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 1
Supplemental Math (English) Grade 1
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 1 | 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 "Alignment Guide"aligns the Texas Essential Knowledge and Skills (TEKS), the learning path for each concept, connects to the "TEKS Mathematical Process Standards," and organizes the English Language Proficiency Standards (ELPS) into a K–3 grouping.TheImplementation Guideidentifies "Embedded Supports for Language Proficiency" and specifies the locations of these supports for each proficiency level. For example, in "Early Numeracy: Perceptual Subitizing Within 5," the guide describes how students at the Pre-Production level, in "Concept Mini Lesson Objective 3," circle groups that show a given number of dots. For students at the Beginning level, in "Concept Mini Lesson, Objective 1," the "LanguageSupportNote" offers guidance on using language as a resource by encouraging students to say numbers in their home languages and then pair them with numbers in English.TheStrand by Grade Scope and Sequencestates, "Math Catalyst Texasprovides a mathematical progression of concepts unbound by the constraints of grade-level standards. . .the Concepts and Objectives within each strand build upon each other to form a ladder of mathematical understanding. . .Equipped with student data that can help inform decisions, teachers can move among the Objectives in a strand independent of grade level to find the most useful support for meeting individual students' needs so that they can continue to climb."
Evaluation for 1.1b
The materials provide anImplementation Guidewith usage recommendations and strategies to support effective educator use, including just-in-time supports, advanced learning opportunities, and full-course implementation. The guide defines the program as "a supplemental instructional resource designed to be used with a Multi-Tiered System of Supports (MTSS). . ." and clarifies its focus on Tier 2 and Tier 3 instruction delivered outside of Tier 1 core instruction. The guide includes visual representations of this definition, the covered concepts, and their vertical and horizontal alignment.In the "Program Implementation" section, teachers receive practical tools such as "Possible Ways to Use Components" and "Sample Schedules" in 15- and 30-minute formats. To support emergent English bilingual learners, the guide offers strategies for setting up center rotations, accompanied by a sample lesson schedule.In the "Concept Internalization" section, educators reflect on guiding questions to determine entry points into "Concept Mini Lessons," advance instruction using "Practice and Application," and assess student progress through the "Progress Check."
Evaluation for 1.1c
The materials include a "Concept Diagnostic Assessment" available at the start of each Concept, designed to measure student mastery of the skills in the Concept. The assessment includes a rubric, and each assessment item is labeled with the correlating TEKS for theobjectives assessed. TheImplementation Guidestates that the provided rubric is "to help teachers analyze student responses, determine a student's proficiency level and identify skill entry points."The materials include aStrand by Grade: Scope and Sequenceand anImplementation Guideused as a TEKS correlation guide. TheImplementation Guidedirects educators, under "Determining Intervention Needs for Students," to administer a district- or school-selected screening tool and analyze the resulting data to determine next steps. These assessments, combined with the "Concept Diagnostic Assessment," provide data that can be used to inform instruction and provide timely intervention.The "Concept Diagnostic Assessment" guides educators to specificobjectives within the Concept of the materials. For example, in the grade 1, "Concept Diagnostic Assessment: Conceptual Subitizing Within 10," the materials direct educators to consider several statements when making "instructional decisions about skill entry points based on the data collected from the Concept Diagnostic Assessment," such as "Can the student see groups of up to 5 objects as smaller recognizable quantities that can be composed to determine the total? (Objective 1), Can the student see groups of up to 7 objects as smaller recognizable quantities that can be composed to determine the total? (Objective 2), Can the student see groups of up to 10 objects as smaller recognizable quantities that can be composed to determine the total? (Objective 3)."
Evaluation for 1.1d
The materials include protocols to help teachers internalize units, supported by theImplementation Guide's "Concept Internalization" section. Guiding questions help teachers use the three components effectively, such as, "Which objective is a good starting point for small-group instruction?" In grade 1, the "Concept Mini Lessons: Compare and Order Numbers to 120" progresses from comparing2quantities to 100byusing place value and comparative language, to ordering whole numbers up to 120 using an open number line.The "Progress Check" section asks, "What does proficiency look like with the content of this concept?" In grade 1, the "Progress Check: Compare and Order Numbers to 120" helps teachers use data from the "Progress Check"tool to guide instruction. Questions focus on whether students can compare numbers up to 100 by using place value and comparative language as well as order those numbers on an open number line.The "Concept Guide"outlines materials, preparation strategies, and how to address misconceptions with step-by-step teacher and student actions. In the grade 1 guide for "Compare and Order Numbers to 120," the teacher uses familiar charts to represent numbers with questions like, "How many hundreds do you see? Tens? Ones? What is the largest place for each number?"
Evaluation for 1.1e
The materials include anImplementation Guidethat instructional leaders can use to support effective program implementation. This guide outlines the program's structure, offers suggestions for using each component, and provides a sample schedule. Additionally, the "Concept Guide"lists the teacher and student materials, recommended preparations, and key considerations for instruction.The materials include a "Concept Internalization" of theImplementation Guideto support teachers and instructional leaders in the use of the materials. Each major component of the materials includes questions for educators that can be used by instructional leaders. For example, the "Concept Mini Lessons" section lists questions 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?"TheImplementation Guidealso includes a "Guidance for Leaders" section that mirrors the guidance in the "Concept Internalization" section. For example, the "Concept Mini Lessons" section lists questions such as, "How are data analysis and the Progression of Mini Lesson Objectives used to determine the appropriate amount of support that will meet students' needs?"
Evaluation for 1.2a
The materials do not include ELPS in either the assessment resources or the learningobjectives, though lessons incorporate ELPS-aligned tasks involving listening, speaking, reading, and writing. Teachers track progress using tools like the "Observational Data Recording Sheet" and informal notes.The materials include 10-minute lesson plans with clearobjectives, time frames, summaries, differentiation strategies, and progress monitoring tools. Each "Concept Guide"lists required materials, preparation tips, supports for addressing misconceptions, language scaffolds, and "FamilyMath" pages. For example, grade1's, "Concept Guide: Compare and Order Numbers to 120" includes "ProgressChecks," mini lessons, manipulatives, templates, and student pages for Objectives 1–4.Assessments are directly aligned with TEKS and increase in complexity acrossobjectives. In grade1, the "ProgressCheck" begins with comparing numbers using place value and ends with ordering numbers to 120 on an open number line. These assessments align with TEKS 1.2E and 1.2F.
