Program Information
- Technical Specifications: Checklist
- Tech Specs: Checklist (pdf 580.63 KB)
- Technical Specifications: Professional Development
- Tech Specs: Professional Development (pdf 249.17 KB)
Math Catalyst Texas, Grade 3
Supplemental Math (English) Grade 3
SBOE Approved | IMRA 2025
Commissioner Recommended
Publisher: Great Minds PBC
Copyright: 2025
Series includes:
Rubric: Supplemental Mathematics K–5 (English) | 2025 (Download Not Available)
* Some programs submit evidence for only part of a standard, while others submit all sections. A 100% score means this program met all the expectations it submitted.
Quality Review
Standards Alignment
Rubric Section
| Grade | TEKS % | ELPS % |
|---|---|---|
| Grade 3 | 100% | 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
The materials include "AlignmentGuides" organized by the following concept strands: "Early Numeracy," "Place Value," "Addition," "Subtraction," "Multiplication," "Division," and "Fractions as Numbers." Each strand presents a vertical alignment of concepts fromK–5, demonstrating increasing complexity. TheStrand by Grade Scope and Sequencedocument reinforces this vertical progression by stating that the concepts within each strand build upon one another to create a ladder of mathematical understanding, unbound by the constraints of grade-level standards.Each "Alignment Guide" includes a chart listing the relevant Texas Essential Knowledge and Skills (TEKS) (numbered and defined), "Correspondinglessons," "Mathematical Process Standards," and English Language Proficiency Standards (ELPS) listening, speaking, reading, and writing competencies.The "Progression of Mini Lessons" section before each unit provides a chart that portrays the rationale for learning paths across grade levels.
Evaluation for 1.1b
The materials include anImplementation Guidethat outlines how to effectively use the program within a Multi-Tiered System of Supports (MTSS), addressing core instruction, supplemental intervention (Tier 2), and intensive intervention (Tier 3). A chart highlights how "Concept Mini Lessons" align with Tier 2 and Tier 3 instruction, while "Practice and Application" support enrichment, extension, and skill reinforcement.TheImplementation Guideprovides a sample schedule with time allotment, possible usage of each component, and teacher and student actions to support effective educator use.TheImplementation Guide's section titled "Tiered Instruction Recommendations and Program Structure and Components" notes that this resource can be flexibly used across various instructional formats—whole-group, small-group, stations, spiral review, and games—making it adaptable to diverse classroom environments and learner needs.
Evaluation for 1.1c
The materials include aconceptdiagnostic for each assessment. The "Concept Diagnostic Assessment" can be used before or during instruction to collect data about a student's current understanding, skills, strengths, and areas for growth. The data collected from this assessment can be used to inform instruction and provide timely intervention. The "Progression Toward Proficiency Rubric" used for scoring each "Concept Diagnostic Assessment" includes the TEKS alignment for each item, along with the "Concept Mini Lesson" objective. The problems in the "Concept Diagnostic Assessment" are sequenced from simple to complex. Questions aligned to each objective are also included to facilitate making instructional decisions about skill entry points based on the data collected from the "Concept Diagnostic Assessment."
Evaluation for 1.1d
TheImplementation Guideincludes detailed information on "Concept Internalization." It provides protocols and guidance for unit and lesson internalization and a list of reflective questions for teachers to consider as they work through each such as, "Which objective is a good starting point for small-group instruction?" "What do my students already know?" "What can they already do?" "What do they need support with?"The "Concept Guides" offer additional tools to support the internalization process. Each guide follows a consistent structure, beginning with a "Materials and Preparation" page that briefly overviews the concept and consolidates required supplies and student materials. Common student misconceptions are addressed, with strategies for prevention or remediation. A "Progress Check" outlines examples of student proficiency and includes guiding questions aligned to each objective. The "Concept Mini Lessons" page introduces four starting points within the unit and provides a visual sequence of the lessons with models.
Evaluation for 1.1e
Materials include resources and guidance for instructional leaders to support educators with implementing the materials as designed.TheImplementation Guidecontains a section titled "Guidance for Leaders."This sectioncontains questions that equip instructional leaders to proactively support educators in creating a classroom environment conducive to meaningful student engagement, learning, practice, and effectively implementing the components ofMath Catalyst Texas.
Evaluation for 1.2a
Each lesson has a TEKS-aligned learning objective such as "Represent numbers to 100,000 in standard form, expanded form, and expanded notation," locatedin Objective 3.The "Teacher Guide"allocates approximately 10 minutes for each objective lesson in every minilesson. The "Progress Check" section before each unit contains progress checks aligned to TEKS, which can be used before, during, or after lessons, along with rubrics to evaluate proficiency.The "Concept Guide" for each unit contains a list of teacher and student materials needed for lessons throughout the unit.The materials do not include assessment resources or learning objectives aligned to the ELPS.
Evaluation for 1.2b
This guidance is not applicable because the program is not designed to be adaptive.
Evaluation for 1.2c
The "Teacher Guide" contains support for families in English and Spanish on the "Family Math/Matemáticas en familia" page. The page begins with a letter to families introducing the concept students will learn and the visuals or models students will encounter. For example, the "Family Math" page forcomposing,decomposing, andrepresenting numbers includes three guiding questions for families to ask their students such as, "What is the largest unit in each number?" Each question includes a sample response that parents can use to guide discussion or listen for during conversation.
