to use academic language to demonstrate understanding. The "Teaching Guide" provides teacher guidance on student discussion in the classroom and activities to practice using mathematical language. In Block 1, Topic 2, Lesson 2 of the "Fractions" Unit, Think-Pair-Share is suggested to discuss different combinations of fraction pieces that could be used to create a given sum. Additionally, "High-Leverage Practices" are given to further this conversation by providing guidance, such as the following: "If students struggle to create an equivalent fraction row, then help them by starting to solve the problem and let them engage as understanding occurs." The "Teaching Guide" includes guidance for teachers to encourage students with sentence frames or provide suggestions, such as the following, when students are asked to explain their answers or ideas: "The answer ____ is right because ____." The materials include a Do Now section for each lesson, which is designed for students to demonstrate what they have learned and provides an explanation for their answer. The explanation section provides sentence stems that act as prompts to help guide students in using precise language. The materials provide guidance to support student application of appropriate mathematical language and academic vocabulary throughout lessons by offering possible student answers to questions. For example, in the "Rates and Ratios Series," Block 2, Topic 2, Lesson 3, Do Now, students describe everything they know about a picture of purple and orange squares. The Do Now provides students with an opportunity to use mathematical and academic vocabulary to explain their answer to the provided questions using a sentence stem. The "Teaching Guide" provides possible student answers to help teachers guide students to use appropriate mathematical and academic vocabulary.

Evaluation for 5.4d
Materials include embedded guidance to facilitate mathematical conversations allowing students to hear, refine, and use math language with peers.

The materials include guidance in the "Teaching Guide" in each lesson, with suggested questions, conversations, and examples to enhance student learning of the content. In the "Fractions" Unit, Topic 1, Lesson 1, Turn and Talk is suggested to have students discuss how to determine if equivalent fractions are equal to the same value. Before this activity, guidance was given on equivalent fractions and how to introduce that vocabulary to students. Each instructional block in the "Teaching Guide" includes a "Professional Development" section for educators to receive guidance on the upcoming block. The "Professional Development" section includes a "Language Goals" section that defines what mathematical language should be used by students during the unit, how it should be used, and other academic words that might be used in addition to the math term. The vocabulary is given in both English and Spanish. The materials include instructional routines embedded in each lesson. For example, Turn and Talk and Think-Pair-Share are designed to give students the opportunity to facilitate mathematical conversations with peers, which enhances students' listening and speaking skills. The materials include a "Topic at a Glance" section for each topic, which features a "Language Goals" section that lists both mathematical vocabulary and relevant academic language. The "Language Goals" section gives students the opportunity to view the academic language, refine it, and use it to meet the language goals. The Math 180 Program Guide provides guidance to facilitate mathematical conversations in the classroom. The Program Guide gives detailed explanations of Think-Pair-Share, Turn and Talk, and "Question Chains." It provides teachers with guidance on when to use these strategies, models of what each strategy can look like, and implementation tips. At the end of each block, students receive a Sum It Up lesson to review key concepts and vocabulary from the block. The "Teaching Guide" provides guidance on how to structure the lesson and how to instruct students to facilitate discussions while answering the provided discussion questions. Each discussion question has a sentence stem for students to use. The "Teaching Guide" provides instructions to assign students into four roles: Facilitator, Reader, Time Keeper, and Presenter. The guide explains the responsibilities of each role and provides sample prompts for students to use during their discussions. The Sum It Up lesson allows students to hear, refine, and use mathematical language.

Evaluation for 5.4e
Materials include embedded guidance to anticipate a variety of student answers including exemplar responses to questions and tasks, including guidance to support and/or redirect inaccurate student responses.