Evaluation for 1.2b
This guidance is not applicable because the program is not designed to be adaptive.
Evaluation for 1.2c
The materials contain support for families in both English and Spanish for each unit for families to use at home to support learning. For example, each concept has a "Family Math" letter for families in both languages.This letter states the objective, explains the objective, and then provides simple practice for home. The letter presents illustrations, sample questions, and correct student answers.The "Family Math" letter presents direct support for students at home using academic vocabulary in both languages. For example, in the grade 1, "Concept Guidefor Compare and Order Numbers to 120," the "Family Math" letter reads, "Your student is working on comparing and ordering numbers to 120 by using place value. They use charts, number bonds, and symbols to compare two numbers. Then they use charts and number lines to compare and order three numbers. You can support your student's progress by asking the questions in the table below as your student uses an open number line to order numbers from least to greatest." The letter ends with sample questions, correct answers, and illustrations of the objective.
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
The materials define various instructional assessments and their purposes. TheImplementation Guidedescribes "Core Math Assessments" as formative and summative tools for measuring student proficiency in specific skills and concepts, useful for identifying intervention needs. It also presents the "Pause and Monitor Tool" as a way for students to reflect on and track their progress.According to theImplementation Guide, the "Analyze Student Progress" section in "Concept Mini Lessons" includes questions for informally assessing student proficiency on current objectives. It also offers guidance on using the "Observational Data Recording Sheet" to document performance and make instructional notes during any lesson component.The "Progress Check"tool serves as both a pre- and post-assessment, with a rubric to evaluate student responses and determine proficiency. Each section explains how to apply the tool to specific objectives. For instance, in grade 1, "Addition: Understanding Equality," the tool is used to collect proficiency data and is not graded.
Evaluation for 2.1b
Each lesson's "Concept Guide"lists the materials and preparation steps needed to administer the "Progress Check" and "Pause and MonitorTool." For example, thegrade 1, "Understand Equality" guide details teacher and student materials, including specific color-coded linking cubes and preparation instructions.The materials support consistent assessment through the "Observational Data Recording Sheet," which helps teachers track performance and adjust instruction. In thegrade 1, "Progress Check: Conceptual Subitizing Within 10," teachers are guided to use specific language, support students in their home language, and pause the assessment if needed for reteaching.Each "Progress Check" includes step-by-step instructions, a teacher script, and expected student responses to ensure standardized administration. For instance, thegrade 1, "Conceptual Subitizing Within 10" assessment includes an overview, guiding questions, and a "Progression Towards Proficiency Rubric" to evaluate understanding.
Evaluation for 2.1c
The materialsneitherinclude digital assessments, nor do they 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 DataRecordingSheet," 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
The materials include a "Concept Diagnostic Assessment" at the beginning of each Concept with TEKS-aligned tasks or questions, and interactive item types with varying complexity levels. TheImplementation Guidestates, "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. It enables educators to monitor students' progress, identify learning gaps, and adapt instruction to meet students' needs."Each "Concept Diagnostic Assessment" includes a rubric that ranks student proficiency from "Not Yet Proficient," "Partially Proficient," and "Proficient," and lists the TEKS for each objective assessed in theconcept. Tasks and questions within each assessment are sequenced from simple to complex, and include various tasks and responses for students to show progression towards mastery. Teachers are directed to end the assessment if the student is unable to answer the first questions and try again after the student receives more instruction.In the grade 1, "'Concept Diagnostic Assessment': Conceptual Subitizing Within 10," students begin by verbally responding to a task before recording their own answer using a writing tool and the included student assessment page.
Evaluation for 2.1e
The "Assessment and Data Collection" section on page 7 of theImplementation Guideoutlines how the program supports ongoing formative assessment. This section details the use of two key tools:the "Observational Data RecordingSheet" and the "Progress CheckTool." The Observational Data Recording Sheet is designed to help educators capture formative assessment data during daily instruction. TheImplementation Guideprovides guidance on using this sheet to collect evidence of student understanding across various components of the program. Additionally, eachconcept includes a "Progress CheckTool" that presents problems aligned to the TEKS, sequenced from simple to complex. This design allows educators to evaluate students' grasp of theconcept's objectives at increasing levels of depth. The "Using the "Progress CheckTool" to Inform Instruction" section provides targeted guidance on interpreting student responses and using the data to inform next steps in instruction—an essential feature of high-quality formative assessment.The "Progress Check Tool: Conceptual Subitizing Within 10" moves from identifying groups of up to5objects to composing totals from groups of up to 10. In the "Compose, Decompose, and Represent Numbers to 120" check, students represent two-digit numbers using tens and ones, progressing from concrete to abstract forms.
Evaluation for 2.2a
The materials do not provide a rationale for correct and incorrect responses.The materials contain instructional assessments, scoring information, and guidance for interpreting student performance. The materials provide a "Progress Toward Proficiency Rubric," which outlines how to assess students' proficiency levels at the end of each unit's "Progress Check." The rubric guides teachers in rating students as"Not Yet Proficient," "Partially Proficient," and "Proficient,"based on descriptors that progress from simple to complex problems. If a student cannot answer the initial, simpler questions, the materials instruct the teacher to "end the assessment and retry after more instruction."In the "Concept Guide"for each strand, the materials include an "Addressing Student Misconceptions" section listing frequent misconceptions and explicit guidance for teachers on how to address them. The "Analyze Student Progress" section within each "Concept Mini Lesson" gathers data on student performance to determine mastery, including questions to "MonitorProgress," "Advance Student Thinking," and "Plan Future Practice."