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.
5 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.
5 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.
0 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
90% (18 out of 20 points)
Evaluation for 2.1a
Math Catalystincludes an "Assessment and Data Collection" section in theImplementation Guidethat defines formative assessments and their purpose of informing instruction, identifying misconceptions, gauging progress, guiding instructional decisions, and helping educators adjust.The materials include examples of how to utilize different formative assessments such as "ApplicationActivities," "ProjectCheckTool" (pre- or post-assessment), "Think-Pair-Share" (under the application "Activities andConsiderations'), "Read-Draw-WriteTool" (under the application "Activities,Structures, andConsiderations"), and "PauseandMonitor Tool."
Evaluation for 2.1b
The materials use "Progress Checks" as their main instructional assessment. The "Progression Toward Proficiency Rubric" supports educators in determining proficiency for each task on the assessment. Students score either"Proficient," "Partially Proficient," or "Not Yet Proficient."The materials provide detailed guidance on how to look for and correct answers for each task.Each "Progress Check" includes "About the Progress Check Tool," "Using the Progress Check Tool to Inform Instruction," and a "Teacher Tip" section. The "ProgressCheck" includes clear instructions for the teacher and students to follow. For example, on the "Represent Contextual MultiplicationProgressCheck," question 1 states, "Use counters to model groups of 4 pears. Circle them. Complete the statement."
Evaluation for 2.1c
The materials neither include digital assessments, nor offer printable versions or accommodations such as text-to-speech, content and language supports, or calculators that educators can enable or disable to support individual students.Although theImplementation Guidedescribes assessment and data collection through tools like "Analyze Student Progress," the "Observational Data Recording Sheet," and the "Progress Check Tool," there are no digital assessments included in the program. TheNavigation Guidestates, "There are no digital components to this curriculum." Therefore, digital assessments with printable versions or accommodations are not available to educators.
Evaluation for 2.1d
Materials contain a "Concept Diagnostic Assessment" for each concept.The problems in the "Concept Diagnostic Assessment" are sequenced from simple to complex. Item types on the assessments include multiplechoice, number lines, place value charts, cards, counters to arrange, fillintheblank, and openresponse. Students are encouraged to show their work to provide additional insight about their thinking to the teacher.
Evaluation for 2.1e
The materials include a variety of TEKS-aligned formative assessments such as quick checks, quizzes, exit tickets, or embedded tasks within the lesson.Quick checks at the end of each objective assess student mastery and include varying levels of complexity. For example, in grade 3, formative assessments include five questions, starting with a simple task of writing a division number sentence with given information and ending with solving a word problem. The student practice pages start with using concrete objects to divide, and move toward abstract thinking by solving word problems. Finally, the materials provide application questions where students answer division word problems in a game setting.Theycan also apply and analyze a real-world situation with "Solve a Task."The materials include interactive item types within the "Progress Check Tool," which include plot the point, order numbers, fill in the blank, and multiplechoice.
Evaluation for 2.2a
Materials include informal and formative instructional assessments, including "Progress Checks." These assessmentsinclude numerical scoring information and guidance for interpreting student performance, including rating students as "Not Yet Proficient," "Partially Proficient," and "Proficient," for each item included in assessments.Materials do not include a rationale for each correct or incorrect response.
Evaluation for 2.2b
The materials provide guidance, including tasks and activities related to student performance on the "Progress Check." For example, in grade 3, in "Round to the Nearest Ten and Hundred," students answer five questions, and based on the level of proficiency, teachers can start students on one of four objectives, ranging from the use of a vertical number line or place value to round to the nearest ten or 100.
Evaluation for 2.2c
The materials include an "Observational Data Recording Sheet" that allows teachers to record individual students' anecdotal notes about each objective. The materials recommend that teachers use it often to inform their understanding of student performance.The materials include a "Pause and Monitor Tool," where students monitor their progress and growth by shading in progress such as "Getting started," "On my way," or "I got it!" Students use this tracker throughout the concept or on a specific objective.
Evaluation for 2.2d
The materials provide prompts to support educators in checking for understanding throughout the lesson. For example, in "Compose and Decompose Numbers to 100,000," Objective 1, there are prompts for teachers to conduct frequent checks for understanding throughout the lesson such as, "Can the student represent numbers to 100,000 by using place value disks and drawings in place value charts?", "Can the student use place value units to compose and decompose numbers to 100,000?", and "Can the student find the value of each place value unit?"During the lessons, the materials provide guidance to support educators in conducting frequent checks for understanding through "Teacher Tips." For example, after students represent the number in unit form, guidance states, "Students can use unit form to represent a number in multiple ways. Consider having students decompose the number by using place value in other ways."
Evaluation for 2.2e
This guidance is not applicable because the program is not designed to be adaptive.
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.
1 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.
1 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.
2 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.
2 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.
0 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
The materials include explicit guidance for educators when students need support in each "Concept Mini Lesson." For example, the "Concept Mini Lesson: Objective 3, Differentiation Support," states,"Some students may need support with drawing number lines. Consider providing number lines that are pre-partitioned or have some of the partitions."In the "Concept Guide" in the "Multiplication Unit," the materials include explicit educator guidance to address a misconception that some students have pertaining to identifying how to multiply using the length and width of an area model versus inefficiently drawing each piece of the array individually. The materials provide explicit guidance to have students identify the length and width of the rectangle by sliding their finger along the top and side while saying the terms aloud.