The materials provide an exemplar response for each activity as well as answer keys for assessments, which include rationales for students who selected the incorrect answer on multiple-choice questions. Rationales provide embedded supports to teachers regarding the anticipation of students' answers and guidance as to why students may have chosen the incorrect answer. Assessments are provided at the end of each block, yet guidance for students misunderstanding the concept during activities is not included. The materials include a "Think Video" in the online student platform that models a similar problem. When an incorrect answer is given, a pop-up is provided that has a similar problem worked out step-by-step. The materials have supports to help students be successful, yet they do not identify the root cause of the misunderstanding or support students beyond solving the problem in a similar context. The materials include guidance in the "Teaching Guide" at the beginning of each lesson, with suggested questions, conversations, and examples that could be used to enhance student learning. Each lesson includes exemplar student answers to key questions and tasks (in blue), along with teacher prompts and suggested feedback for addressing common misconceptions or errors. Additionally, the "High-Leverage Practice" in each lesson provides suggestions for "if/then" statements if a student is struggling with a particular concept. In the "Linear and Nonlinear Functions Series," Block 1, Topic 1, Lesson 3, the materials provide "if/then" scenarios to address misconceptions as well as guidance on how to modify the task if needed. Teachers receive explicit directions on how to address a misconception through a guided example of graphing ordered pairs on a line to check if their solution is positive or negative. Teachers are given an alternate strategy to show students how to determine patterns in a table. The materials include answer keys and rationales for each assessment given from the textbook in mSpace. Each question includes all answer-choice rationales as well as a justification for the correct answers, enabling teachers to anticipate common misconceptions, understand the reasoning behind student errors, and respond effectively.

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

The materials highlight a "Mathematical Thinking" strategy throughout each lesson and specify how the concept connects to the strategy. The strategy "[h]ow to make use of structure" makes connections for educators to select appropriate tools. The Math 180 online student platform integrates the TEKS process standards by beginning each lesson in the "Learn Zone" with an instructional video that models key mathematical skills and thinking strategies. Students then engage in repeated, interactive practice that supports the development of reasoning, pattern recognition, and other essential habits of mathematical thinking. This structure ensures that process standards, such as problem-solving, reasoning, and making connections, are embedded throughout the learning experience. The materials include the integration of the TEKS process standards in the "Learn Zone." In the "Learn Zone," students complete repetitive practice that supports reasoning, pattern recognition, and other TEKS process standards. Each lesson includes a Do Now and an Exit Ticket question, which prompt students to use multiple TEKS process standards, such as problem-solving and communicating mathematical ideas. The materials provide students with opportunities to apply the TEKS process standards through problem-solving lessons. For example, in the "Rates and Ratios Series," Block 2, Topic 1, Lesson 1, students are given a real-world problem to solve using rates and predictions. Students are asked to analyze data, create a model, explain their reasoning, and make predictions based on their work. The materials provide students with opportunities to apply the TEKS process standards through Performance Tasks at the end of each block. The Performance Tasks allow students to analyze real-world problems, formulate plans, explain their thinking, and evaluate their work. For example, in the "Proportional and Linear Relationship Series," Block 3, Performance Tasks, students are prompted to determine the profitability of their business through a variety of scenarios. Students determine the revenue, cost, and profit; calculate the amount of time spent on their business to determine their rate per hour; and then use those to answer "Explain" and "Reflect" questions. The Alignment Guide indicates where each of the TEKS process standards is addressed in lesson materials. The Alignment Guide provides the process standard that is covered and where, which questions and tasks cover the standard, and a direct link to the lesson materials. While the materials do not reference the TEKS process standards explicitly, the ideas and concepts from the process standards are addressed in the materials.

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

In each topic, students experience a variety of the process standards throughout the lessons. Students are provided with opportunities to represent the same content in various representations, such as tables, graphs, and equation form. The content tied to problems relates to the real world, society, and the workplace. At the end of each block, students are given a Performance Task that provides a problem-solving model to follow. The Math 180 Program Guide includes educator guidance on how to develop, model, and reflect on mathematical thinking and reasoning within the content. Eight "Mathematical Thinking Skills" are given to achieve this within the content: "1. How to persevere and solve problems, 2. How to use tools strategically, 3. How to reason abstractly, 4. How to attend to precision, 5. How to construct viable arguments, 6. How to make use of structure, 7. How to model with mathematics, 8. How to use repeated reasoning." The materials include guidance at the beginning of each lesson on which "Mathematical Thinking Skills" will be used within each lesson. One or more skills from the predefined eight in the Program Guide will be used during the given lesson. At the beginning of each topic in a block, the "Teaching Guide" has a "Topic at a Glance" section that states the standards for each lesson. The standards are separated into "Mathematical Thinking" and "Grade Level Content Connections."

