Program Information
HMH Math 180 Texas Grade 5
Supplemental Math (English) Grade 5
IMRA 2025
Commissioner Recommended
Publisher: HMH Education Company
Copyright: 2026
Series includes:
Quality Review
Standards Alignment
Rubric Section
| Grade | TEKS Student % | TEKS Teacher % | ELPS Student % | ELPS Teacher % |
|---|---|---|---|---|
| Grade 5 | 100% | N/A | N/A | N/A |
Criteria for Quality
Rubric Section 1
Intentional Instructional Design
Materials support educators in effective implementation through intentional course, unit, and lesson-level design.
Total
91% (21 out of 23 points)
Evaluation for 1.1a
HMHMath 180includes anAlignment Guideforgrade 5, outlining the Texas Essential Knowledge and Skills (TEKS), the English Language Proficiency Standards (ELPS), and concepts covered with a path toward algebra readiness.Activities for a given TEKS or ELPS can be found by clicking a link under a given TEKS standardor ELPS in theMath 180Alignment Guide.
Evaluation for 1.1b
Math 180forgrades 3–5 includes aProgram Guidethat is presented at the beginning of the teacher-facing materials, which includes an implementation guide providing various structures in which the materials can be implemented. Examples include rotations, whole-group lessons, and shortened periods.Using adaptivelearning technology, the program is designed to provide every studentwith a personalized learning experienceeach time they log into their dashboard. Thisincludes situated instruction,problem-solving, and skill-centered digital games. One activitycalled"Brain Arcade" continuously adjusts the learning path based on student progress and includes differentiated real-world application tasks for students at different stages of learning.Each series contains a "Teaching Guide"thatprovideseducators with instructional strategies or optional lessons for use during small-group practice. Within the"Teaching Guide"for the "Decimals"Blockfor grade 5, there are "High Level Patterns of Practice" within each lesson, providing just-in-time support—especially addressing misconceptions and challenges—topersonalizeinstruction in small groups based on students' proficiency levels.
Evaluation for 1.1c
The HMH Ed website has an "Assessment Standards Report" that provides results from the "mSkills Assessments"for HMH Math 180 blocks in a series. The results are correlated to the TEKS. Educators can look at the TEKS and obtain a report on students that are below level, on level, and above level for a TEKS in a mathematics domain covered in HMH Math 180. These diagnostic results offer recommendations for skill entry points for the TEKS covered in the materials.
Evaluation for 1.1d
HMHMath 180forgrades 3–8 includes protocols with corresponding guidance for lesson and unit implementation. The"Teaching Guide"provides unit internalization by previewing the unit with key standards, unit objectives, vocabulary, materials, and assessments, as well as providing the learning progression.Activities are also included for students to complete within the learning progression, suchasDo Now,Guided Practice,Practice in Pairs,Exit Ticket,and High-Leverage Practices.These help teacherschallenge all levels in small groups. The"Teaching Guide"also has a process for educators to thoroughly understand and prepare to teach lessons, with annotations, checks for understanding, and success criteria. "Professional Learning" sections are provided in eachseries, explaining the learning progression and giving explanations and examples of strategies taught.
Evaluation for 1.1e
An "All About HMHMath 180"document is available in the "Program Support" section on the HMH Eddashboard,providingan overview of the program and instructions on how to use it in different classroom settings. TheProgram Guideoffers suggested instructional time frames that educators and coaches can choose to best fit the mathematical instructional day for their students and campus. It also includes multiple data analysis tools, such as mSpace Progress Monitoring and themSkills assessment.The guide also explains how to read and interpret testing data. Instructional leaders can use these resources to support team meetings and coach educators on how to continue using the materials as intended.
Evaluation for 1.2a
This guidance is not applicable because the program is not designed to be static.
Evaluation for 1.2b
Each lesson inMath 180contains objectives that are not explicitly stated in the language of the TEKS in the"Teaching Guide"; however, theAlignment Guideprovidesthe TEKS and ELPSfor lessons within the content for grade levels 3–5. Every lesson within ablockof aseriesbegins with a10-minute introductory video, followed by segments such as discussion, group lesson, guided group practice, partner practice, and an independentExit Ticketaligned with the lesson's objective. TheProgram Guideoffers a Flexible Implementation Model for different times and days for math lessonblocks that explain the Blended Learning Experience.On theMath 180dashboard, educators can browse "TeachersResources"materials by the TEKS number.The materials do include guidance on the ELPS expectations for assessments. The assessments align with the TEKS and ELPS within the scope of theMath 180program. TheMath 180Alignment Guideforgrades 3–5 lists the ELPS and TEKS numbers for lessons inaseries. The"Teaching Guide"for eachseriesincludes a language goal with mathematical thinking that is aligned to the ELPS. Some lessons in aseriesfeature "Language Support at a Glance" to assist multilingual learners. This document details the ELPS language expectations and offers strategies that leverage linguistic assets and differentiate by language for all proficiency levels included in the ELPS. Nonetheless, educators must understand how to apply this to other lessons within theseries.
Evaluation for 1.2c
The materials include strategies for supporting students and providing progress updates for families in English, but not in Spanish.Math 180for grades 3–5 communicates with families through letters in English that contain detailed suggestions on how they can support their students' understanding of the concept focus and procedural skills in eachblockof aseries. In the letter from the "MultiplicationSeries,"the teacher outlines instructional goals for both the teacher and students related to the procedural skill of multiplication. A list of strategies is provided, such as learning to use the factors of a number, with detailed graphics and mathematical language to describe the procedure being used.Math 180provides a "Math 180Progress Update" to support families in English—for eachlesson in atopicwithin aseries—regarding their student's progress.
1.1 Course-Level Design
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.
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.
5 out of 5 points
Evaluation for 1.1a
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.
5 out of 5 points
1.1b
Materials include an implementation guide with usage recommendations and strategies for effective educator use in various contexts, such as just-in-time supports, advanced learning, or as a course.
Materials include an implementation guide with usage recommendations and strategies for effective educator use in various contexts, such as just-in-time supports, advanced learning, or as a course.
3 out of 3 points
Evaluation for 1.1b
Evaluation for 1.1b
Materials include an implementation guide with usage recommendations and strategies for effective educator use in various contexts, such as just-in-time supports, advanced learning, or as a course.
3 out of 3 points
1.1c
Materials include a TEKS correlation guide with recommended skill entry points based on diagnostic assessment results.
Materials include a TEKS correlation guide with recommended skill entry points based on diagnostic assessment results.
2 out of 2 points
Evaluation for 1.1c
Evaluation for 1.1c
Materials include a TEKS correlation guide with recommended skill entry points based on diagnostic assessment results.
2 out of 2 points
1.1d
Materials include protocols with corresponding guidance for unit and lesson internalization.
Materials include protocols with corresponding guidance for unit and lesson internalization.
2 out of 2 points
Evaluation for 1.1d
Evaluation for 1.1d
Materials include protocols with corresponding guidance for unit and lesson internalization.
2 out of 2 points
1.1e
Materials include resources and guidance for instructional leaders to support educators with implementing the materials as designed.
Materials include resources and guidance for instructional leaders to support educators with implementing the materials as designed.
2 out of 2 points
Evaluation for 1.1e
Evaluation for 1.1e
Materials include resources and guidance for instructional leaders to support educators with implementing the materials as designed.
2 out of 2 points
1.2 Lesson-Level Design
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.
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.
0 out of 7 points
Evaluation for 1.2a
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.
0 out of 7 points
1.2b
If designed to be adaptive, materials include responsive learning objectives, lesson components with suggested timeframes, and assessment resources aligned with the TEKS and ELPS.
If designed to be adaptive, materials include responsive learning objectives, lesson components with suggested timeframes, and assessment resources aligned with the TEKS and ELPS.
Not scored
Evaluation for 1.2b
Evaluation for 1.2b
If designed to be adaptive, materials include responsive learning objectives, lesson components with suggested timeframes, and assessment resources aligned with the TEKS and ELPS.
5 out of 0 points
1.2c
Materials contain support for families in Spanish and English for each unit, with suggestions on supporting the progress of their student(s).
Materials contain support for families in Spanish and English for each unit, with suggestions on supporting the progress of their student(s).
2 out of 2 points
Evaluation for 1.2c
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).
2 out of 2 points
Rubric Section 2
Progress Monitoring
Materials support educators in effective implementation through frequent, strategic opportunities to monitor and respond to student progress.
Total
95% (19 out of 20 points)
Evaluation for 2.1a
Math 180provides aroad map that gives the assessment tool's name, as well asa description of the toolandits purpose, and informs teachers about what is being assessed.
Evaluation for 2.1b
TheMath 180Program Guideoffers clear guidance for consistent and accurate administration of themSkills assessmentsfound at the end of eachinstructionalblock.Before assessment assignments, reminders are included for students to review the Mindset Strategy,Card Sort,Sum It Up, and mSkills Strategylessons. Detailed instructions on how to assign themSkills assessmentsto students are provided. EachmSkills assessmenthas 20 questions of various item-type formats that canbe completed within a class period or a testing window, as directed by the teacher, to allow students to work at their own pace. Though the time it takes to complete the assessment varies, most students complete the test in 45–60 minutes. These clear guidelines allowstudentsto receive their assessment with the same instructions and testing environments, leading to more reliable and comparable results.