Evaluation for 3.1b
The materials include explicit educator guidance for language supports in the "Language Support" section in the "ConceptGuide" for each unit. For example, in the "Mini Lesson for Place Value,Objective 1," teachers describe how to compare the value of the digits in the largest unit when comparing two numbers while gesturing to the corresponding place value disks.In the "Mini Lesson for Place Value,Objective 3," the materials provide explicit educator guidance to make an anchor chart utilizing the specific terms that will be needed for the lesson in order to pre-teach and develop academic vocabulary.The materials provide explicit educator guidance to pre-teach unfamiliar terms in the text. For example, in Objective 1 of "Round Numbers to the Nearest Ten Using Vertical Number Lines," teachers are given explicit guidance to, "Consider formally naming the graduated cylinder if your students are not familiar with it, or use less specific terminology, such as container."The "Concept Guide" includes "Key Terminology" cards, which include student-friendly definitions and visual representations that provide a flexible opportunity for pre-teaching andreinforcing academicmathematical language.
Evaluation for 3.1c
The materials include explicit guidance for enrichment and extension activities for students with proficiency in grade-level skills. For example, in theteacher's"Concept Guide" in "Round to the Nearest Ten and Hundred," under the heading and chart "Activities, Structures, and Considerations," explicit teacher guidance is given on utilizing the enrichment and extension activities in this component. Students work on these activities independently or through partner work. The "Teacher Tips" section provides educator guidance for extending learning for students who have demonstrated grade-level proficiency.Each unit has an "Application" section that includes explicit educator guidance for enrichment and extension activities for students who have demonstrated proficiency in grade-level content and skills. Each unit has "Solve a Task" and "Partner Games" designed to extend and enrich the content.TheStrand by Grade Scope and Sequencedocument provides teachers with a clear view of howconcepts build across grades, enabling them to identify opportunities for extending learning beyond the current grade level. Additionally, the "Start here if students can. . ." statements in the "Progression of Mini Lesson Objectives" chart for the above-grade-level skill can point the teacher to the appropriate enrichment or extension activity for the student.
Evaluation for 3.1d
Digital materials are not interactive for students; accommodations are not evident in the materials available.These materials are static and do not include accommodations like text-to-speech, content and language supports, or calculators that educators can enable or disable to support students.
Evaluation for 3.1e
The materials include educator guidance on how to allow students to demonstrate understanding through various formats. For example, in "Compare and Order Numbers to 100,000," the "Teacher Tip" in Objective 2 states, "Other methods for renaming numbers into standard form are valid. For example, expanded form can be stacked vertically and added." This guidance shows an additional option for students to represent the value of a number to demonstrate their level of understanding.The materials include educator guidance for offering options for students to demonstrate understanding in various formats. For example, in "Understand Division Concepts, Objective 1," the materials provide guidance for offering options for students to demonstrate their understanding of division. One suggestion is to model "the concept of equal sharing by having students act out sharing a collection of items among several people." Another option allows students to represent division by using paper and pencil. By the end of Objective 1, students represent division with equal groups with drawings of groups and objects.
Evaluation for 3.2a
Materials include explicit prompts and guidance for educators to build knowledge by activating prior knowledge and anchoring big ideas. In the "Concept Guide" of Objective 1 of "Representations of Multiplication," the teacher connects the relationship between addition and multiplication by writing4 threes is 12as repeated addition, in unit form, and as a multiplication equation. The materials state, "Multiplication is another way to write repeated addition. Instead of writing addition of the same number over and over, we can write the number of groups times the number of objects in each equal group."The materials highlight and connect key patterns, features, and relationships through multiple means of representation. In "Multiplication as Multiplicative Comparisons," students are directed to use a variety of models to represent multiplication comparisons such as cubes in Objective 1, strip diagrams in Objectives 2 and 3, and expressions in Objective 4. The materials state, "When we describe multiplication as a comparison, the first factor tells us how many times to repeat the unit. The second factor tells us which unit is being repeated." This links multiplication to addition, a skill students should have shown proficiency in prior to starting multiplication.
Evaluation for 3.2b
Materials include educator guidance for effective lesson delivery and facilitation using various instructional approaches. In "Representations of Multiplication," students use tiles, arrays, and number lines to represent multiplication, providing an opportunity for hands-on exploration. At the end of Objective 1, "Plan Future Practice" instructs educators to use the provided practice page for students needing additional support. The guidance states,"Structure the additional practice strategically to allow for teacher support or peer support."In "Place Value—Composing, Decomposing and Representing Numbers," educators are guided to allow students to use place value disks for hands-on exploration, followed by drawing on place value charts when students order and compare multi-digit numbers. Additionally, the materials connect this to real-world scenarios in "Solve aProblem" word problem cards, when they order the number of books different libraries have from greatest to least.