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

The materials provide the process standards, which are outlined with relevant activities. For each process standard, there are two resources linked. The resources link directly to a limited number of mSpace resources, but the interactive component includes similar problems. The Math 180 program includes a grade-level Alignment Guide that lists all the TEKS process standards and the ELPS that are covered in the content. It also provides direct links to each lesson that addresses the given standard. The materials explain how the TEKS process standards are incorporated into some lessons but do not indicate how they are incorporated into each lesson. The "Lesson Overview" in the "Teaching Guide" explicitly states the mathematical thinking skills, but it does not explicitly state the TEKS process standards.

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

The materials include educator guidance for students to think mathematically and make sense of mathematics, with guiding questions throughout the lesson. Students process the information provided and interpret how to use the tools to explain their solution. The materials include Performance Task activities at the end of every instructional block. These combine multiple mathematical concepts that were learned in the unit to encourage more complex mathematical thinking and help students make sense of mathematical concepts in a broader, more applicable way. The "Resources for Differentiated Instruction" activities included in each instructional block provide open-ended opportunities for students to think mathematically through challenging questions. The activities allow students to use more than one strategy to solve the problem. Students then receive more complex versions of the same problem and are challenged to find a solution using a different strategy. After they find the solution, students reflect on their answer and the strategies used. Guiding questions are included in the "Annotated Teaching Guide" to encourage students to think more deeply. The materials include Boost lessons at the end of each lesson. Boost lessons include open-ended word problems that promote students' use of mathematical thinking to solve math problems and include partially filled-in graphs and diagrams to help prompt students' thinking. The "Challenge" and "Reflect" questions at the end help students to make sense of and explain their thought process. The materials include the "Explore Zone," which gives students a simulation of a real-world situation. To solve, students must face the challenge presented and use strategies they have learned to solve the problem. These simulations prompt students to think critically and show their mathematical understanding by solving the problem. The materials provide opportunities for students to think mathematically, persevere through solving problems, and make sense of mathematics through Boost and Stretch lessons. Students solve nonroutine, open-ended problems and make sense of math by explaining their work. In Stretch Lesson 1A, students solve a multistep percent problem. When students are done solving, they reflect on their answer and explain their problem-solving process.

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

The materials include opportunities for students to compare multiple strategies to solve a similar problem. It is recommended that they look for patterns or write an equation to solve. Included teacher guidance for questioning during this process gives students the opportunity to explain. At the end of each activity, students have to "wrap it up" with a justification of how they can use the patterns to write an equation. The materials include a series of problems that scaffold upon each other (e.g., multiplying a one-digit number by another one-digit number, a one-digit number by a two-digit number, etc.). During the scaffolds, students model the distributive property both algebraically, using expressions, and visually, using rectangular area models. These scaffolds provide students with an opportunity to build an understanding of the property. Teachers receive guidance to prompt students to explain their understanding during the lesson, and at the end, students justify their thinking and reflect on how using multiple methods supports their learning. The "Resources for Differentiated Instruction" activities included in each instructional block provide open-ended opportunities for students to think mathematically through challenging questions. The activities often begin with a presented math problem and allow students to use multiple strategies to solve it, such as write an equation, draw a model, look for patterns, make a list, guess and check, work backward, or simplify the problem. Students then solve a more complex version of the problem using a different strategy and reflect on their solution and methods. Each lesson in the materials contains Exit Tickets, which include questions that ask students to solve a given problem and then either explain their answer or justify the strategy they used to solve the problem. The materials include a Performance Task at the end of each block, where students are prompted to solve problems and determine the result in multiple ways. The Performance Task provides students with a word problem and then a prompt and explanation on how to solve the problem.

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/or educators.