Evaluation for 2.1c
The materials do not include accommodations for content and language supports to be enabled or disabled to support individual students.Text-to-speech and calculator accommodationsareavailable in all program assessments. Each of the stated accommodationscanbe delivered to individual students or the entire class in all program assessments.There are printable PDFs available for the "Baseline I" and "Baseline 2"digitalassessments. ThemSkills assessmentsare provided in a printable version and are identical to the digital assessment. For example, the "Multiplication and DivisionSeries"contains a printable version of the mSkills Digital Assessment available to students online. The mSkills Digital Assessment can also be viewed on the HMHEdwebsite by clicking"Categories," then clicking"Assessments."By going to "ClassSettings" on HMH Ed, teachers can enable or disable the calculator for an individual student or the class.
Evaluation for 2.1d
Math 180includes diagnostic assessments with TEKS-aligned tasks or questions, including interactive item types with varying levels of complexity. Ingrade 5, Depth of Knowledge (DOK) 1: "Recall,"the items involve basic recall of math facts or procedures. The following areexamples:"Which fraction is equivalent to 6/8?"(requires recognition of equivalent fractions)"Which is another way of writing 3 ÷ 2?" (requires recognition of a fraction representing division)"Which temperature is the lowest?" (simple comparison of numeric value)InDOK 2: "Skills and Concepts,"the items require applying models or procedures in familiar contexts.The following are examples:"Pedro planted 6 rows of flowers. Each row had 18 flowers. Which shows how many flowers did Pedro plant?" (applies multiplication in a real-world context)"Jamila had 12 pencils. She lost 9. What fraction of her pencils did she lose?" (applies subtraction and fraction concepts)"Which model represents the sum of 0.5 + 0.29?" (requires interpreting a visual model to match a decimal sum)InDOK 3: "Strategic Thinking,"the items require reasoning across multiple steps or concepts. The following areexamples:"A car wash collected $320 to wash 25 cars and some trucks. Cars cost $8 and trucks $10. How many trucks were washed?" (requires setting up and solving a multistep word problem with reasoning about operations)"A bakery made 140 buns. A restaurant bought 80. The rest were bagged in groups of 4. How many bags?" (involves subtraction and division, with reasoning about quantities)TheMath 180mSkills Interactive Assessments offer multiple interactive item types, such as text entry, drag-and-drop, multi-select, and multiple-choice questions.
Evaluation for 2.1e
Math 180formative assessments have more than two levels of complexity, from DOK 1 to DOK4, and have more than two unique interactive item types of questions, such as ordering, select-all-that-apply, and fill-in-the-blank.ThePerformance Tasktitled "Fraction Concepts: Take the Chef's Challenge" contains varying question types and prompts that align with the TEKS in all four DOK levels. The instruction to "[f]ind groups of ingredients that you think would work well together in an appetizer, main course, and dessert" involves basic recall and categorization, aligning with DOK Level 1. Writing recipes using fractions and including ingredients from each food group reflects DOK Level 2, asthese tasksrequire the application of fraction concepts and moderate reasoning. The following promptmeets DOK Level 3, involving justification, strategic thinking, and clear mathematical communication:"Explain how 3/4 cup of milk could be split among two or three recipes. Include equations." Finally, "[r]ewrite one recipe so that it serves four people" exemplifies DOK Level 4, as it involves multistepproblem-solving, proportional reasoning, and reflection on how to adapt quantities for new conditions.ThroughoutMath 180learning pathways, students are provided with multiple scaffolded practice and assessment opportunities that are purposefully aligned to the TEKS. These activities progress in complexity, encouraging students to apply, analyze, and synthesize knowledge in ways that demonstrate deep understanding. Formative checks,Performance Tasks,and real-world problem-solving scenarios ensure that students engage meaningfully with TEKS-aligned content, which equips educators with actionable data that captures a broad range of student performance and understanding.
Evaluation for 2.2a
TheProgram Guide,under the"Assessment, Progress Monitoring & Data"section,instructseducators on how to interpret student performance on assessments, reflect on levels of understanding and proficiency, and provide direction on what students need next.The "Assessment Report" displays results from themSkills assessmentsfor theblocks assessed in a class. Results from this report are used to monitor student learning and provide ongoing feedback. Scoring provides teachers with a detailed breakdown of class and individual performance. The "Assessment Report" displays mSkills scores for all students.mSkills assessmentresults can be used to determine instructional pacing and to identifytopics and objectiveswith whichstudents experienced challenges. Teachers may confer about results with students, adjusting goals as needed.Results from the "Standards Report" evaluate student performance against the TEKS to help inform small-group instruction. The "Standards Report" can be customized to provide guidance on determining students' strengths, weaknesses, and gaps;identifyingcommon misconceptions;and setting performance goals in an Individualized Education Program.Math 180hasPerformance Tasksthat assess theapplication of learned skills, reasoning, planning, analysis, judgment, and creative thought. A scoring rubricprovidesclear guidelines for interpreting student performance and responses.EachmSkills assessmenthas an answer key that provides the "Assessment Rationales." These answer keys include a brief explanation of why each answer is correct or incorrect. For incorrect answers, the materials provide possible misconceptions. For example, in the "Decimals and IntegersSeries,"Block1mSkills assessment,Question 20 explains that Option D is incorrect because "[t]he student may not have recognized that having multiple different values on the pan balance denotes addition (between thenvalues and the 6.25) rather than multiplication."It explainsthat Option C is correct because "[t]he equation 8.45 =n+ 6.25 +ndirectly represents the pan balance." Arationale is included for each correct and incorrect response.
Evaluation for 2.2b
Math 180materials provide guidance for the use of student applications to respond to student trends in performance on assessments. The "Teacher's Corner" tab has a section under "Program Support." Within this area, there is an articletitled"Program Activity Report (PAR) for Math 180." This article instructs teachers how to analyze the data to inform instruction. Teachers can customize the"Program Activity Report" to monitor class or individual student performance in thestudentapplications. The materials include instructional guidance for tasks and activities to target various skills, as determined by assessment data. For example, teachers follow guidelines to group students based on assessment results and provide targeted activities to address specific skills.Math 180has a pathway for students to use based on performance data. Once students are placed in aseriesbased on assessment data, they proceed to the "Zone" menu, which displays the threezones, and the "Brain Arcade" thattheywill work in as they progress through ablock. Students must complete specific activities within a particularzone to unlock access to otherzones. Theystart inthe "Explore Zone," where they view theanchorvideo and completea simulation,thengo to the "Learn Zone" to complete tasks,andfinally moveto the "Success Zone." Once in the "Success Zone," students use their problem-solving abilities to apply learned concepts and skills.
Evaluation for 2.2c
The HMHMath 180Program Guideexplains how teachers are able to track class and student progress and growth data over time in adatatable. For Performance lessons, teachers can track the class needs and ensure that students' needs are being met. When discussing the importance of evaluating data from the student's view, theProgram Guidestates, "This personalized data is crucial for tailoring instruction to meet each student's unique needs and for tracking their progress over time."HMHEd is the educator dashboard that provides reports on student performance dataforthe different types of assessments, such as mSkills, and other student tasks. There isaclassoverview that tells educators how many students are considered "Not Yet" or "On Track."There is also a way to view individualstudentdata to see how to specifically help students.mSpace ProgressMonitoring is provided throughout the lessons as a formative assessment tool. Multiple opportunities for quick checks allow teachers to track student progress and growth, such as in theDo Now,practice activities, andExit Ticketwithin eachseriesandblock.Students can view their learning progress when they have a conference with their teacher, as the teacher shares with them the "Summary,""Performance," and "Brain Arcade"reports at the student level. Students do not have access to data trackers unless one is provided by their teacher. TheProgram Guidestates, "Compare these results with a teacher-created student log that students use to track their work (optional)." However, the materials do include a student progress tracker, both in English and Spanish, for eachseriesandtopicfor students to check off if they are in the"Learn Zone"so that theycan make it to the "Success Zone." Eachserieshas acertificate that is to be provided to students upon completion of the specificseries.Math 180does provide a student-friendly data tracker called "The Student Goal Setting Template," which is a reflection sheet that can be used with each assessment, allowing students to make note of their strengths and learning opportunities. The program encourages teachers to use the student-completed reflection sheets during one-on-one conferences with students to facilitate goal setting.
Evaluation for 2.2d
This guidance is not applicable because the program is not designed to be static.
Evaluation for 2.2e
TheMath 180studentapplication platform includes adaptive assessments that are embedded within each lesson, providing real-time data on student understanding, adjusting the lesson pacing and complexity based on student responses, and offering differentiated practice problems to reinforce skills."Fast Track"is an accelerated path through eachMath 180lesson that allows students to demonstrate mastery by correctly solving three challenging problems. Students have the option to"Fast Track"any lesson before beginning a new"Learn Zone"lesson or at any point during"Think," "Try,"Practice,or "Master." If students do not demonstrate mastery in"Fast Track," they will automatically return to the"Learn Zone." In the"Learn Zone"of thestudentapplication, students work on their mastery of concepts with varying levels of scaffolding and feedback. The application progresses from guided to independent practice using visual models, corrective feedback, and support resources. Depending on performance, students receive3–20 problems in each"Learn Zone"lesson.In eachseriesinMath 180, the lessons are laid out so that students complete aDo Nowrelated to the lesson. Then, they see a worked example before havingGuided Practiceand a handful of practice problems. Then,they completeanExit Ticket.These frequent checks for understanding allow teachers to continuously have feedback to adjust the difficulty of tasks as students progress through the material.Three CheckPointdays are built within eachblock, one after eachtopicis covered. Teachers can use the data to determine a student's need for aBoostorStretchlesson. This system provides teachers with frequent checks for understanding throughout the lesson or activity, ensuring that misunderstandings are addressed before they become barriers to learning and allowing for adjustments in the difficulty of the task as students progress.