Evaluation for 3.2c
Educators use the "Progress Tool" and rubric to determine the objective lesson students would benefit from starting on, based on the student's level of proficiency on the specified TEKS. In "Representations of Multiplication," students would begin on Objective 3 if they "need support identifying the size of equal groups and the number of equal groups in an area model." In Objective 3, guided practice involves using tiles and creating arrays. Students then complete an independent practice page. After students reach proficiency, they work independently or collaboratively on "Application" activities.In "Multiplication as Multiplicative Comparisons," students would start on Objective 3 if they "need support representing and understanding a multiplicative comparison in story contexts." In Objective 3, guided practice involves using strip diagrams and sentence stems to compare multiplication. Students then complete an independent practice page. After students reach proficiency, they work independently or collaboratively on "Application" activities.TheImplementation Guideincludes guidance that "Progress Checks" can be used as a pre-post assessment or as a small-group assignment. Teachers use "Concept MiniLessons" for small groups with direct instruction. Students can complete "Practice and Application" independently, with a partner or during small-group time.
Evaluation for 3.2d
Materials include enrichment and extension methods that support various forms of engagement, and guidance to support educators' effective implementation. In "Representations of Multiplication," students solve tasks such as "Solve a Problem," "Play a Game," "Study a Solution," and "Solve a Task." In "Solve a Problem," students work independently or with a partner. Teacher guidance includes "consider inviting students to share their work with a partner; students compare solution paths and make connections between different representations." In "Solve a Task," teacher guidance includes scaffolding such as "consider providing manipulatives for students to use to represent and solve the multiplication problems."In the "Fractions as Numbers" unit, the "Application" section includes word problems based on real-life stories such as using strip diagrams to model placing bananas equally in cereal, illustrating fractions of eaten bread, and using a number line to represent the amount of fence painted.
Evaluation for 3.2e
Materials include prompts and guidance to support educators in providing timely feedback during lesson delivery. In the "Teacher Guide"under"Multiplicative Comparisons," the teacher is guided to ask students what the factors in an equation represent related to sticky notes labeled with. After students answer what they represent, guidance is provided to address common misconceptions such as, "When we describe multiplication as a comparison, the first factor tells us how many times to repeat the unit. The second factor tells us which unit is being repeated."In "Representations of Multiplication," the teacher guides students to represent an expression on a number line in Objective 4. The teacher asks, "How can I use the number line to show the repeated addition? What do you think?" When students can make the connection between repeated addition and a number line, the teacher discusses labeling the number line and asks, "What number did we land on when we added 3? How do you know?" This gives the teacher opportunities to check for understanding and for students to explain their thinking.
Evaluation for 3.3a
The materials include educator guidance on providing and incorporating linguistic accommodations for all levels of language proficiency. The "Alignment Guide" for each concept provides alignment to theELPSand highlights embedded supports for different levels of language proficiency. For example, in "Representations of Non-Unit Fractions," the "Alignment Guide" contains descriptors that account for accommodations for all levels of language proficiency—including pre-production, beginning, intermediate, high-intermediate, and advanced—such as creating anchor charts and turn-and-talk opportunities for speaking practice.The grade 3 "Alignment Guide" for "Compare and Order Numbers to 100,000" addresseslistening,speaking,reading, andwriting skills at all ELPS levels and includes strategies such as having students discuss the meaning of comparison symbols, gesturing with place value disks and charts, writing practice with guidance, collaboratively playing games, listening and sharing with others, and writing and drawing activities to explain their thinking.
Evaluation for 3.3b
This guidance is not applicable to the program because it is not designed to be adaptive.
Evaluation for 3.3c
The materials include a section in theImplementation Guidededicated to specifically supporting emergent bilingual students and guidance for implementation to build vocabulary, comprehension, and knowledge. As stated in theImplementation Guide,"To support language output, teachers are encouraged to leverage the elements referenced above through strategically grouping students based on varied levels of mathematical proficiency or varied levels of English language proficiency. Teachers are also encouraged to complement any of these groupings by pairing students who speak the same language and encouraging them to use their home language alongside English to make sense of the directions and the mathematics." Further guidance states, "To support emergent bilingual students in making cross-linguistic connections through written discourse, teachers are encouraged to create cross-linguistic connections anchor charts. The chart should include terminology that is related to the current concept in the student's home language, the same terminology in English, and images to support understanding."TheImplementation Guideincludes a section called "Using Math Catalyst in State-Approved Bilingual/ESL Programs." This guidance outlines how the program aligns with various instructional models, including dual-language one-way and two-way approaches, and it offers strategies to support emergent bilingual students in building both language skills and math understanding.
Evaluation for 3.3d
The materials include embedded guidance to support emergent bilinguals. "LanguageSupports" embedded in the "Concept Mini Lessons" provide 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. In "Compose, Decompose, and Represent Numbers to 100,000," a "LanguageSupport" prompts the teacher to use "precise terminology" with the question, "What is the value of the thousands disks?" The support suggests that precise language supports students with place value concepts. In Objective 3, the "LanguageSupport" suggests making an anchor chart that labels the different ways to represent numbers with examples. The chart would include the number 43,215 in standard form, expanded notation, expanded form, and unit form. In Objective 4, the "Language Support" suggests another anchor chart, this time to make writing and spelling numbers accessible to students as they represent numbers in word form.In "Compare Fractions with the Same Numerator or Denominator," teachers are provided with a "Language Support" in Objective 1. The support states, "Consider activating students' prior knowledge of the meaning of each symbol by displaying an anchor chart with each symbol and its matching comparison language." Objective 3's "Language Support" suggests a word bank that includes "greater than, less than, equal to, unit fraction tiles, gaps, overlaps, numerator, denominator, unlike units, and compare." In Objective 4, the "Language Support" provides guidance to support the understanding of a position of a fraction on a number line, with phrase stems.The "Concept Guide" includes "Key Terminology" cards, which include student-friendly definitions and visual representations that provide a flexible opportunity for pre-teaching and reinforcing of academic mathematical language.