Evaluation for 2.2b
The materials provide guidance on using included tasks and activities to respond to student trends in assessment performance. TheImplementation Guideidentifies the "Progress Check" as a tool for collecting data on student proficiency, supported by a rubric that highlights strengths and intervention needs.TheImplementation Guideprovides direction for using tools like the "Analyze Student Progress" section, "Observational Data RecordingSheet," and "Progress Check Tool" to respond to performance trends. These tools help track proficiency, record notes during lessons, and analyze student work to determine next steps.Each "Concept Mini Lesson" includes a "Progression of Mini Lesson Objectives" aligned with the previous "Progress Check," and provides skill-specific guidance. Lessons include scripted support, examples, activities, and differentiation tips. For example, in grade 1, "Place Value: Compose, Decompose, and Represent Numbers to 120," teachers are directed to begin with students who can read, write, and represent whole numbers from 0 to at least 20, but need support representing two-digit numbers as tens and ones.
Evaluation for 2.2c
The materials include tools for teachers to track student progress and growth, as well as tools for students to monitor their own development. One tool is the "Observational Data Recording" Sheet, embedded in every concept. This sheet allows teachers to document performance on each objective and make notes during any lesson component, including written practice.The "Pause and Monitor Tool" supports student self-assessment by prompting reflection on learning and progress. According to theImplementation Guide, students use it to write"I can"statements, track skill development, gather evidence, and collaborate on goals.The "Progress Check Tool" is used as a pre- and post-assessment to evaluate proficiency with skills taught in "Concept Mini Lessons." It includes a rubric to help teachers analyze responses, celebrate progress, and plan for mastery.
Evaluation for 2.2d
The materials provide prompts and guidance to support educators in conducting frequent checks for understanding at key points throughout each lesson or activity. "Teacher Tips" in the "Application" section offer strategies for monitoring progress and differentiating instruction. For example, in grade 1, "Addition: Add Within 100 by Using Mental Strategies," a tip suggests facilitating a small-group activity to informally assess understanding and provide support.Each "Concept Mini Lesson" includes an "Analyze Student Progress" section with targeted questions to help teachers assess understanding. In the grade 1, "Addition: Add Within 100 by Using Mental Strategies" lesson, teachers monitor learning by asking if students can say the presented number sentence in unit form or if the student can represent a number sentence with cubes and drawings.Scripted questions embedded in each "Concept Mini Lesson" guide teachers in checking for understanding during instruction. For example, in the grade 1, "Addition: Add Within 100 by Using Mental Strategies," the teacher asks students to write a number sentence to match your drawn representation of a 2-digit number and determine the total or sum while explaining how they know.
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
81% (29 out of 36 points)
Evaluation for 3.1a
The materials provide explicit guidance for lessons and activities scaffolded for students who have not yet mastered prerequisite or grade-level concepts and skills. According to the "Determining Intervention Needs for Students" section of theImplementation Guide, teachers should collect informal data by asking students to explain their thinking during math instruction. Recording classroom observations and student conversations offers an additional data point when identifying appropriate interventions.TheImplementation Guide's "Possible Ways to Use Components" section explains how to incorporate the "Concept Mini Lessons." These mini lessons give explicit guidance and activities for students who have not yet reached proficiency. The materials suggest that teachers review or preview concepts in small groups and embed the appropriate content within lessons to strengthen skills.Each "Concept Mini Lesson" opens with a "Progression of Mini Lesson Objectives." Under each objective, the materials tell the teacher where to begin based on the student's current proficiency. For instance, in the grade 1 lesson, "Place Value: Compose, Decompose, and Represent Numbers to 120," Objective 1 advises starting with students who can "read, write, and represent whole numbers from 0 to at least 20, but need support identifying one ten as a unit and need support representing two-digit numbers as tens and ones."
Evaluation for 3.1b
The materials include explicit educator support for pre-teaching unfamiliar references in text or for developing academic vocabulary. The "Development of Academic Mathematical Language" of theImplementation Guidedescribes the embedded support for teachers to help students understand and use precise mathematical language such as using manipulatives and visuals and following the "Language Support" in "Concept Mini Lessons" to scaffold vocabulary growth. Further, the materials include "Key Terminology" cards in each "Concept Guide." The cards include "student-friendly definitions and visual representations that provide a flexible opportunity for pre-teaching andreinforcing academicmathematical language." Each set of cards can be used as flashcards, portable word walls, and sorting activities.The materials embed support for developing academic vocabulary during instruction. In the lesson "Concept Mini Lessons: Compose, Decompose, and Represent Numbers to 120," Objective 1 begins with students creating the number 23 by linking cubes and saying the number while the teacher explains, "It is important to say 2 tens, not just 2. Tens is the unit. Units tell us what we are counting, like tens or ones. We say the unit so that it is clear what we mean." The teacher then uses place value cards to model the number 23 while saying, "23 is a two-digit number, so it has two places. The digit 2 is in the tens place and tells us that there are 2 tens in the number. The digit 3 is in the one's place and tells us that there are 3 ones in the number."The materials also embed supports for unfamiliar references in text. In the lesson, "Subtraction: Subtract Within 20," students work on subtraction by counting on to 10. The included Language Support contains a visual cue and states, "As students add strategies for subtraction to their mental toolbox, pair the strategy name, Count On to 10, with a visual to support students in using and discussing the strategy. Consider creating an anchor chart for reference."