2.1 Instructional Assessments
2.1a
Materials include the definition and intended purpose for the types of instructional assessments.
Materials include the definition and intended purpose for the types of instructional assessments.
2 out of 2 points
Evaluation for 2.1a
Evaluation for 2.1a
Materials include the definition and intended purpose for the types of instructional assessments.
2 out of 2 points
2.1b
Materials include guidance to ensure consistent and accurate administration of instructional assessments.
Materials include guidance to ensure consistent and accurate administration of instructional assessments.
2 out of 2 points
Evaluation for 2.1b
Evaluation for 2.1b
Materials include guidance to ensure consistent and accurate administration of instructional assessments.
2 out of 2 points
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.
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.
Not scored
Evaluation for 2.1c
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.
0 out of 0 points
2.1d
Materials include diagnostic assessments with TEKS-aligned tasks or questions, including interactive item types with varying complexity levels.
Materials include diagnostic assessments with TEKS-aligned tasks or questions, including interactive item types with varying complexity levels.
4 out of 4 points
Evaluation for 2.1d
Evaluation for 2.1d
Materials include diagnostic assessments with TEKS-aligned tasks or questions, including interactive item types with varying complexity levels.
4 out of 4 points
2.1e
Materials include a variety of formative assessments with TEKS-aligned tasks or questions, including interactive item types with varying complexity levels.
Materials include a variety of formative assessments with TEKS-aligned tasks or questions, including interactive item types with varying complexity levels.
4 out of 4 points
Evaluation for 2.1e
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.
4 out of 4 points
2.2 Data Analysis and Progress Monitoring
2.2a
Instructional assessments include scoring information and guidance for interpreting student performance, including rationale for each correct and incorrect response.
Instructional assessments include scoring information and guidance for interpreting student performance, including rationale for each correct and incorrect response.
3 out of 3 points
Evaluation for 2.2a
Evaluation for 2.2a
Instructional assessments include scoring information and guidance for interpreting student performance, including rationale for each correct and incorrect response.
3 out of 3 points
2.2b
Materials provide guidance for the use of included tasks and activities to respond to student trends in performance on assessments.
Materials provide guidance for the use of included tasks and activities to respond to student trends in performance on assessments.
1 out of 1 points
Evaluation for 2.2b
Evaluation for 2.2b
Materials provide guidance for the use of included tasks and activities to respond to student trends in performance on assessments.
1 out of 1 points
2.2c
Materials include tools for teachers to track student progress and growth, and tools for students to track their own progress and growth.
Materials include tools for teachers to track student progress and growth, and tools for students to track their own progress and growth.
2 out of 2 points
Evaluation for 2.2c
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.
2 out of 2 points
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.
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.
0 out of 2 points
Evaluation for 2.2d
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.
0 out of 2 points
2.2e
If designed to be adaptive, materials provide frequent checks for understanding at key points throughout each lesson or activity.
If designed to be adaptive, materials provide frequent checks for understanding at key points throughout each lesson or activity.
Not scored
Evaluation for 2.2e
Evaluation for 2.2e
If designed to be adaptive, materials provide frequent checks for understanding at key points throughout each lesson or activity.
1 out of 0 points
Rubric Section 3
Supports for All Learners
Materials support educators in reaching all learners through design focused on engagement, representation, and action/expression for learner variability.
Total
100% (36 out of 36 points)
Evaluation for 3.1a
Math 180offers a video in the Teacher Success Pathway that provides clear guidance for teachers on lessons. Teachers are guided through the program, showing where (resources for differentiation), what (Resources for Differentiated Instruction [RDI] Index and RDI Lesson), and how (teacher pathway video) to use the curriculum to support students who have not yet achieved proficiency.The lessons in theMath 180"Teaching Guide"include a section called "High-Leverage Practices,"whereteacherscanmodify and scaffold the language and activities for students in need.The "Learn Zone" ispart ofMath 180's online program with built-in algorithms that provide students with content, practice problems, and feedback based on their current level of understanding. The application gradually releases students from guided to independent practice using visual models, corrective feedback, and support resources. The "Learn Zone" has four sections: "Think," "Try,"Practice,and "Master."
Evaluation for 3.1b
TheProgram Guideincludes a section that provides pre-teaching support that educators should be implementing in each lesson in the Vocabulary Routine (VR). The VR explicitly provides teachers with consistent directions to introduce new math vocabulary during teacher-facilitated instruction. TheProgram Guideincludes implementation tips, including reminders to do the following: pre-teach the vocabulary and definitions on the teacher display using the"Routine" button on the whiteboard, encourage the students to use the terms in discussions, and use the terms consistently for repeated exposure. An online glossary is available in mSpace for teachers and students to use when needed.To address educator guidance for supports for unfamiliar references in text,Math 180includesa "Language Support at a Glance" document.Additionally, there isa "Spanish Academic Language" document for eachseries. The "LanguageSupport at a Glance" document provides sentence stems and offers differentiation based on students' varying levels of language proficiency.TheMath 180materials include a "LanguageSupportat a Glance" section for eachseriesblock. In the "Decimals and IntegersSeries,"Block3, "LanguageSupportat a Glance" outlines different structures based on students' language proficiency. Teachers are provided with guidance such asthe following:"Practice using the prepositional phrases 'to the left of/rightof' to describe the position of two numbers on the number line. Point to each number as you describe it."
Evaluation for 3.1c
ThePerformance Tasksinclude explicit educator guidance for enrichment activities for students who have demonstrated proficiency in grade-level content and skills. There are extensions to these activities for students who have demonstrated proficiency in above-grade-level content skills.TheMath 180materials includeStretchlessons to be used for students who have demonstrated mastery (as evidenced by the "Program Activity Report") and proficiency with above-grade-level content and skills. Students not identified as "Developing" or "Not Yet" are intended to use theStretch lessons.For example, in the "Decimals and IntegersSeries,"Block2,Topic1, studentsreceive the following prompt from the educator:"Let's read the problem again carefully. What information do we have? How can we identify if each statement is true or false? Remember that there may be more than one answer to the problem." Students then practice determining which statements are true based on decimal place value and must explain their thinking.TheRDI Guideprovides explicitMath 180adaptive onlineapplications, including the"Fast Track" and the "Success Zone," which are extensions and enrichments for students on and above grade level. "Fast Track" automatically provides advanced learning paths for students who can answer three "Master"-level questions consecutively to skip to the next lesson. When students have mastered all of the "Learn Zone," they will unlock the "Success Zone," where they review the previoustopicwith a game board of choices.Math 180hasa video in the Teacher Success Pathway that provides explicit teacher guidance for enrichment and extension activities. Teachers are given explicit guidance as to where enrichment and extension activities are located (resources for differentiation), unfold the meaning of theResources for Differentiated InstructionIndex and RDI Lessons, and see how (teacher pathway video) to use theMath 180material to help students who have demonstrated proficiency in grade-level and above-grade-level content and skills.
Evaluation for 3.1d
The materials do not include accommodations for content and language supports that canbe enabled or disabled to support individual students.Text-to-speech and calculator accommodationsareavailable in all program assessments. Each of the stated accommodationscanbe delivered to individual students or the entire class in all program assessments.Math 180digital materials guide educators on how to enable or disable the calculator for the entire classandfor individual students (this is done bygoing tothe "My Classes" tab and selecting "Class Settings"). This allows the calculator to be used throughout the materials.
Evaluation for 3.1e
TheMath 180"Teaching Guide"for "Decimals and Integers,"Block1,Topic2, Lesson 1 includes educator guidance to offer varied options and supports for students to demonstrate their understanding of multiplying decimals by whole numbers. The lesson plan has students estimate products, rename decimals as fractions, and calculate products using thedistributiveproperty. The lesson plan also gives teachers guidanceon providing questions to drive discussions,allowing students to express their understanding orally and through written reasoning. The"LanguageSupport" section guides teachers to explicitly connect math terms with representations and equations. Other support gives guidanceon allowing students to work individually or in pairs.The "Modify Tasks"section has suggestions on how to simplify or extend problems if needed.TheMath 180materials contain rubrics for thePerformance Taskswithin eachseriesfor students to showcase their thinking. For example, in the "Decimals and IntegersSeries,"Block2Performance Task,"Manage a Tutor Business," students must create a schedule and a table of figures showing hours and the amount paid. Students must also explain why each tutor was assigned their subject.Math 180provides aPerformance Taskwhere students apply math skills and concepts to solve real-world, career-related tasks involving more abstract reasoning. This is to becompleted at the end of eachblockin aseries. The materials include educator guidance in both the"Teaching Guide"and "mSpaceAnnotated" on howto allow students to demonstrate understanding by drawing models and using written explanations.