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.
0 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.
2 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.
2 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.
4 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.
4 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.
0 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
56% (9 out of 16 points)
Evaluation for 4.1a
Student practice activities guide students in exploring rounding. In the "Round two-digit numbers to the nearest 10 on a vertical number line,Objective 1" student activity, students use graduated cylinders to visualize a vertical number line. Students then use vertical number lines to solve real-world rounding problems in connection with temperature, progressing to word problems. Students use vertical number lines of different sizes and visualize their thinking before justifying their solutions in practice objectives.The "Progress Check Tool" for "Round to the Nearest Ten and Hundred" has problems related to these ideas.
Evaluation for 4.1b
Each "Concept Mini Lesson" breaks up learning into learning objectives that increase in rigor and complexity. For example, in the "Representation ofMultiplication"lessons,Objective1begins with students representing multiplication facts using equal groups, Objective2 hasstudents representing multiplication facts with arrays,Objective3has students representing multiplication facts using area model, andObjective4has students representing multiplication facts using equal jumps on a number line.Enrichment and extension tasks are embedded rather than offered separately. For example, students engage in enrichment through application activities.The materials do not include questions and tasks that increase in rigor and complexity, leading to above-grade-level proficiency in the mathematics TEKS.
Evaluation for 4.2a
The materials demonstrate coherence across concepts horizontally. In "Representations of Multiplication," strategies are built upon one another to velcro ideas for students. For example, in Objective 1 of "Representing Multiplication," students use tiles in equal groups to connect repeated addition to multiplication. In Objective 2, students use arrays to begin skip counting. InObjective 4, students can use a number line to skip count, count with repeated addition, or model a multiplication equation.Students also see connections to multiplication in other areas such as relating multiplication to finding the area of objects.
Evaluation for 4.2b
Materials do not demonstrate coherence vertically, including connections up to grade 6, by connecting patterns, big ideas, and relationships.The materials do provide an overview of progression in theStrand by Grade Scope and Sequence. They explain that in grade 3, the students compose, decompose, and represent numbers to 100,000. In grade 4, they build on this concept to compose, decompose, and represent numbers to the hundredths, incorporating decimals. In grade 5, the students progress to representing decimals to the thousandths place.
Evaluation for 4.2c
In the "Concept Mini Lessons," the sample dialogue provides direct prompts that help teachers activate prior knowledge at the start of instruction. For example, in the "Teacher Tip" in"Representations of Non-Unit Fractions, Objective 2," the teacher is guided to activate students' prior knowledge of unit fractions to understand non-unit fractions. This encourages students to draw on their previous understanding of fractions as a foundation for engaging with new fraction concepts in the lesson.In grade 3, the area model is consistently used with basic multiplication facts to lay the groundwork for understanding the more complex use of the area model with multi-digit multiplication in later grades. This intentional design helps students build on what they already know while preparing them for future mathematical concepts, ensuring both horizontal and vertical coherence throughout the program.The "Teacher Tips" embedded in the "Concept Mini Lessons" component provide targeted guidance to help educators connect students' current learning to future mathematical concepts. For example, in Objective 4 of the "Concept Multiplication as Multiplicative Comparison," a "Teacher Tip" offers guidance on how to advance strategies for students who might use less efficient multiplication strategies such as repeated addition and drawing arrays. This intentional prompt helps teachers deepen student understanding while building a conceptual bridge to more advanced mathematical ideas, supporting students' readiness for future learning.
Evaluation for 4.3a
Materials do not provide spaced retrieval opportunities with previously learned skills and concepts across learning pathways. The materials do not review previously learned skills or concepts across learning pathways and focus only on current learning.
Evaluation for 4.3b
The materials do not provide interleaved practice opportunities, as the activities and interventions provided focus on solo objectives without addressing interleaved topics and skills.
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.
2 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.
2 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.
0 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.
0 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.
0 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.
0 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.
0 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.
0 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
97% (37 out of 38 points)
Evaluation for 5.1a
The materials include questions and tasks that prompt students to interpret, analyze, and evaluate models and representations. For example, in "Compare and Order Numbers to 100,000," students use place value disks to compare and order numbers. Then, students use a place value chart and are asked, "What is the next largest unit? How do you know?" The prompts require students to analyze the place value chart and provide reasoning for the next unit available. Last, students create a number line and evaluate the placement of numbers on the number line compared to other numbers such as placing 20,000 and 22,000 on the number line and determining where to place 21,064 on the same line.In "Understand Division Concepts," questions and tasks provide opportunities for students to interpret, analyze, and evaluate division models and representations. Students use cubes to distribute into equal groups. The teacher asks, "What does the number 10 represent in this problem?," prompting the student to interpret the meaning of the dividend. Students analyze the different parts of a division equation when asked, "What number represents the total? The number of groups? The size of each group?" Last, students evaluate models when asked, "How do I know when to stop drawing dots?"