Evaluation for 3.1c
TheStrand by Grade Scope and Sequencedocument shows how concepts build across grades, enabling teachers to identify opportunities for extending learning beyond the current grade level. The "Start here if students can. . ." statements in each "Progression of Mini Lesson Objectives" chart allow teachers the opportunity to work with students on above-grade-level skills for enrichment or extension. Teachers then use the "Solve a Task" in the "Application" activities to promote enrichment through open-ended problem-solving and flexible reasoning.TheImplementation Guidestates the, "Practice and Application" sections are to "provide enrichment and extension opportunities." Each "Practice and Application" has a chart with listed activities, the purpose of the activity, and considerations. These considerations make suggestions on how to modify the activities to meet the needs of the student based on proficiency level.The materials include specific prompts for advanced questioning during discussions. At the end of each objective in the "Concept Mini Lesson," there are "Questions to Advance Student Thinking." For example, in lesson "Subtraction: Subtract Within 20," Objective 3 asks, "How can you break apart the total into a ten and some ones? Where should you take nine from, the ones or the ten? After you take nine from ten, what do you need to add?"
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 a "Read-Draw-Write Tool" for students to use throughout the lesson, independently, with a partner, and in stations. TheImplementation Guidestates, "The "Read–Draw–Write Tool" can support students as they use the Read–Draw–Write process to solve problems." This tool provides visuals, prompts, and questions to remind students how to approach solving a variety of problems.Section "TEKS Mathematical Process Standards" in theImplementation Guidestates, "The TEKS Mathematical Process Standards (MPS) are seamlessly woven into different components of the program. Students use objects, drawings, numeric representations, and precise language to communicate mathematical ideas. In the "Application" section, students select tools and techniques to solve problems, and in "Concept Mini Lessons," they analyze relationships to connect prior learning to new concepts."Each "Concept Mini Lesson" guides teachers in supporting student demonstrations of understanding mathematical concepts. For example, in the lesson, "Place Value: Concept Mini Lessons: Compose, Decompose, and Represent Numbers to 120," students use linking cubes, place value cards, pictures, number bonds, and addition sentences. At the end of the lesson, students compose, decompose, and represent numbers using their own pictorial skills.
Evaluation for 3.2a
Materials do not 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.While the materials do offer connections between patterns and big ideas, the materials do not offer prompts and guidance for educators to build knowledge. The connections are embedded on the student side of the materials.
Evaluation for 3.2b
The materials offer educator guidance for effective instruction using strategies like "sharing the learning objective with students visually and verbally," which theImplementation Guidecalls "an essential instructional approach" for supporting students not yet proficient in math. This practice connects new learning to prior knowledge, introduces terminology, and builds student confidence. Additional strategies such as choral reading, partner reading, and visual support enhance understanding.TheImplementation Guideoutlines how to structure instruction through components like "Possible Ways to Use Components," "Sample Schedules," and "Station Rotations." For example, the "Concept Mini Lessons" station provides small-group instruction, while the "Practice and Application" stations support aligned practice and enrichment. The "Bring Your Own Tech"station allows students to complete teacher-selected digital activities related to the concept.Under "Tiered Instructional Recommendations," the guide states, "For supplemental support, instruction can be delivered in a small-group setting," and for intensive support, it "can be individualized, adapted, and delivered in a group size that meets the needs of students."Math Catalystoffers short, targeted Tier 2 and Tier 3 lessons outside of core instruction. These lessons follow three–four sequenced objectives and use the "Progression of Mini Lesson Objectives" to address specific student needs.
Evaluation for 3.2c
The materials offer multi-tiered intervention strategies and educator guidance for implementation. In the "Possible Ways to Use Components" section of theImplementation Guide, "Concept Mini Lessons" are recommended for small-group instruction to "review, preview, strengthen skills and concepts," while "Practice and Application" components can "build stations" or offer direct instruction. Practice Pages support "spaced retrieval, spiral review, and interleaved practice," and "Application" tasks offer "enrichment and extension opportunities" and help "build fluency and automaticity."According to theImplementation Guide, "Math Catalystis a supplemental instructional resource designed to be used within a Multi-Tiered System of Supports (MTSS) to maximize student achievement in mathematics." It supports Tier 2 and Tier 3 instruction through short, targeted lessons delivered outside of core instruction and sequenced across three–four objectives. Lessons can be used in small groups or individualized settings, with Practice and "Application" activities offering aligned, guided, or independent practice.In kindergarten, these are combined into a single "PracticeandApplication" component.The "PracticeandApplication" sections help teachers choose flexible activities based on student needs. For example, in grade1,"Place Value: Compose, Decompose, and Represent Numbers to 120," materials suggest using any mix of activities to support understanding. Examples include solving word problems with the Read–Draw–Write process, playing number games, and completing multi-part tasks with a partner. "Practice Helpers" offer worked examples with sample solutions and guiding questions to support independent or partner work and can also be used during "Concept Mini Lessons" to model problem-solving strategies.
Evaluation for 3.2d
The materials include enrichment and extension methods that promote varied student engagement, along with implementation guidance for educators. TheImplementation Guidestates, "The Practice and Application stations can be used flexibly to engage students in aligned practice and enrichment activities," allowing them to "work independently, with a partner, or in a small group" to build fluency and automaticity. These components support differentiated instruction through targeted practice."Concept Internalization" in theImplementation Guideprovides guiding questions for planning enrichment and extension across lesson components. In "Concept Mini Lessons," teachers are prompted to ask, "What do my students already know? What can they already do? What do they need support with?" Similarly, in "Practice and Application" and "Progress Check," teachers reflect on questions such as, "How do the Practice Pages progress from simple to complex?" and "What does proficiency look like with the content of this concept?"Additional support is embedded in each concept's "Practice and Application" section. For example, in grade 1, "Place Value: Compose, Decompose, and Represent Numbers to 120," the materials advise teachers to use a chart to "determine how to use the activities to best meet the needs of your students." Teachers can support students in solving problems involving composing, decomposing, and representing numbers to 120 by providing the "Read–Draw–Write Tool," encouraging partner work to compare solution paths and explore different representations, offering the "Solve a Problem Recording Page" as an alternative to personal whiteboards, and using place value charts and linking cubes to help students build models and deepen their understanding.
Evaluation for 3.2e
The materials do not include prompts and guidance to support educators in providing timely feedback during lesson delivery. Guidance for educators comes at the beginning of the unit as teachers choose a starting point based on student skills, and at the end of lessons and units in the form of progress monitoring, but not as feedback.