Evaluation for 3.2a
Math 180provides educators with direct prompts and guidance for teaching students and activating students' prior knowledge in theConnectportion of every lesson. In the "Decimals and Integers Series," Block3, theConnectsection explicitly instructs teachers on what to say. The curriculum then gives educators guidanceonhow to activate prior knowledge by referencing the example fromBlock1,Topic3, Lesson 1.TheTeacherDisplayTools include theConnectfeature, with the specific example that teachersareprompted to discuss from the previous "Concept" lesson. The pictorial representation allows teachers and students to highlight and connect key patterns, features, and relationships and contains visual models to support students in visualizing concepts and understanding how they connect to other mathematical concepts and skills.
Evaluation for 3.2b
This guidance is not applicable because the program is not designed to be static.
Evaluation for 3.2c
The materials include a variety of methods and structures for intervention practice. For example, in the "Decimals and IntegersSeries,"Block2,Topic2, Lesson 1 begins with a class brainteaser and a whole-group lesson. Students are givenGuided Practiceto work through with a partner before partner work and an independentExit Ticket.The RDI Index provides explicit instructions and recommendations for teachers to effectively implement multitiered intervention onCheckPointdays (after the fifth lesson inTopics 1 and 2 and after themSkills assessmentinTopic3). After reviewing "Program Activity Report" data, teachers can create groups and choose assignments according to students' learning needs.Stretchlessons are designed for Tier 1 students, andBoostlessons are designed for Tier 2 and Tier 3 students. The RDIIndex also gives guidance on which lessons are intended for individuals, pairs, or small groups.
Evaluation for 3.2d
Math 180includes aPerformance Taskat the end of everyblock.Performance Tasksare higher-level thinking activities where students must insert themselves into real-world roles, providing great levels of engagement. The"Teaching Guide"provides instructions with explicit prompts that guide effective implementation of extension methods. For example,Block1 of the "Decimals and IntegersSeries"has students acting in the role of athletic trainers preparing athletes for the next Olympic Games.Educatorsareprovided with multiple prompts to serve as a springboard to activate students' thinking.The RDI Guide provides explicit instructions and recommendations for teachers to effectively implement interventions onCheckPointdays, including how to choose enrichment (Stretch) and extension (BoostandFocus) activities.CheckPointdays occur after the fifth lesson inTopics 1 and 2 and after themSkills assessmentinTopic3. After reviewing "Program Activity Report" data, teachers can create groups and choose assignments according tostudents' learning needs. An example is provided to show teachers one approach.
Evaluation for 3.2e
In the"Teaching Guide,"teachers are provided with prompts, such as the following, to give when students may still have gaps:"IF students struggle to divide whole numbers, Then review using multiplication to find quotients. How are multiplication and division related? How can I find 240 divided by 12 using multiplication?" These structured prompts enhance educators'ability to deliver timely feedback, improve engagement with students, and refine their instructional practices, leading to more responsive teaching.TheProgram Guideincludes guidance on how to implement instructional routines as informal assessments during discussions to adjust instruction and provide timely feedback after a task. Think-Pair-Share,Turn and Talk, Question Chains, Show of Thumbs, and Answers Up encourage active participation by all students, provide low-risk opportunities to engage in discussion and clarify misconceptions, give teachers insight into students' thought processes to gauge understanding, provide teachers with an opportunity to adjust instruction at any point during the lesson, andprovideimmediate feedback.
Evaluation for 3.3a
This guidance is not applicable because the program is not designed to be static.
Evaluation for 3.3b
In the "Decimals and IntegersSeries,"Block2, "Language Support at a Glance" offers linguistic accommodations for every language level. Teachers display, review, and rehearse explicit sentence frames using gestures and visuals to support students at Pre-production and Beginning levels. For students at Intermediate and High-Intermediate levels, teachers use helping verbs and add details from the problem using base verbs. These students discuss tasks with partners and evaluate solutions. The materials encourage them to use academic language and justify their reasoning. Advanced students use precise math language in complete sentences and suggest revisions to incorrect solutions. They explain and justify their answers orally and in writing.Eachseriesincludes a "Topicat a Glance" document with language objectives and key academic terms. This document supports academic language development at every proficiency level, focusing on speaking skills and correct terminology. In the "Decimals and IntegersSeries,"Block1, the materials guide educators to help Pre-production and Beginning students use sentence frames, reading aloud with them. Some sentence frames use conjunctions to compare numbers and build academic vocabulary.In the "Learn Zone," students can toggle between English and Spanish. Students can also play thelessonvideo in Spanish. These features support students at all language proficiency levels, from Pre-production to Advanced.
Evaluation for 3.3c
The "Teacher's Corner" inMath 180includes a "Discourse" section featuring video explanations of thelanguagedevelopment materials, along with modeled lessons that demonstrate strategies,such asleading discussions, vocabulary building, andThink-Pair-Share.Eachblockwithin aseriesprovides a "Language Support at a Glance" document to help educators implement the state-approved ELPS effectively, offering practical tips for scaffolding content and language development differentiated by language proficiency.
Evaluation for 3.3d
TheMath 180"Integrating Language Routines Into Instruction" material provides educators with guidance on how to support emergent bilingual(EB)students with structured opportunities to expand content-specific vocabulary, boost comprehension, and build background knowledge through oral and written academic discourse. It also supports making crosslinguistic connections through oral discourse. The "Compare and Connect" routine helps EB students find similarities and differences between math strategies or representations. "Critique, Correct, and Clarify" provides students with opportunities to analyze and revise flawed math explanations and encourages deeper comprehension with both content and language. "Stronger and Clearer Each Time" guides students through structured conversations in which they articulate and revise their mathematical ideas orally. The repeated verbal rehearsal supports language development and fosters academic vocabulary use and oral and written discourse fluency. The "Three Reads" strategy scaffolds students' reading comprehension and interpretation of math word problems through repeated readings with distinct purposes.The "Three Reads" strategy can be utilized with EB students to make crosslinguistic connections through oral discourse. This allows EB students to make sense of both the everyday and mathematical language used in the problems, which they can relate to equivalent structures in their home language through oral discourse.Math 180providesthe"Language Support at a Glance"document,whichgives educators guidance in partnering students that share a home language and encouragingthem to first introduce concepts to each otherthroughoral discourse using their home language and a variety of language structures, such as connectingwords(ELPS 2C). The materials do give guidance for crosslinguistic connections through written discourse in "Language Support at a Glance."
Evaluation for 3.3e
This guidance is not applicable because the program is not designed for dual language immersion (DLI) programs.
3.1 Differentiation and Scaffolds
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.
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.
1 out of 1 points
Evaluation for 3.1a
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.
1 out of 1 points
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.
Materials include explicit educator guidance for language supports, including pre-teaching and embedded supports for developing academic vocabulary and unfamiliar references in text.
4 out of 4 points
Evaluation for 3.1b
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.
4 out of 4 points
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.
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.
2 out of 2 points
Evaluation for 3.1c
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.
2 out of 2 points
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.
Digital materials include accommodations, including text-to-speech, content and language supports, and calculators that educators can enable or disable to support individual students.
Not scored
Evaluation for 3.1d
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.
2 out of 0 points
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.
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.
2 out of 2 points
Evaluation for 3.1e
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.
2 out of 2 points
3.2 Instructional Methods
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.
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.
5 out of 5 points
Evaluation for 3.2a
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.
5 out of 5 points
3.2b
If designed to be static, materials include educator guidance for effective lesson delivery and facilitation using various instructional approaches.
If designed to be static, materials include educator guidance for effective lesson delivery and facilitation using various instructional approaches.
0 out of 2 points
Evaluation for 3.2b
Evaluation for 3.2b
If designed to be static, materials include educator guidance for effective lesson delivery and facilitation using various instructional approaches.
0 out of 2 points
3.2c
Materials include multi-tiered intervention methods for various types of practice and structures and educator guidance to support effective implementation.
Materials include multi-tiered intervention methods for various types of practice and structures and educator guidance to support effective implementation.
3 out of 3 points
Evaluation for 3.2c
Evaluation for 3.2c
Materials include multi-tiered intervention methods for various types of practice and structures and educator guidance to support effective implementation.
3 out of 3 points
3.2d
Materials include enrichment and extension methods that support various forms of engagement, and guidance to support educators in effective implementation.
Materials include enrichment and extension methods that support various forms of engagement, and guidance to support educators in effective implementation.
2 out of 2 points
Evaluation for 3.2d
Evaluation for 3.2d
Materials include enrichment and extension methods that support various forms of engagement, and guidance to support educators in effective implementation.
2 out of 2 points
3.2e
Materials include prompts and guidance to support educators in providing timely feedback during lesson delivery.
Materials include prompts and guidance to support educators in providing timely feedback during lesson delivery.
2 out of 2 points
Evaluation for 3.2e
Evaluation for 3.2e
Materials include prompts and guidance to support educators in providing timely feedback during lesson delivery.
2 out of 2 points
3.3 Support for Emergent Bilingual Students
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.
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.
0 out of 4 points
Evaluation for 3.3a
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.
0 out of 4 points
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.
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.
Not scored
Evaluation for 3.3b
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.
4 out of 0 points
3.3c
Materials include implementation guidance to support educators in effectively using the materials in state-approved bilingual/ESL programs.
Materials include implementation guidance to support educators in effectively using the materials in state-approved bilingual/ESL programs.
1 out of 1 points
Evaluation for 3.3c
Evaluation for 3.3c
Materials include implementation guidance to support educators in effectively using the materials in state-approved bilingual/ESL programs.
1 out of 1 points
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.
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.
8 out of 8 points
Evaluation for 3.3d
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.
8 out of 8 points
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.