Evaluation for 5.1b
The materials provide opportunities for students to create concrete and pictorial models to represent mathematical situations. For example, in the "Teacher Guide"under"Understand Division Concepts," students start by using cubes to model division. Then, students go from drawing models of buttons, to dividingand extending drawing strip diagrams to show equal groups of a given total.In the "Compare and Order Numbers to 100,000" lesson, students begin by using place value disks. In the next lesson, students use a place value chart and compare numbers based on the largest units. Last, students create number lines to place numbers in order between benchmark numbers.
Evaluation for 5.1c
The materials provide opportunities for students to apply conceptual understanding to new problem-solving situations and contexts. For example, in the "Teacher Guide"under"Place Value and Rounding," students extend their understanding of rounding to the nearest ten and hundred by solving problems in real-life contexts. For example, students solve the following problem by using a visual aid/table with concert ticket cost information,"Mr. Davis buys 2 adult tickets and 3 child tickets. What is the total cost of the tickets, rounded to the nearest ten dollars?"Early in the multiplication unit, students use concrete objects to understand multiplication. Later, in the "Application Section" of the unit, questions and tasks provide opportunities for students to apply conceptual understanding to new problem situations and contexts such as opportunities for students to make up stories that fit a given two-digit by one-digitmultiplication problem, and finally, students are given a cake recipe and asked to find the amount of each ingredient based upon multiplying quantities.
Evaluation for 5.2a
In Grade 3, the materials provide tasksthat includefluency-building games designed to build automaticity and fluency with composing, decomposing, and place value representations of numbers. For example, in the "Teacher Guide" for the"Play a Game" application,"Compose, Decompose, and Represent Numbers to 100,000," students look for a pair of cards that represent a number in standard form and the same number in word form or expanded form. If the cards form a matching pair, students take the cards and continue, turning over two more cards. If the cards do not make a matching pair, they turn the cards back over, and it is the next partner's turn.The "Application"section of "Fractions as Numbers; Representations of Unit Fractions" includes a game where students use unit fractions match cards to match the model and the matching unit fraction, which builds student automaticity and fluency necessary to complete grade-level tasks.
Evaluation for 5.2b
In "Representations of Multiplication," students use concrete objects to build multiplication number sentences. As students become proficient in using concrete models, they build arrays and number lines. Students apply their understanding and solve problems, including "Study a Solution" in "Application." Students are asked, "How does the drawing help you see a solution path for finding the unknown?" This givesstudents opportunities to select their methods to solve problems and analyze accurate models.Throughout the "Comparing Fractions" unit, students compare fractions with the same denominator using fraction tiles. They are then asked to draw two given fractions on a number line and compare them. Students do this repeatedly to ensure efficiency, flexibility, and accuracy with the comparison procedures.
Evaluation for 5.2c
In "Representations of Multiplication," students build concrete models, arrays, and number lines to represent multiplication as repeated addition. Next, students analyze a model and determine the strategy that does not belong. Students answer, "Which representation does not represent the multiplication shown on the number line?" Students complete an activity called "Study a Solution," where they analyze a correct solution and choose a path that they would use to solve the same problem.The "Error Analysis Tasks" in each practice component provide opportunities for students to evaluate mathematical representations, models, strategies, and solutions throughout the learning pathways. In the "Represent Numbers to 100,000 in Unit Form" unit, students represent numbers to 100,000 in unit form and show each digit's value. Students then analyze the visual representation of a number and identify the error. Students have flexibility when choosing a strategy to solve the problem themselves.
Evaluation for 5.2d
Materials provide guidance to support students in more efficient approaches to solving mathematical problems. In "Multiplication as Multiplicative Comparisons," students compare numbers as multiples of one another through concrete and semi-abstract strategies. As students become more proficient in one strategy, the materials introduce more efficient strategies to solve mathematical problems.The materials include educator notes about which tool, method, or approach is appropriate and efficient for solving a task when the task requires students to select an approach. For example, in the "Objective 4 Mini Lesson: Two-digit by one-digit multiplication: Teacher Tip," the materials provide guidance to teachers that state, "In grade 3, students solve by using strategies, such as repeated addition and drawing arrays. Although those strategies can be used to multiply accurately, they are generally not the most efficient strategies. Support students in advancing their strategies. Ask them to identify similarities between their strategies and strategies that might be more efficient."
Evaluation for 5.3a
TheImplementation Guideprovides information on the "Balance of Conceptual Understanding and Procedural Fluency." This informative guidance explains that, "The objectives in Concept Mini Lessons progress in complexity and provide opportunities for students to develop conceptual understanding and procedural fluency. The Practice component helps students solidify their conceptual understanding and procedural skills."In the "Teacher Guide" under"Place Value—Compose, Decompose and Represent,"thereis explicit guidance on the link between using linking cubes to build arrays and sticky notes to build strip diagrams to solve multiplication.In the "Progression of Mini Lesson Objectives for the Multiplication" unit, the materials state how students move from 1) multiplying using concrete models of the distributive property to 2) multiplying using place value drawings and partial products to 3) multiplying by recording partial products in vertical form to finally 4) multiplying by using the standard algorithm.