Evaluation for 3.3a
The materials include educator guidance on providing linguistic accommodations for all English language proficiency levels, as outlined by the ELPS. Although theImplementation Guidestates that "Guidance for supporting EB students in making cross-linguistic connections through oral and written discourse is embedded in theConcept Guide," this guidance is uniform across grades K–2. The materials offer tips for EBs, including differentiated accommodations by proficiency level at the beginning of each concept's "Alignment Guide," which supports advancing students toward higher levels of academic language across lesson components.TheImplementation Guidenotes that the "Alignment Guide for each concept includes alignment to the English Language Proficiency Standards and highlights embedded supports for different levels of language proficiency." Most lessons include one embedded support, which often consists of gestures or visuals like number cards, and are similar across all lessons.The materials include "Language Support"notes within some "Concept Mini Lessons," offering guidance to build vocabulary, comprehension, and background knowledge. However, not every lesson contains this support, and when provided, it typically consists of teacher-modeled phrases and simple sentence frames that are uniform across lessons. These methods primarily assist students at the beginning level of language acquisition and offer a scaffold for students progressing toward advanced proficiency.
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 implementation guidance to support educators in effectively using the materials in state-approved bilingual/ESL programs. TheImplementation Guidecontains support in the "Using Math Catalyst in State-Approved Bilingual/ESL Programs" section of the materials. A table is presented for educators with the "Instructional Model, Recommended Structure, and Recommended Modification" available to support educators in their specific program.The "Using Math Catalyst in State-Approved Bilingual/ESL Programs" guidance includes references to the other sources of support available to the teacher. For example, in the row designated as the "Transitional Bilingual Early Exit/Late Exit" program, educators can use the materials "as designed, allowing the certified bilingual teacher to use materials ("Key Terminology," "Play a Game," "Family Math") creatively to support learning."TheImplementation Guidestates that materials include "built-in support for emergent bilingual (EB) students so they can gain proficiency with the English they need to access the mathematics." Supports are embedded in the "Concept Guide," "Alignment Guide," and "Language Support"notes, including opportunities for students to speak with a partner before sharing with their peers and an exemplar response for teachers to clarify, restate, or summarize student output.
Evaluation for 3.3d
The materials include embedded guidance to support emergent bilinguals in increasing comprehension, building background knowledge, or making cross-linguistic connections through written discourse or increasing comprehension through oral discourse. Each "Concept Guide"contains "Key Terminology" cards and a "Family Math" page that references the same cards. When used in the classroom and at home, the cards increase "comprehension through discourse, leveraging home language through cross-linguistic connections, or supporting writing or spelling of key vocabulary."The materials include guidance to support emergent bilingual students in building academic vocabulary, background knowledge, and making cross-linguistic connections through oral discourse. For example, in "Subtraction: Subtract Within 20," students "turn and talk" to explain reasoning, and in "Compose, Decompose, and Represent Numbers to 120, Objective 1," the teacher definesunitand uses place value cards to aid understanding. These strategies help build content knowledge but primarily address early language development.The materials offer repeated, generic guidance for supporting oral cross-linguistic connections across all "Concept Guides." In "Place Value: Compose, Decompose, and Represent Numbers to 120," teachers are advised to create cross-linguistic anchor charts with key terms in English and students' home languages, along with images. The materials provide examples of "KeyTerminology" along with visual support in English and Spanish to aid in the creation of these charts.
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.
0 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.
0 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.
0 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.
0 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
31% (5 out of 16 points)
Evaluation for 4.1a
The materials provide TEKS-aligned practice opportunities that develop conceptual understanding. Each concept includes worksheets, games, and hands-on activities in the "Practice and Application" section. For example, in the grade 1 lesson, "Early Numeracy: Conceptual Subitizing Within 10," students use printed dot cards and a partner to play "How Many?," a game where students say how many dots they see without counting.Students demonstrate understanding by responding to teacher questions and completing structured tasks. For example, in the grade 1, "Concept Mini Lessons: Compose, Decompose, and Represent Numbers to 120," the teacher uses a show-and-tell method with linking cubes to build sets of ten with some left over, then guides students to determine the place value of "CorrespondingLesson" cards. The teacher uses the "Monitor" section to identify gaps or misunderstandings in student responses.In the grade 1, "Progress Check: Compose, Decompose, and Represent Numbers to 120" assessment, students use linking cubes and a printed "Student Page" to show understanding of TEKS 1.2C. Students are assessed using a rubric that measures proficiency in correctly representing a two-digit number as tens and ones, representing a two-digit number in standard and expanded forms, using objects and a picture to represent a number to 120, and representing a number to 120 in standard and expanded forms.
Evaluation for 4.1b
The materials do not include opportunities that move students beyond grade-level TEKS; however, they do include enrichment and extension tasks that increase in rigor. For example, the "Place Value" strand ranges from Kindergarten tograde 5.This allowsteachers to select lessons based on student needs, but these lessons remain within grade-level standards.Instruction is organized into "Concept Mini Lessons" with hands-on "Practice and Application" activities for Tier 2 and Tier 3 support. In Grade 1, students complete multi-part tasks using contextual clues and visuals to practice conceptual subitizing within 10. These activities support real-world application and extend learning within TEKS 1.2A.Each lesson ends with an "Analyze Student Progress" section to assess learning, deepen thinking, and guide instruction. Enrichment and extension tasks are embedded rather than offered separately, but the limited number of extension questions and activities may not sufficiently support learning beyond the TEKS.