If designed for dual language immersion (DLI) programs, materials include resources that outline opportunities to address metalinguistic transfer from English to the partner language.
Not scored
Evaluation for 3.3e
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.
0 out of 0 points
Rubric Section 4
Depth and Coherence of Key Concepts
Materials are designed to meet the rigor of the standards while connecting concepts within and across grade levels/courses.
Total
100% (16 out of 16 points)
Evaluation for 4.1a
Practice opportunities throughout learning pathways require students to demonstrate a depth of understanding aligned to the TEKS.Eachseriesbuilds complexity in the materials presentedand inpractice opportunities. For example, in the "Decimals and IntegersSeries,"Block1,Topic1, Lesson 1 begins with students naming decimal parts, such as tenths and hundredths, using models on paper (i.e., paper divided into tenths and a hundred squares). Theseriesbuilds to students naming decimals in multiple ways.Topic3, Lesson 2, has students comparing decimals on a number line, using models, and renaming the decimals within the same place value.In the "Decimals and Integers Series," Topic 3, thePerformance Tasktitled "Train Olympic Athletes" requires students to choose target distances and create a graph based on the times, ordered in a least-to-greatest format. A rubric is provided to assess student understanding and performance.
Evaluation for 4.1b
Throughout theMath 180learning pathways, students are provided with multiple scaffolded practice and assessment opportunities that are purposefully aligned to the TEKS. These activities progress in complexity, encouraging students to apply, analyze, and synthesize knowledge in ways that demonstrate deep understanding. Formative checks,Performance Tasks,and real-world problem-solving scenarios ensure that students engage meaningfully with TEKS-aligned content. RDI are provided for teachers to use during interventions (Boost lessons) to reinforce foundational skills with routine problems or as an extension (Stretchlessons) to challenge students with nonroutine problems to extend skills.TheStretchlesson "Solve Complex Division Problems" demonstrates a clear increase in rigor and complexity, supporting both grade-level and above-grade-level proficiency in alignment with the TEKS. TheStretchlessonallows students to solve balance-scale problems, where they must write and solve equations to find the value of a variable representing a fractional weight. Reinforcement of foundational algebraic thinking is achieved by visualizing equivalent expressions in the context of real-world situations. The lesson extends the rigor with some problems that require interpreting and solving multistep balance scenarios involving multiple fractional components and units. Students are asked to reflect on how solving balance problems helped them understand equivalence and justification to support mathematical communication.Then, theychoose a strategy to solve a problem that will improve their learning.
Evaluation for 4.2a
TheMath 180"Teaching Guide" for the"Decimals and IntegersSeries"lists the learning progression and connections to other concepts in each lesson within a grade level. TheBlock1Topic1, overview highlights the connections to prior and future lessons. For example, in grade 5, the learning progressions list the current objectives (express numbers in tenths and hundredths as decimals, express fractions less than 1 as decimals, express decimals in equivalent forms, and use decimals to solve problems) that will lead to connections with other grade-level standards (understand that integers can be divided and every quotient of integers is a rational number).Within teacher- and student-facing materials, a "Why This Matters" section is included to provide context and relevance to the lesson being taught. Thematerials contain a "Why This Matters"statement:"Making estimates helps students assess answers to calculations, evaluate everyday situations, and find and fix errors."
Evaluation for 4.2b
TheMath 180scope and sequence is built around a curriculum that enables students to progress toward grade-level standards and algebra readiness. The "Program Overview" has a concept map that demonstrates coherence vertically across concepts and grade bands, including connections from grades K–6, by connecting patterns, big ideas, and relationships. For example, in the grade 5 "Decimals and IntegersSeries,"the learning progression begins with thegrade 3and grade4 prerequisites of performing arithmetic with whole numbers, decimals, and fractions,thenleads to using ratio reasoning to solve problems in grade 6.Alignment Guidesareavailable for each grade level within the "Teacher Materials." Using these guides, teacherscandetermine connections made within the materials across grade levels.Throughout theProgram Guide,teachers are presented with how the materials are designed to prepare students for the "Algebra 1" course.Theadaptive programallowsstudents to move in and out of theseriesthey are placed in, with a predictableseriesstructure to ensure that students are successful.
Evaluation for 4.2c
TheMath 180"Teaching Guide" for the "Decimals and IntegersSeries"lists the learning progression and connections to other concepts in each lesson within a grade level. TheBlock1,Topic1, overview highlights the connections to prior and future lessons. For example, in grade 5, the learning progressions list the current objectives (express numbers in tenths and hundredths as decimals, express fractions less than 1 as decimals, express decimals in equivalent forms, and use decimals to solve problems) that will lead to connections with other grade-level standards (understand that integers can be divided and every quotient of integers is a rational number).The learning progressions provided at the beginning of eachblockwithin aseriescreate coherence across lessons and activities. Students are required to build upon prior knowledge to continue to move through theseriesand be successful. For example, students begin by multiplying by 10 and examining the patterns that emerge. The educator explains that when multiplying by 10, there will always be a zero in the ones place. Students use this knowledge to connect what happens when multiplying by 100 and 1,000. Then, students move into division and relate the pattern to the movement of the decimal.In theMath 180"Teaching Guide" for the "Decimals and IntegersSeries,"there is a "Blockat a Glance" that overviews how each lesson builds upon the last one. For example,Block1,Topic1, is "Fraction and Decimal Relationships." Within thistopic, students mustnamefractions usingdecimalnotation, thennamefractions asdecimals before theydevelopreasoning withdecimals with a game. Students continue toexpressdecimals in more than one way before building their mastery with problem-solving. At the end of eachblock, students tie together all of their learning with aPerformance Taskthat utilizes all the skills learned within theblock.
Evaluation for 4.3a
TheMath 180mSkills assessmentdecimal and integer assessment revisits skills learned at the beginning, middle, and end of the lesson. This provides students with a spaced retrieval opportunity to revisit skills previously taught in a timelier manner.Within each lesson, aDo Nowsection contains a practice/retrieval activity connected to the concept and learning for the day. IntheMath 180"Decimals and IntegersSeries,"Block2,Topic2, Lesson 3 containsaDo Nowactivity that requires students to estimate products of multiplication expressions that contain decimals. Students must pick which product does not belong after their estimation and multiplication.Studentsmustplay the "Brain Arcade" daily. In the"Brain Arcade,"students have the opportunity to practice facts, perform quick multi-digit operations, and more. These opportunities provide continuous assessment of student progress, helping educators adjust their teaching strategies as they review the report. As students finish atopic, they have access to the "Success Zone," wheretheysolve problems that review previoustopics.Multiple components of thestudentapplication ("Learn Zone," "Success Zone," and "Brain Arcade") provide spaced retrieval opportunities with previously learned skills and concepts across learning pathways. In the "Master" portion of the "Learn Zone," students demonstrate mastery of a new concept, skill, or strategyandreview problems from prior lessons. After students master the lessons in atopicin the "Learn Zone," the "Success Zone" unlocks a game board that students can use to review thetopic. The "Brain Arcade" helps students practice their fluency with procedural math skills.
Evaluation for 4.3b
TheMath 180"Decimals and IntegersSeries Teaching Guide"provides a "Blockat a Glance" for eachblockin aseries. The"Block at a Glance"is a visual map of the lessons within the threetopics, with an example of the strategy students are introduced to in each lesson. Ingrade 5, the mSpace lessons provide various strategies for fraction and decimal relationships, including using decimal grids, number lines, equations, the division standard algorithm, and Venn diagrams. Through the learning progression, students learn more than one strategy to solve fraction and decimal relationship problems and engage in problem sets that require understanding word problems to plan whether to use an appropriate strategy.In theMath 180"Decimals and IntegersSeries,"students use area models to divide decimals.Teachersareprovided with a guiding question:"To divide 2 wholes by 2 tenths, I ask myself, 'How many groups of 2 tenths are in 2?'"In eachseries, students can complete a Card Sort,which provides interleaved practice. For example, in Card Sort: "Decimals and Place Value," students group cards based on a rule or commonality. This allows students to think flexibly about fractions, decimals, and visual representation.TheProgram Guideexplains the purpose behind each segment of theMath 180materials. These explanations explicitly identify the use of previously taught concepts.Do Nowis 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. Conceptlessonshelpstudents connect previously learned concepts, build new understandings, and acquire skills. Lessons are designed to build students' conceptual understanding of math. "Problem-Solving"lessons are in allblocks. Students apply conceptual understanding to new problem situations through multistep and contextualized problems, which allowsthem to interpret, analyze, and evaluate mathematical concepts and complex, real-world situations. In "Game"lessons, with two or three games perblock, students engage in collaborative practice to help build fluency and flexibility with learning objectives from "Concept" lessons.
4.1 Depth of Key Concepts
4.1a
Practice opportunities throughout learning pathways (including instructional assessments) require students to demonstrate depth of understanding aligned to the TEKS.
Practice opportunities throughout learning pathways (including instructional assessments) require students to demonstrate depth of understanding aligned to the TEKS.
2 out of 2 points
Evaluation for 4.1a
Evaluation for 4.1a
Practice opportunities throughout learning pathways (including instructional assessments) require students to demonstrate depth of understanding aligned to the TEKS.
2 out of 2 points
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.
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.
4 out of 4 points
Evaluation for 4.1b
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.
4 out of 4 points
4.2 Coherence of Key Concepts
4.2a
Materials demonstrate coherence across concepts horizontally within the grade level by connecting patterns, big ideas, and relationships.