Evaluation for 5.3b
The materials provide opportunities for students to engage with concrete models, pictorial representations, and abstract models throughout the "Concept Mini Lessons." In "Compose, Decompose, and Represent Multi-Digit Numbers," students use place value disks to compose and decompose numbers into a place value chart in Objective 1. In Objective 2, students use the pictorial representation of the place value to write numbers in unit form.In "Compare Fractions with the Same Numerator or Denominator," students use fraction tiles to compare fractions with the same denominator in Objective 1. In Objectives 2 and 3, students transition to pictorial representations such as strip diagrams and number lines. In Objective 4, students use comparison symbols to show the concept of greater than/less than.
Evaluation for 5.3c
In "Compose, Decompose, and Represent Numbers to 100,000," students use place value disks to represent numbers using concrete models in Objective 1. As students regroup, they explain their thinking to answer questions, such as, "When I bundle ten thousands, what is the name of the unit? What do you think?" Students progress to pictorial representations with place value charts in Objective 2. In Objective 4, students use the place value charts, replacing the dots with digits to write numbers in word form.In "Compare Fractions with the Same Numerator or Denominator," students represent fractions with fraction tiles. In Objective 1, the teacher prompts the students to explain their thinking: "I can ask myself, How many one-sixth unit fraction tiles do I need to represent 5/6? What do you think?" In Objective 2, students transition to using number lines. Students answer, "Is3/4greater than, equal to, or less than 1/4? How do you know?" Students transition to comparison symbols to represent fraction comparisons in Objective 4.
Evaluation for 5.4a
In the grade 3 "Teacher Guide"under"Place Value Composing and Decomposing," students use unit fraction tiles, repetition from the teacher, visual cues from the teacher, and strip diagrams to develop and explore academic mathematical language such as numerator and denominator, to describe fractional parts.In the grade 3 "Teacher Guide"under"Multiplication: Relate Multiplication to Area," students use tiles to develop their mathematical language using visuals (pictures of the tiles) and manipulatives in the mastery of words such asarea,side length,rows,column,multiply, andsquare unit.
Evaluation for 5.4b
In the "Teacher Guide"under"Multiplication," the materials include embedded educator guidance to scaffold and support students' use of academic mathematical vocabulary in context when communicating with peers and educators. Objective 1 provides sentence stems for students to communicate with peers, such as "You have _____ cubes. I have _____ times as many cubes as you. I have _____ times as many as _____."In the "Teacher Guide"under"Representations of Multiplication," language support scaffolding is suggested to provide sentence frames to help students verbalize how many equal groups there are and how many in each group. The sentence frames state, "There are __ equal groups of __. There are __ in each group. There are __ groups."The "Concept Guide" includes "Key Terminology" cards, which include student-friendly definitions and visual representations that provide a flexible opportunity for pre-teaching and reinforcing of academic mathematical language, as well as extending students' use of academic vocabulary in context when communicating with peers and educators.
Evaluation for 5.4c
In the "Teacher Guide"under"Compare and Order Numbers to 100,000," students compare numbers using place value disks or a place value chart. Guidance in Objective 1 includes a turn-and-talk with students explaining how they used place value to compare numbers. Additional questions include, "What digit is in the largest unit of each number? What is the value of the digit?" In discourse, students use vocabulary such ascompare,equal to,greater than,less than, andunit.In the "Teacher Guide"under"Multiplication of Two-Digit Numbers by One-Digit Numbers," the Objective 2 "Teacher Tip" instructs the teacher to "invite students to turnandtalk about how they can find the area of a shape composed of rectangles by subtracting from a larger area."
Evaluation for 5.4d
Materials provide guidance that allows students to hear and refine the use of math language with peers. In the "Teacher Guide"under"Compare and Order Numbers to 100,000," students compare numbers using place value disks or a place value chart. Guidance in Objective 1 includes a turn-and-talk with students explaining how they used place value to compare numbers. The materials also include guidance for students to advance and refine their thinking in discourse with questions such as, "What is the largest unit in each number?" and "What is the next largest unit in each number?"In the "Teacher Guide"under"Fractions as Numbers: Representations of Non-Unit Fractions," the materials guide the teacher to, "Invite students to turn and talk about how they can represent non-unit fractions on the number line."
Evaluation for 5.4e
The materials provide one exemplary response to the question and tasks. For example, in the "Teacher Guide"under"Compare and Order Whole Numbers to 100,000" in Objective 2, the materials include questions followed by exemplar student responses, such as Q: "What is the next largest unit? How do you know?" R: "The next largest unit is thousands. 3,000 represents 3 thousands." Guidance continues, Q: "Next, the expanded form shows one ten. Is the tens column the next column in the place value chart?" R: "No. The hundreds column is next."In the "Teacher Guide"under"Compare and Order Numbers to 100,000" in Objective 2, the materials ask questions such as, "Look at the next number we are comparing, the number written in expanded form. What is the largest unit in that number? How do you know?" The exemplar response follows: "We know the largest unit is ten thousands because the expanded form shows 60,000. The number has six ten thousands."The "Concept Mini Lesson" component features visual examples of sample student work, providing teachers with clear expectations for what proficient solutions may look like. The "Analyze Student Progress" section of every "Concept Mini Lesson" offers "Questions to Advance Student Thinking." These prompts help teachers interpret a variety of student strategies, identify misconceptions, and provide scaffolded guidance to support students in correcting inaccuracies. Beyond the "Concept Mini Lessons," the "Addressing Student Misconceptions" section of each "Concept Guide" provides explicit guidance for responding to common misunderstandings, ensuring that teachers have actionable strategies to redirect inaccurate responses.