Evaluation for 4.2a
The materials demonstrate coherence across concepts horizontally within the grade level by connecting patterns, big ideas, and relationships. TheImplementation Guidenotes that concepts build upon one another—for example, understanding multiplication foundations supports multiplying two-digit by one-digit numbers. The sequence of objectives highlights this horizontal alignment across lessons.The "Strand by Grade: Scope and Sequence" outlines both horizontal and vertical alignment, showing how concepts build across and within grades. It states, "Concepts and Objectives within each strand build upon each other to form a ladder of mathematical understanding." In grade 1, students progress from "Compose 10" through "Understand Equality," then transition to "Add Within 100 by Using Mental Strategies."In grade 1, students begin composing, decomposing, and representing numbers up to 120 using linking cubes to create sets of tens and ones before applying the concept with number bonds, pictorial representations, and expanded form. This progression from concrete to abstract is reinforced in the "Addition: Add Within 100 by Using Mental Strategies" lesson, where students decompose an addend to make the next 10.
Evaluation for 4.2b
The materials do not demonstrate coherence vertically across concepts and grade bands, including connections from grade K–6. The materials only go through grade 5.In theImplementation Guideunder "Supplemental Instructional Materials Design," the materials state, "Within a grade level, concepts are structured to build upon one another. For example, students learn about the basic foundations of multiplication to apply this understanding when multiplying a two-digit number by a one-digit number. Similarly, concepts build across grade levels, such as when students apply their understanding of whole-number multiplication to multiply decimals."In the "Strand by Grade: Scope and Sequence," the materials list the concepts in strands with the vertical alignment of the concept from grades K–5. The materials state, "Math Catalyst Texasprovides a mathematical progression of concepts unbound by the constraints of grade-level standards. Although the Texas Essential Knowledge and Skills (TEKS) are provided as a useful reference for teachers, the "Concepts" and "Objectives" within each strand build upon each other to form a ladder of mathematical understanding. Theseobjectives can be used to find a student's last secure rung on that ladder—the rung where their knowledge is sturdy enough to stand on."
Evaluation for 4.2c
The materials do not demonstrate coherence across lessons or activities by connecting students' prior knowledge of concepts and procedures to the mathematical concepts to be learned in the current grade level and future grade levels. The materials do not include prompts or reviews for students to connect to prior learning or explanations about how their current learning is connected to future learning.While each "Concept Mini Lesson" includes a "Progression of Mini Lesson Objectives" that helps teachers assess prior knowledge before instruction.In grade 1, "Subtract Within 100 by Using Mental Strategies," students begin with subtracting like units while using a number line and progress to taking from a ten to subtract from a two-digit number. While this structure enables students to build on what they already know, it does not explicitly connect prior knowledge to current or future grade levels.
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.Though theImplementation Guiderecommends starting each lesson by sharing objectives and connecting them to prior learning and key terms and emphasizes using "Concept Mini Lessons" to help students analyze mathematical relationships between past and current concepts, there are no opportunities for spaced retrieval with previously learned skills across the learning pathways.
Evaluation for 4.3b
The materials do not provide interleaved practice opportunities, as the activities and interventions provided focus on solo objectives without addressing interleaving topics and skills.Though the materials suggest stations built from "Practice and Application" components where teachers are encouraged via the "Components" and "Possible Ways to Use Components" sections of theImplementation Guideto assign practice pages for spaced retrieval, spiral review, enrichment, and fluency-building, these stations are not interleaved as part of the lessons or activities and are separate.
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.
0 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.
0 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
TheImplementation Guideexplains that the program balances conceptual understanding and procedural skills through progressively complex "Concept Mini Lessons" and supporting "Practice" activities. "Application" tasks extend learning by having students transfer knowledge to new contexts using tools and strategies of their choice. "TEKS Mathematical Process Standards" are integrated throughout as students use objects, drawings, numeric representations, and precise language to build understanding.The materials provide opportunities for students to interpret and analyze visual models. In grade 1, "Place Value: Compose, Decompose, and Represent Numbers to 120, Objective 3," students examine a place value chart with linking cubes making the number 95. The lesson encourages the students to continue counting and adding linking cubes to make the number 100 before moving the cubes into the proper place on the place value chart.The materials use common misconceptions to deepen understanding of models and representations. In the grade 1"Concept Guide," "Place Value: Compose, Decompose, and Represent Numbers to 120", students use place value charts, place value cards, and linking cubes to create representations of numbers to 120. Teachers are prompted to ask, "The 4 in 43 tells us about the tens. Where do you see the tens in your linking cubes?. . .Say 43 in unit form. Use your linking cubes to help. What is the value of 4 tens?" to guide interpretation.
Evaluation for 5.1b
The materials include tasks that prompt students to create concrete and pictorial models of math situations. TheImplementation Guidehighlights the "Read–Draw–Write Tool," which uses visuals, prompts, and questions to support problem-solving. Students read the problem, create or adjust drawings as new information is discovered, and write number sentences or equations to represent their thinking.Each "Concept Mini Lesson" provides questions and tasks for students to create models and pictorial representations. For example, in grade 1, "Place Value: Concept Mini Lessons: Compose, Decompose, and Represent Numbers to 120," students use linking cubes, provided images, place value cards, and place value charts to then create their own number bonds and pictorial representations of numbers to 120. By the end of the lesson, students create their own models and pictorial representations to build a number to 120 using an addition sentence.The "Progress Check Tool" includes tasks that progress from simple to complex, requiring students to create concrete and pictorial representations of learned concepts. In grade 1, "Place Value: Compose, Decompose, and Represent Numbers to 120," students use linking cubes to create a two-digit number, write the number as tens and ones, and then write the total. Later, students create number bonds and use linking cubes to complete a place value chart.
Evaluation for 5.1c
The materials provide opportunities for students to apply conceptual understanding to new contexts through all curriculum components. TheImplementation Guidestates, "The objectives in Concept Mini Lessons progress in complexity and provide opportunities for students to develop conceptual understanding and procedural fluency," while the "Practice" and "Application" components help students "solidify" skills and "transfer knowledge to new applications and build fluency."Each strand's "Progression of Mini Lesson Objectives" supports applying conceptual understanding across tasks. In grade 1, "Addition: Concept Mini Lessons: Add Within 20," students move from using a number path and the support of counters and a ten frame to creating a "ten when either part is 7 or 8." Students then apply this understanding to write new equations based on the creation of 10.Students extend learning in the "Practice and Application" sections by applying conceptual understanding in new situations. For example, in grade 1, "Addition: Add Within 20," students play "Addition Top It" with the optional support of a number path to 20 and use a deck of cards to create addition sentences, determine the total, and then determine which player has created the larger sum.