Materials demonstrate coherence across concepts horizontally within the grade level by connecting patterns, big ideas, and relationships.
1 out of 1 points
Evaluation for 4.2a
Evaluation for 4.2a
Materials demonstrate coherence across concepts horizontally within the grade level by connecting patterns, big ideas, and relationships.
1 out of 1 points
4.2b
Materials demonstrate coherence vertically across concepts and grade bands, including connections from grade K–6, by connecting patterns, big ideas, and relationships.
Materials demonstrate coherence vertically across concepts and grade bands, including connections from grade K–6, by connecting patterns, big ideas, and relationships.
1 out of 1 points
Evaluation for 4.2b
Evaluation for 4.2b
Materials demonstrate coherence vertically across concepts and grade bands, including connections from grade K–6, by connecting patterns, big ideas, and relationships.
1 out of 1 points
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.
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.
4 out of 4 points
Evaluation for 4.2c
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.
4 out of 4 points
4.3 Coherence and Variety of Practice
4.3a
Materials provide spaced retrieval opportunities with previously learned skills and concepts across learning pathways.
Materials provide spaced retrieval opportunities with previously learned skills and concepts across learning pathways.
2 out of 2 points
Evaluation for 4.3a
Evaluation for 4.3a
Materials provide spaced retrieval opportunities with previously learned skills and concepts across learning pathways.
2 out of 2 points
4.3b
Materials provide interleaved practice opportunities with previously learned skills and concepts across learning pathways.
Materials provide interleaved practice opportunities with previously learned skills and concepts across learning pathways.
2 out of 2 points
Evaluation for 4.3b
Evaluation for 4.3b
Materials provide interleaved practice opportunities with previously learned skills and concepts across learning pathways.
2 out of 2 points
Rubric Section 5
Balance of Conceptual and Procedural Understanding
Materials are designed to balance conceptual understanding, procedural skills, and fluency.
Total
100% (38 out of 38 points)
Evaluation for 5.1a
In theMath 180"Decimals and IntegersSeries,"Block3,Topic3, Lesson 5 provides multiple opportunities for students to interpret, analyze, and evaluate models and representations as they solve real-world problems using bar models and decimal operations. Students are asked to interpret bar models that represent parts of a whole using fractions(e.g.,3/4 of Ken's earnings)and decimal models. In the "Who Is Right?" task, students must evaluate Jenna and Anna's different solution strategies and justify which is correct based on decimal representation.Math 180provides opportunities for students to interpret, analyze, and evaluate mathematical concepts within aPerformance Taskto solve real-world, career-related tasks involving more abstract reasoning.Performance Tasks arecompleted at the end of eachblockin aseries. The materials include educator guidance in both the"Teaching Guide"and "mSpaceAnnotated" on how to allow students to demonstrate understanding by drawing models and using written explanations.InMath 180, students are shown a scale to visually represent an equation. Students must then write an equation for the problem before solving it. This task provides students with the opportunity to interpret a model to better understand how to solve decimal problems with equivalence.
Evaluation for 5.1b
In theMath 180"Decimals and IntegersSeries,"Block2,Topic1, Lesson 5, students add and subtract decimals to solve multistep problems. Students are given a word problem to analyze and determine the appropriate strategy to use to solve. The strategy chosen is that of part-part-whole. Students then use strip diagrams to model their thinking, and they must evaluate their work by checking for accuracy.In theMath 180"Decimals and IntegersSeries,"Block2,Topic3, Lesson 5 provides multiple opportunities for students to use models and representations to solve real-world problems using bar models and equations. Students are asked to create bar models that represent equal parts of a whole using fractions and decimals.In theMath 180"Decimals and IntegersSeries,"Block2,Topic1, Lesson 3, students create their own open number line to create an estimate and solve the problem given in theExit Ticket.Students then determine if their answer is reasonable based on the number line they create and which benchmark they jumped to first in solving the problem.
Evaluation for 5.1c
TheMath 180"Explore Zone" has simulations where students make choices in real-world scenarios and determine how their choices influence the math. Students are aquarium architects who are tasked withattracting tourism to the city bydesigning exhibits with a variety of speciesbased ontheir habitat and characteristics (e.g., size as a fraction of the tank, preferences, and popularity). Students must pick species for the surface, reef, and floor of the tank in combinations that will make one whole, using their skills of addition with unlike denominators. Feedback is given at the end.In theMath 180"Decimals and IntegersSeries,"Block2,Topic2, Lesson 1, students are given a brainteaser. Students must use the given list of numbers,organizingthem into factor pairs that all have the same product.Teachersprovideguiding questions to assist students in their analysis.TheMath 180Performance Taskat the end of eachblockof aseriesprovides a direct correlation for students to see math at work in real-life situations. In the "Decimals and IntegersSeries,"Block2, students are tasked with managing a tutoring business. Students apply their knowledge of decimals, including tenths and hundredths, to create a work schedule for the amount of time employees workandcalculate their wages.
Evaluation for 5.2a
The "Brain Arcade" provides a multitude of games that are designed to help students become fluid, fluent, and flexible. All games are divided into chapters that are then divided into levels, which progress in difficulty. Educators and students can use "Brain Arcade"recommendations byseries,block, andtopicto focus on specific skills that align with daily lessons. For example, the game "Jelly Drop" aligns with the "Decimals and IntegersSeries"and involves building fluency and automaticity by helping students relate the numerical representation of a fraction with unit representations.In the "Decimals and IntegersSeries,"students add decimals using decimal and fraction notation. The grade-level connection that promotes fluency statesthat"adding decimals up to the hundredths place prepares students to flexibly reason how to simplify any expression of rational numbers whether the student chooses decimal or fractional notational form."
Evaluation for 5.2b
TheMath 180"Teaching Guide" for the "Decimals and IntegersSeries"featuresa "Blockat a Glance," which provides a visual map of the lessons within the threetopics, with an example of the strategy students are introduced to in each lesson. Ingrade 5, the mSpace lessons provide various strategies for fraction and decimal relationships, including using decimal grids, number lines, equations, the division standard algorithm, and Venn diagrams. Through the learning pathway, students learn more than one strategy to solve fraction and decimal relationship problems and engage in problem sets that require understanding word problems to plan whether to use an appropriate strategy.
Evaluation for 5.2c
TheMath 180Program Guideexplains how the curriculum offers "Comprehensive Support for Students." This information is listed under "Program Overview" and details student opportunities to evaluate mathematical representations, models, strategies, and solutions for efficiency, flexibility, and accuracy through the use of the following sections: "Learn Zone," "Instructional Videos," "My Examples," "Think Aloud," "Targeted Suggestions," "Answer Reveal," and"Success Zone."The "Brain Arcade" offers adaptive math games that support students in developing and evaluating efficient, flexible, and accurate computational strategies. Games are organized by number type, operation, and level of complexity, allowing students to explore various mathematical representations and procedures across chapters. Within each chapter, games increase in difficulty, guiding students to apply prior knowledge in new contexts. As students demonstrate procedural fluency, they unlock higher levels of the game, encouraging reflection on the accuracy and efficiency of their problem-solving approaches.
Evaluation for 5.2d
In theMath 180"FractionsSeries,""Learn Zone" lessons guide students to identify equivalent fractions.Students are guided to usetiles to build equivalent fractions, draw pictorial models, and write equations of equality for the fractions built. As they become proficient in this strategy, students are introduced to other strategies. The application progresses from guided to independent practice using visual models, corrective feedback, and support resources. As students progress through the program, support is given in recognizing patterns and selecting more efficient approaches to solve problems fluently in different contexts.In the RDI Index, there is a "Strategy Bank" that suggests one strategy per lesson for application in a contextualized problem. This encourages teachers to help students compare strategies and choose more efficient ones duringBoostorStretchlessons.
Evaluation for 5.3a
The "Learning Matrix" in theMath 180Program Guideclearly highlights the program's focus on both concepts and procedures. Additionally, theMath 180Alignment Guideoffers direct links to sample lessonsin which theTEKS are covered, including notes that specify how each lesson promotes conceptual understanding and procedural skills.In theMath 180"Teaching Guide,"teachers are specifically instructed to include "Why This Matters" at the start of each lesson. Ingrade 5, "[n]aming a number in multiple ways helps students become more efficient at solving problems involving decimals." The clear link between naming a number and improving problem-solving skills supports conceptual understanding. The "Blockat a Glance" provides a procedural overview of how a TEK will be addressed. The progression for understandingdecimaloperations begins with applying place value to add decimals, then multiplying decimals greater than one, and finally using patterns to divide decimals.
Evaluation for 5.3b
The TEKS selected for the grade 5seriesonly call for pictorial or abstract models, not concrete models. The materials do provide opportunities for students to use pictorial and abstract models. In the "Decimals and IntegersSeries,"students are instructed to draw a model of the presented word problem. Using a decimal grid, students shade in the amounts from the problem to determine their solution and then write an equation to represent the action in the problem. This task offers opportunities for students to use pictorial representations and abstract models.