Evaluation for 5.5a
TEKS process standards are integrated into the materials. In "Compare and Order Numbers to 100,000," students compare numbers (content) in "Solve a Problem" in the "Application" section (process) while using a place value chart (process) to align digits.In "Representations of Multiplication," students play a game in the "Application" section where they multiply (content) the two numbers turned over on cards while using square inch tiles or grid paper (process) to solve the equations.
Evaluation for 5.5b
TheImplementation Guideincludes a paragraph detailing how the process standards integrate into different components of the program. TheImplementation Guidestates, "In 'Compare and Order Numbers to 100,000,' students use manipulatives and visuals, including place value disks and place value charts, to represent numbers."In "Representations of Multiplication," theImplementation Guidedescribes how students will use objects and visuals such as tiles and number lines to represent multiplication.The "Alignment Guide" for each math strand lists the process standards incorporated in that unit. For example, the "Alignment Guide" lists the following process standards in the multiplication pathway: "1A, 1C, 1D, 1E, 1F, 1G." The "Alignment Guide" lists the process standards for each math strand and how they connect throughout the pathway.
Evaluation for 5.5c
Materials do not include an overview of the TEKS process standards incorporated into each lesson. The materials include an "Alignment Guide" for each unit, which includes a section listing the process standards but does not highlight which process standards fit into each lesson.
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.
0 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.
0 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
89% (17 out of 19 points)
Evaluation for 6.1a
In the "Teacher Guide"under"Multiplication as Multiplicative Comparisons," each conceptminilessonobjective and question increases in difficulty, allowing students to build confidence before tackling more complex problems.Questions provide opportunities for students to think mathematically and make sense of the mathematics such as "Which factor represents the unit that is repeated? How can you show that with your cubes?," "Which factor represents how many times the unit is repeated? How can you show that with your cubes?," and "How can you use times as many to describe the multiplication expression?"In the "Teacher Guide"under"Multiplication: Representations of Multiplication," students solve a task involving multiplication. Students use the provided information and image to solve three problems. The materials instruct teachers that students must think critically to determine the solution.
Evaluation for 6.1b
In the "Teacher Guide"under"Round to the Nearest Ten and Hundred," the "Solve a Problem" activity in "Application" supports students in understanding, explaining, and justifying their way of solving a problem by asking them to, "Consider inviting students to share their work with a partner. Students can compare solution paths and make connections between different representations."In "Multiplication of Two-Digit Numbers by One-Digit Numbers," the "Read-Draw-WriteTool" provides scaffolding for students to understand the problem, explain what they know, and justify their thinking.
Evaluation for 6.1c
The "Round to the Nearest Ten and Hundred" application activities in the"Teacher Guide"provides opportunities for students to write about and discuss math with peers. In "Solve a Problem," students share their work with peers to discuss the different solution paths and make connections between different representations. Students use the "Read-Draw-WriteTool" to organize and reflect on their problem-solving.In "Represent numbers to 100,000," the materials ask students to represent numbers in multiple ways. The teacher asks students to "decompose the number by using place value in other ways." Students use provided examples of renaming numbers using different place value units.In "Find the Area of Composite Shapes by Using Rectangles," Objective 4, students "choose a strategy to use to find the area of the shaded shape." Students use different strategies to find the area of the rectangle such as finding unknown lengths in different ways and decomposing the rectangle in different ways. Students then share their work with others.
Evaluation for 6.2a
Materials support educators in guiding students to share and reflect on their problem-solving approaches with explanations, arguments, and justifications. In the "Teacher Guide"under"Compare and Order Numbers to 100,000," students turn and talk, explaining how comparing and ordering numbers are similar and different in Objective 3.In the "Compare and Order Numbers to 100,000"application, students compare numbers byplaying a game "Three in a Row." The materials provide opportunities to argue and justify student solutions when comparing work, including prompts such as, "If you disagree, share your work with each other and find the mistake."In the "Compare Fractions"application, students play a game where they are comparing fractions and writing comparison statements on whiteboards with partners. To explain, justify, and argue their solutions, students answer the following prompt: "If you disagree, share your work with each other and find the mistake."
Evaluation for 6.2b
Materials include prompts to support educators in providing feedback for anticipated misconceptions. In the "Teacher Guide"under"Fractions as Numbers: Compare Fractions with the Same Numerator or Denominator," in the "Addressing Student Misconceptions section," prompts support educators for possible misconceptions such as, "How many partitions do you need to make from 0 to 1 to represent each fraction?" and "What do you notice about the size of the parts on the number line?"The materials include guidance on how to support educators in anticipating misconceptions. In the "Teacher Guide"under"Relate Multiplication to Area," the materials identify students' thinking that they need to fill in the entire array as a misconception and provide suggestions on addressing this throughout the lesson. For example, the materials suggest teachers emphasize vocabulary terms with tactile movements and connect them to a corresponding multiplication sentence. They also suggest that the teacher explicitly connect the multiplication sentence to the number of rows and columns.The materials do not include prompts or guidance for explanatory feedback based on student responses. The materials include "Teacher Tips," which include various types of support.However, the tips do not include prompts or guidance that support the educator in providing explanatory feedback based on student responses.
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.
2 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.
2 out of 4 points