Evaluation for 5.2a
In the "Station Rotations" section of theImplementation Guide, the materials include two suggested schedules to support the use of the included materials to build student automaticity and fluency. Rotations include working with the teacher, one practice station, and two application stations for working independently or with peers on grade-level mathematical tasks.According to theImplementation Guide, "Practice and Application" supports fluency-building through "spaced retrieval, spiral review, and interleaved practice," as well as through games. In grade 1, "Place Value: Compose, Decompose, and Represent Numbers to 120," students "identify 1 ten as a unit and represent two-digit numbers as tens and ones, represent two-digit numbers by using standard and expanded forms, represent numbers to 120 by using objects and pictures, [and finally] represent numbers to 120 by using standard and expanded forms" to reinforce TEKS 1.2C by using "objects, pictures, and expanded and standard forms to represent numbers up to 120."Each "Concept Mini Lesson" includes an "Analyze Student Progress" section with "Questions to Advance Student Thinking" that are paired with student tasks. For example, in the same grade 1 unit, the teacher asks, "How many groups of ten are there? How many leftover ones? Show me. What number is the same as __ tens __ ones? What is the value of each digit? How do you know?" These questions guide students in applying and articulating their understanding of place value concepts.
Evaluation for 5.2b
The materials provide consistent opportunities for students to apply efficient, flexible, and accurate mathematical procedures. TheImplementation Guidehighlights the "Read–Draw–Write Tool," which offers visuals, prompts, and questions such as, "Can I draw something?" and "What can I draw?" to support students as they solve problems and write equations that reflect their thinking."Concept Mini Lessons" include tasks that build procedural fluency through a progression of strategies. For example, in grade 1 "Addition: Count On to Add Within 10," students begin with dice and printed amounts to practice counting on from a number, using their fingers and cards with groups of five, show sets using a number bond, and finally count on to find the total of an addition expression by using their fingers and a number path. During the "Progress Check," students demonstrate procedural accuracy and flexibility by choosing among multiple methods to solve problems.In the "Practice and Application" section of grade 1 "Addition: Count On to Add Within 10," students apply procedures using hands-on and visual tools. Activities include using the "Read–Draw–Write process to solve word problems involving counting on to add within 10, working with a partner to "Play aGame" involving adding within 10, working with a partner to solve a multi-part task involving adding within 10," and completing independent practice of counting on from or determining a part and counting on, then filling in a number bond and writing a matching number sentence. Students then apply their new skills to add using their fingers or a provided number path, moving the student from concrete models to abstract representations while reinforcing fluency.
Evaluation for 5.2c
The materials provide opportunities for students to evaluate mathematical representations, models, strategies, and solutions for efficiency, flexibility, and accuracy. In grade 1, "Concept Mini Lessons" for "Subtraction: Subtract Within 20," students build representations with linking cubes, find a set of ten, and use a counting path to solve subtraction problems within 20. Students then apply this understanding to subtraction expressions by decomposing a ten number into tens and ones, then subtracting from the ten rather than relying on linking cubes to count sets.Teachers use questions paired with tasks to assess students' ability to evaluate mathematical thinking. For example, in the "Analyze Student Progress" section ofObjective4in grade 1, "Subtraction: Subtract Within 20," questions include, "How can you break apart the total into a ten and some ones? Where should you take 7 or 8 from, the ones or the ten? After you take 7 or 8 from ten, what do you need to add?"The "Practice and Application" component allows students to evaluate models and strategies independently or with a partner. In grade 1, "Subtraction: Subtract Within 20," students use the Read–Draw–Write process to solve subtraction word problems within 20, recording their work on a whiteboard or the "Solve a Problem Recording Page." They solve "take from and take apart" problems, play a subtraction game with a partner, and complete a multi-part task involving subtracting a one-digit number from a teen number. These activities reinforce subtraction concepts through multiple representations.
Evaluation for 5.2d
The materials contain guidance to support students in selecting the most efficient approaches when solving mathematics problems. For example, in theImplementation Guideunder the "About the Read–Draw–Write Tool" section, the materials state, "the tool provides visuals, prompts, and questions to remind students how they can approach solving a variety of problems." Students approach problem-solving by carefully reading the problem, breaking it into parts, and using drawings to represent their thinking. They revise their drawings as they gather more information, label known and unknown elements, and use the visual to guide their understanding. Finally, they write equations, solve the problem, and write a statement that answers the original question.The "Progress Check Tool" contains guidance to support students in selecting efficient approaches. For example, in the grade 1 "Addition: Count On to Add Within 10," the materials state, "The Progress Check Tool has problems that are sequenced from simple to complex. Problems 1–3 involve counting on by using visible parts, either given or of the student's choice. Problem 4 involves using a number path to model counting on by using hops to add within 10." In the "Progress Check," students progress from determining parts from a total to determining the parts in an addition problem and counting on by using their fingers or a provided number path to find the sum.The "Progression of Mini Lesson Objectives" in each concept provides guidance in the progression of approaches to mathematics problems from least to most efficient. For example, in grade 1, "Subtraction: Subtract Within 20," the materials begin with using a number bond to decompose the subtrahend and counting back to 10 by using a number path with additional support provided by the use of linking cubes. Finally, the student solves subtraction problems by decomposing a teen number as a ten and some ones, then taking away from the ten and adding the remaining parts.