Evaluation for 5.3c
The materials in the "Decimals and IntegersSeries"do not fully support students in connecting, defining, and explaining concrete models to abstract concepts, as the TEKS require, becauseMath 180includes the TEKS that support students in connecting representational models to abstract concepts. The TEKS involving concrete models are not covered within the scope of the materials for theMath 180"Decimals and Integers Series"supplementaryprogram. In the"Decimals and Integers Series,"students make connections using visual models to abstract concepts as they sketch decimal grids to model fractions and write equivalent numeric expressions, reinforcing the use of visual models to abstract concepts, as required by the TEKS. The lesson explicitly prompts students to explain how the visual model represents the numeric expression, using sentence frames and discussion prompts embedded throughout the lesson.
Evaluation for 5.4a
Math 180allows students to further develop their academic mathematical language throughout the "Learn" Zone portion of the curriculum.Block1,Topic1, Lesson 3: "Express Decimals in More Than One Way,"can orally walk students through the process of representing a decimal in multiple ways.Students name a mixed fraction using the visual decimal grid.For assistance,studentsmay also choose the mTool, Think Video, or Example Problem to help them complete the task. Language development is increased by allowing students to use the accessible online glossary for assistance in identifying unfamiliar academic vocabulary.TheMath 180materials include integrated opportunities to develop academic math language through lesson plans with specific language goals and interactive"Teaching Guides"with practical tips for scaffolding content and language development (e.g., sentence frames, partner talk, andVRs) andusingvisual representations and manipulatives.
Evaluation for 5.4b
In the "Decimals and IntegersSeries,"the "High-Leverage Practices" section provides the following embedded scaffold for educators to use in developing academic mathematical language: "If students confuse tenths and hundredths places in decimals, then discuss specific examples. What are two ways to write one-tenth as a decimal? How do I write one-hundredth? Why do you need to write a zero before the decimal point?" The scaffolds support educators in having students communicate with them and their peers.TheMath 180 Program Guideincludes a section that provides pre-teaching support that educators should be implementing in each lesson in the VR. The VR explicitly provides educators with consistent directions to introduce new math vocabulary during teacher-facilitated instruction.TheProgram Guideincludes implementation tips, including reminders to do the following: pre-teach the vocabulary and definitions on the teacher display using the "Routine" button on the whiteboard, encourage the students to use the terms in discussions, and use the terms consistently for repeated exposure to ensure development of academic vocabulary.
Evaluation for 5.4c
Appropriate mathematical discourse is encouraged, with embedded guidance in theMath 180"Decimals and Integers Series," Block2,Topic1, Lesson 1, where instructorsareprompted to lead a discussionin whichstudents can connect the relationship between adding whole numbers and decimals. Instructors are prompted to askthe following questions:"How is adding decimals like adding whole numbers? Why is place value important in both kinds of addition problems?"All lessons inMath 180include a scripted think-aloudin whicheducators model how to use academic vocabulary. After the think-aloud, the materials provide questioning strategies to engage students in academic discourse, suchas"Why cannot we rename 1/4 with 10 as the denominator? How can we rename 1/4 with 100 as the denominator?"
Evaluation for 5.4d
In theMath 180"Decimals and IntegersSeries,"students sort fractions and decimals using a Venndiagram based on predetermined categories. Using theTurn and Talkstructure, students are guided by the educator to discussthe following promptwith a partner:"Rename 7/10 and 2/5 as fractions with denominators of 100" (70/100 and 40/100). The educator is then prompted to"[a]sk a student to record the fractions on screen and have the students record them in their mSpaces."TheMath 180curriculum provides explicit guidance for educators to use the embedded prompts in each lesson for math class discussions. Through video demonstrations, effective instructional strategies (e.g., discussion, vocabulary, language development,Think-Pair-Share,andTurn and Talk) are modeled by educators with their students. These discourse strategies allow students to hear, refine, and use math language with peers and educators.
Evaluation for 5.4e
The "Learn Zone" in theMath 180materials includes automated feedback on student responses. If a student provides an incorrect answer, the digital platform will provide the correct answer and then provide students with the opportunity to correct their answer. If students continue to make mistakes, step-by-step Example Problems will pop up to support or redirect student responses to the correctanswers. Exemplar responses are available in the Example Problem.Math 180offers a redirect for inaccurate student responses within the "High-Leverage Practices" box called "Modify Tasks." The "Modify Task" in the "Decimals and IntegersSeries"Block3,Topic2, Lesson 1, says the following: "If students need help understanding how the number line shows adding two quantities, then demonstrate with objects. Use a ruler as a number line and two objects to represent two addends. Demonstrate how placing the objects end to end will give you the length of the objects combined."
Evaluation for 5.5a
In the "Decimals and IntegersSeries,"students use a Venndiagram to organize and communicate mathematical reasoning to determine numbers greater or less than given numbers. Students explain and justify their thinking throughout the lesson.In the"Decimals and Integers Series,"students solve problems involving positive and negative numbers (content) using open number lines (process). Students apply TEKS-aligned process standards, such as modeling with mathematics (process), selecting tools (process), and justifying and explaining mathematical ideas and arguments using precise mathematical language.
Evaluation for 5.5b
Eachblockin theMath 180seriesintegrates process standards throughout its lessons. Lessons start with aDo Nowactivity for students to evaluate and explain reasoning, followed by whole-group instruction using models and tools for communication. For example, in the "Decimals and IntegersSeries,"Block1,Topic3, Lesson 1, students usethumbs-up,thumbs-down, and number lines to assess and justify expressions. Every fifth lesson features problem-solving tasks that reinforce process standards acrosstopics.InMath 180, the fifth lesson of eachtopicfocuses on a problem-solving model that is consistent with content and vocabulary objectives in thattopic. Educators are provided with guidance, including prompts and strategies for using mathematical tools. Students are prompted to explore multiple approaches and justify their solutions. Problem-solving activities in every fifth lesson of atopicare designed to connect process standards across the learning pathways.
Evaluation for 5.5c
-The Math 180 program includedes an “Alignmnet Guide” that list all TEKS process standards by grade level that are covered in the program. There are direct links to each lesson where the TEKS and ELPS are addressed.-Materials provide the process standards with activities that are relevant. Each process standard has from two to four resources linked to parts of of the program that include: mSpce, Exit Tickeets, Performance Task,Do Now’s or Guided Practice.The Alignment guide indicates wth
5.1 Development of Conceptual Understanding
5.1a
Questions and tasks provide opportunities for students to interpret, analyze, and evaluate models and representations for mathematical concepts and situations.
Questions and tasks provide opportunities for students to interpret, analyze, and evaluate models and representations for mathematical concepts and situations.
3 out of 3 points
Evaluation for 5.1a
Evaluation for 5.1a
Questions and tasks provide opportunities for students to interpret, analyze, and evaluate models and representations for mathematical concepts and situations.
3 out of 3 points
5.1b
Questions and tasks provide opportunities for students to create concrete models and pictorial representations to represent mathematical situations.
Questions and tasks provide opportunities for students to create concrete models and pictorial representations to represent mathematical situations.
2 out of 2 points
Evaluation for 5.1b
Evaluation for 5.1b
Questions and tasks provide opportunities for students to create concrete models and pictorial representations to represent mathematical situations.
2 out of 2 points
5.1c
Questions and tasks provide opportunities for students to apply conceptual understanding to new problem situations and contexts.
Questions and tasks provide opportunities for students to apply conceptual understanding to new problem situations and contexts.
1 out of 1 points
Evaluation for 5.1c
Evaluation for 5.1c
Questions and tasks provide opportunities for students to apply conceptual understanding to new problem situations and contexts.
1 out of 1 points
5.2 Development of Fluency
5.2a
Materials provide tasks that are designed to build student automaticity and fluency necessary to complete grade-level mathematical tasks.
Materials provide tasks that are designed to build student automaticity and fluency necessary to complete grade-level mathematical tasks.
2 out of 2 points
Evaluation for 5.2a
Evaluation for 5.2a
Materials provide tasks that are designed to build student automaticity and fluency necessary to complete grade-level mathematical tasks.
2 out of 2 points
5.2b
Materials provide opportunities for students to practice the application of efficient, flexible, and accurate mathematical procedures throughout learning pathways.
Materials provide opportunities for students to practice the application of efficient, flexible, and accurate mathematical procedures throughout learning pathways.
3 out of 3 points
Evaluation for 5.2b
Evaluation for 5.2b
Materials provide opportunities for students to practice the application of efficient, flexible, and accurate mathematical procedures throughout learning pathways.
3 out of 3 points
5.2c
Materials provide opportunities for students to evaluate mathematical representations, models, strategies, and solutions for efficiency, flexibility, and accuracy throughout learning pathways.
Materials provide opportunities for students to evaluate mathematical representations, models, strategies, and solutions for efficiency, flexibility, and accuracy throughout learning pathways.
3 out of 3 points
Evaluation for 5.2c
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.
3 out of 3 points
5.2d
Materials contain guidance to support students in selecting increasingly efficient approaches to solve mathematics problems.
Materials contain guidance to support students in selecting increasingly efficient approaches to solve mathematics problems.
1 out of 1 points
Evaluation for 5.2d
Evaluation for 5.2d
Materials contain guidance to support students in selecting increasingly efficient approaches to solve mathematics problems.
1 out of 1 points
5.3 Balance of Conceptual Understanding and Procedural Fluency
5.3a
Materials explicitly state how the conceptual and procedural emphasis of the TEKS are addressed.
Materials explicitly state how the conceptual and procedural emphasis of the TEKS are addressed.
2 out of 2 points
Evaluation for 5.3a
Evaluation for 5.3a
Materials explicitly state how the conceptual and procedural emphasis of the TEKS are addressed.