The student application includes interactive simulations that students work on collaboratively. The "Teaching Guide" suggests that educators play the simulations as a game and that students work together to do the math and determine a correct solution. When the class comes back together, the student groups justify their solution. The materials include lessons that incorporate collaborative learning strategies, such as Think-Pair-Share and Turn and Talk, to facilitate student collaboration with their peers. The Do Now activities, Guided Learning, Practice, and Card Sort often include structured partner activities that encourage students to verbalize their thinking, compare strategies, and clarify their understanding to their peers and teacher. Each of the lessons in the textbook contain Exit Tickets at the end of the lesson. The Exit Tickets often include areas where students are asked to solve a given problem and then either explain their answer or justify the strategy they used to solve the problem. Sentence frames are provided to support students in writing about their problem-solving process or choices. At the end of each block, the Sum It Up lesson gives students the opportunity to do, write about, and discuss math with peers. In the "Proportional and Linear Relationship Series," Block 3, students write and discuss vocabulary words learned throughout the block. Students solve problems that cover key concepts and have structured discussions about key concepts learned from the block. The materials provide Stretch lessons where students work with peers to solve problems related to a previously learned topic. Students are given open-ended questions to solve with a partner and are given the opportunity to reflect on their work by writing about how the methods they used helped them solve problems.

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

The materials include teacher guidance for the "High-Leverage Practices," with questions to ask that encourage students to justify and argue their understanding, such as "What are some advantages of using . . . ?" and "How could you use __________ to complete __________?" Students justify their understanding of math concepts during the "Analyze" stage in the Performance Task. Students explain their reasoning and reflect on the tools they used to complete the task. The materials include guidance in the "Resources for Differentiated Instruction" that includes questions, strategies, and responses to give students when working on Boost, Focus, and Stretch lessons. The questions, such as the following, ask students to justify their answer or strategy: "Why did you choose to solve the problem in this way?" and "If I changed the problem to say nine days instead of six days, would that change the way you solved your problem?" The materials include Exit Tickets at the end of every lesson in the textbook, which have students solve a problem and reflect on their thinking, justify their answer, or discuss which strategy was best to use. Additionally, Exit Tickets include several problems where students must compare the work of two different examples and write about which problem was solved correctly and why. The materials include a Do Now section in each lesson, which includes support for educators in guiding students to share their problem-solving approaches through targeted questions that elicit a response from students to explain and justify their answers. Students have the opportunity to share their answers as well as justify and reflect on their explanations. The materials include a Card Sort lesson at the end of each block. The Card Sort gives teachers tools that encourage students to solve problems using multiple strategies, offering opportunities to explain and argue their reasoning and then reflect on their thinking. In the "Rates and Ratios Series," Block 1, Topic 3, Lesson 5, students complete a problem-solving lesson where they use rates and ratios to solve a real-world problem. Students recall the different models learned in the unit and are asked to create two models to represent a situation. The "Teaching Guide" includes questions for teachers to ask that encourage students to discuss and reflect on the problem-solving strategies they applied. The guide provides questions, such as the following: "What types of visual models can be used?" and "Are there some situations where a table is more useful than a graph?" These questions allow students to share and reflect on their problem-solving approaches and allow for multiple points of entry.

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

The materials prompt teachers through a view of the student pages and give prompts for when to intervene if students are struggling, such as "If they are confusing this, try this." The materials include answer keys for all assessments given in mSpace. The answer keys include rationales for all multiple-choice problems. The following is an example of a given rationale on one incorrect answer for a question about whether a table is proportional: "The student may not understand how to get a ratio from an x/y table." The materials include a "High-Leverage Practice" section in each lesson that provides guidance to teachers on how to redirect students if they are answering questions incorrectly. The following is an example from a "High-Leverage Practice" box: "If students have difficulty expressing their answers, then help them draw a diagram for each object." The "High-Leverage Practice" also includes prompts for students who are struggling to understand and also for those who need a challenge. Prompt examples include the following: "How many intervals do you need to represent the time?" and "If both objects are moving at a constant speed, will the slower object ever catch up?" In the "Decimals and Integers Series," Stretch Lesson 3B provides guidance on how to address student responses. The guidance states that "if students struggle with subtracting integers, use an open number line," and provides a script on how to model using the number line. The guidance also provides scaffolded questions for teachers to ask throughout the lesson. The materials do provide guidance for when mistakes are made by providing hints to help students successfully answer problems.