2 out of 2 points
5.3b
Questions and tasks provide opportunities for students to use concrete models, pictorial representations, and abstract models as required by the TEKS.
Questions and tasks provide opportunities for students to use concrete models, pictorial representations, and abstract models as required by the TEKS.
3 out of 3 points
Evaluation for 5.3b
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.
3 out of 3 points
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.
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.
6 out of 6 points
Evaluation for 5.3c
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.
6 out of 6 points
5.4 Development of Academic Mathematical Language
5.4a
Materials provide opportunities for students to develop academic mathematical language using visuals, manipulatives, or other language development strategies.
Materials provide opportunities for students to develop academic mathematical language using visuals, manipulatives, or other language development strategies.
1 out of 1 points
Evaluation for 5.4a
Evaluation for 5.4a
Materials provide opportunities for students to develop academic mathematical language using visuals, manipulatives, or other language development strategies.
1 out of 1 points
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.
Materials include embedded educator guidance to scaffold, support, and extend students’ use of academic mathematical vocabulary in context when communicating with peers and educators.
2 out of 2 points
Evaluation for 5.4b
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.
2 out of 2 points
5.4c
Materials include embedded guidance to support student application of appropriate mathematical language and academic vocabulary in discourse.
Materials include embedded guidance to support student application of appropriate mathematical language and academic vocabulary in discourse.
1 out of 1 points
Evaluation for 5.4c
Evaluation for 5.4c
Materials include embedded guidance to support student application of appropriate mathematical language and academic vocabulary in discourse.
1 out of 1 points
5.4d
Materials include embedded guidance to facilitate mathematical conversations allowing students to hear, refine, and use math language with peers.
Materials include embedded guidance to facilitate mathematical conversations allowing students to hear, refine, and use math language with peers.
2 out of 2 points
Evaluation for 5.4d
Evaluation for 5.4d
Materials include embedded guidance to facilitate mathematical conversations allowing students to hear, refine, and use math language with peers.
2 out of 2 points
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.
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.
2 out of 2 points
Evaluation for 5.4e
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.
2 out of 2 points
5.5 Process Standards Connections
5.5a
TEKS process standards are integrated appropriately into the materials.
TEKS process standards are integrated appropriately into the materials.
1 out of 1 points
Evaluation for 5.5a
Evaluation for 5.5a
TEKS process standards are integrated appropriately into the materials.
1 out of 1 points
5.5b
Materials include a description of how process standards are incorporated and connected throughout the learning pathways.
Materials include a description of how process standards are incorporated and connected throughout the learning pathways.
2 out of 2 points
Evaluation for 5.5b
Evaluation for 5.5b
Materials include a description of how process standards are incorporated and connected throughout the learning pathways.
2 out of 2 points
5.5c
Materials include an overview of the TEKS process standards incorporated into each lesson.
Materials include an overview of the TEKS process standards incorporated into each lesson.
1 out of 1 points
Evaluation for 5.5c
Evaluation for 5.5c
Materials include an overview of the TEKS process standards incorporated into each lesson.
1 out of 1 points
Rubric Section 6
Productive Struggle
Materials support students in applying disciplinary practices to productive problem-solving, including explaining and revising their thinking.
Total
100% (19 out of 19 points)
Evaluation for 6.1a
The materials allow students to think mathematically, understand models and representations involving decimal division, and persist in problem-solving. Students interpret and analyze decimal grid models to represent problems—such as figuring out how many groups of .20 are in 2—which buildsconceptual understanding through visual reasoning. They rename decimals as fractions, use common denominators to analyze equivalence, and explain the relationships among the dividend, divisor, and quotient. Students are expected to evaluate the reasonableness of their answers by applying inverse operations and comparing the quotient to the size of the divisor and dividend. Students reflect on patterns—such as why dividing by a decimal less than one results in a larger quotient—which supportsmathematical reasoning and perseverance in problem-solving.Do Nowexercises allow students to think mathematically. In this example, students practicerepeated reasoning. In the "Decimals and IntegersSeries,"students apply number sense as they determine the best way to rearrange five integers to add. While students view this information in mSpace, teachersareprompted to ask students to share their solutions,guide students to analyze the problem further, and ask questions,such as the following:"How does adding the numbers in a specific order make it easier to add? Is there another way you could arrange the numbers?"Teachers support students with questioning, and students check their work after answering the first question. Students work through aseriesof similar problems with a partner before solving theExit Ticketon their own. For theExit Ticket,students are expected to think mathematically and use tools strategically, such as usingan open vertical number line to represent a problem.
Evaluation for 6.1b
In the "Decimals and IntegersSeries,"students use various strategies learned throughout the unit to solve multistep decimal problems. They work with a partner and choose their preferred method, such as a number line, a standard algorithm, or strip diagrams. Students then discuss and justify their solutions with peers and the educator.Do Nowexercises allow students to understand, explain, and justify that there can be multiple ways to solve problems and complete tasks. Students analyze and compare two different solutions to a decimal division problem, determine which is correct, and justify their reasoning using place value and conceptual understanding. Students explore different approaches, such as renaming decimals as hundredths or using equivalent fractions. They engage in meaningful mathematical reasoning by discussing possible misconceptions and using inverse equations to verify solutions. This task encourages flexible thinking and demonstrates that there are multiple valid strategies for solving and checking division problems.
Evaluation for 6.1c
Think-Pair-Shareis a structured discussion method used across aseries. It involves students independently reflecting on a question, problem, or task using sentence stems. Then, students pair up to share and discuss their ideas.Think-Pair-Sharehelps students to do, discuss, and write about math with peers and allows them to justify their solutions with educators.The materials are designed to help students understand mathematics through multiple opportunities to do math, write about it, and discuss it. For example, in thePerformance Task of the"Decimals and IntegersSeries,"students use various strategies learned from theblockto answerthe following prompt:"In today'sPerformanceTask, you are athletic trainers helping athletes prepare for the next Olympic Games. You will compare decimals and make line graphs." Students are grouped by mixed abilities and discuss their potential solutions. At the end of thePerformance Task,students share findings with peers and write about their experiences.
Evaluation for 6.2a
Turn and Talksare embedded throughout aseries. Educators are prompted to have students share their problem-solving approaches, including explanations, arguments, and justifications.The materials support educators in guiding students to share and reflect on their problem-solving approaches by incorporating "High-Leverage Practices" that promote explanation, justification, and mathematical discourse. Educators are provided with scaffolded questions, targeted responses to misconceptions, and task modifications that help students articulate their thinking. For example, renaming decimals as fractions supports conceptual understanding, while prompts like "What is your first step?" or "How do you know how many parts to divide the bar into?" encourage students to explain their thinking. These practices provide differentiated supports that prompt students to verbalize their thought processes and engage in meaningful peer discussions using explanations, arguments, and justifications.
Evaluation for 6.2b
The materials prompt teachers through a view of the student pages. Thematerialsgive generic prompts for when to intervene if students are struggling, such asthe following:"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 anexample of a given rationale on one incorrect answer 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 students are answering questions incorrectly. The following is anexample froma"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 understandandto challenge further student thinking. The following are prompt examples: "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 IntegersSeries"StretchLesson 3B provides guidance on how to address student responses. The guidance statesthat"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. However, it does not provide prompts or guidance togivefeedback on common misconceptions, only if students struggle with subtracting integers.The "Practice" portion of the "Learn Zone" offers targeted hints and guidance if students encounter difficulties. The hints are based on possible student misconceptions.Educators can also experience the feedback by going to the "Teacher View"of theStudent Application.
6.1 Student Self-Efficacy
6.1a
Materials provide opportunities for students to think mathematically, persevere through solving problems, and to make sense of mathematics.
Materials provide opportunities for students to think mathematically, persevere through solving problems, and to make sense of mathematics.
3 out of 3 points
Evaluation for 6.1a
Evaluation for 6.1a
Materials provide opportunities for students to think mathematically, persevere through solving problems, and to make sense of mathematics.
3 out of 3 points
6.1b
Materials support students in understanding, explaining, and justifying that there can be multiple ways to solve problems and complete tasks.
Materials support students in understanding, explaining, and justifying that there can be multiple ways to solve problems and complete tasks.
3 out of 3 points
Evaluation for 6.1b
Evaluation for 6.1b
Materials support students in understanding, explaining, and justifying that there can be multiple ways to solve problems and complete tasks.
3 out of 3 points
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.
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.
3 out of 3 points
Evaluation for 6.1c
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.
3 out of 3 points
6.2 Facilitating Productive Struggle
6.2a
Materials support educators in guiding students to share and reflect on their problem-solving approaches, including explanations, arguments, and justifications.
Materials support educators in guiding students to share and reflect on their problem-solving approaches, including explanations, arguments, and justifications.
6 out of 6 points
Evaluation for 6.2a
Evaluation for 6.2a
Materials support educators in guiding students to share and reflect on their problem-solving approaches, including explanations, arguments, and justifications.
6 out of 6 points
6.2b
Materials include prompts and guidance to support educators in providing explanatory feedback based on student responses and anticipated misconceptions.
Materials include prompts and guidance to support educators in providing explanatory feedback based on student responses and anticipated misconceptions.
4 out of 4 points
Evaluation for 6.2b
Evaluation for 6.2b
Materials include prompts and guidance to support educators in providing explanatory feedback based on student responses and anticipated misconceptions.
4 out of 4 points