Evaluation for 5.3a
The materials explicitly state how the conceptual and procedural emphasis of the TEKS are addressed. TheImplementation Guidestates that program components are "structured to balance the development of conceptual understanding with procedural skills," with "Concept Mini Lessons" building complexity, "Practice" solidifying understanding, and "Application" promoting fluency through real-world contexts. This structure ensures students develop a deep understanding while gaining procedural accuracy and flexibility.In "Concept Mini Lessons: Subtract Within 20," students develop subtraction strategies through four objectives using number bonds, number paths, and linking cubes to represent their thinking. Teachers assess understanding in Objective 4 using "Analyze Student Progress: Monitor" questions, such as whether students can "decompose the total into a ten and some ones" and "add the parts that are left over."In "Application: Subtract Within 20," students work independently or with a partner to solve word problems using tools like number paths and the "Read–Draw–Write Tool." Activities include playing games and completing multi-part tasks that reinforce subtraction within 20. These experiences help students apply and explain their thinking while building procedural accuracy and flexibility.
Evaluation for 5.3b
The materials include questions and tasks that provide opportunities for students to use concrete models, pictorial representations, and abstract models as required by the TEKS. TheImplementation Guidedescribes the "Read–Draw–Write Tool" as a support for problem-solving with visuals, prompts, and questions. Prompts such as "Can I draw something? What can I draw?" encourage students to create, revise, and label visual representations, then write equations and a final answer statement.Each "Concept Mini Lesson" begins with a progression from concrete to abstract representations. In "Addition: Add Within 20," students count on using number paths and fingers, then transition to using number bonds and other tools to make a ten. Tasks ask students to count on, use two-sided counters, and explain why starting with the larger number is more efficient.The "Progress Check Tool" provides opportunities for students to apply concrete, pictorial, and abstract models to solve addition problems. In "Addition: Add Within 20," students use number paths, place value cards, and printed number bonds to model addition, find totals, and write three-part number sentences. These tasks assess students' understanding and fluency using multiple representations.
Evaluation for 5.3c
Each "Concept Mini Lesson" contains "Teacher Tips" and "Language Support"notes, which offer guidance to educators to support students in explaining and defining concrete models, representational models, and abstract concepts. Guidance includes how to engage students in mathematical discourse with their peers to explain models and concepts, sentence frames and sentence starters to support students in defining and explaining concrete and representational models, and ideas for creating anchor charts to support understanding of models and concepts.The materials support students in connecting and creating concrete and representational models to abstract concepts, as required by the TEKS. The "Read–Draw–Write Tool" guides students through solving problems using visuals, prompts, and questions that encourage drawing, labeling, writing equations, and forming complete responses. Additionally, theImplementation Guideemphasizes using objects, drawings, and numeric representations to help students analyze relationships and build conceptual understanding in both "Concept Mini Lessons" and "Application" tasks."Family Math" pages extend this support beyond the classroom by helping students apply representational and abstract thinking at home. For example, in grade 1, "Family Math: Compose 10," students use a number path and visual models toCompose 10 with two or three addends, while families ask guided questions like, "How does the number path help you see the parts that make 10?" and "How can you use an addition sentence to represent your number path?" These tasks promote meaningful connections between school learning and at-home reinforcement.
Evaluation for 5.4a
The materials provide opportunities for students to develop academic mathematical language using visuals, manipulatives, or other language development strategies using the "Read-Draw-WriteTool." For example, theImplementation Guidestates, "The tool provides visuals, prompts, and questions to remind students how they can approach solving a variety of problems." Prompts include, "Ask, 'Can I draw something?' Then ask, 'What can I draw?' Draw to represent the problem as you reread. . .Label what is known and unknown. Ask, 'What does my drawing show me?' Write number sentences or equations to represent your thinking. Solve. Write a statement that answers the original question."The materials includelanguagesupport for students to develop academic mathematical language. For example, in grade 1, "Concept Mini Lesson: Compose, Decompose, and Represent Numbers to 120," the materials state, "A unit is a label that describes what is being counted, measured, or manipulated, such as apples, cubes, tens, or ones. Encourage students to use unit labels in their responses, as appropriate, such as saying '2 tens' instead of '2.'"In the "Application" sections of the materials, students use manipulatives and a place value chart to develop their academic language. For example, in grade 1, "Place Value: Compose, Decompose, and Represent Numbers to 120," students collaborate in pairs to solve a multi-part task involving composing, decomposing, and representing numbers up to 120. They use contextual information to support their understanding and apply critical thinking with precise mathematical language to solve three related problems.
Evaluation for 5.4b
The materials include embedded educator guidance to extend students' use of academic mathematical vocabulary in context when communicating with peers and educators. Each "Concept Guide"contains "Key Terminology" cards. Mathematical terms paired with visuals and a definition are presented in English and Spanish. Students and educators use these cards in various ways to extend academic vocabulary between peers, such as using the cards "as flashcards, as a portable word wall, to build background knowledge, or to use in semantic sorts."The materials include embedded educator guidance to scaffold and support students' use of precise mathematical vocabulary during communication with peers and teachers. TheImplementation Guidestates, "Math Catalystincludes embedded support to help students understand and use precise mathematical language," noting that teachers model precision by restating student responses and using visuals. "Language Support"notes in "Concept Mini Lessons" provide additional scaffolding strategies to develop and reinforce vocabulary.The guide emphasizes vocabulary consistency, especially when teaching composition and decomposition of place value, stating, "Math Catalyststrives for consistency by using the terms as indicated in the chart." Teachers are encouraged to "validate and restate students' statements" using alternative terms to deepen understanding. Students apply academic language with support. For example, in grade 1, "Place Value: Compose, Decompose, and Represent Numbers to 120," teachers offer a review of mathematical terms by stating, "It's important to say 2 tens, not just 2. Tens is the unit. Units tell us what we're counting, like tens or ones. We say the unit so that it's clear what we mean."
Evaluation for 5.4c
The materials include embedded guidance to support student use of appropriate mathematical language and academic vocabulary in discourse. TheImplementation Guiderecommends the "Read–Draw–Write Tool," which "provides visuals, prompts, and questions to remind students how they can approach solving a variety of problems." It offers two versions of the tool, advising teachers to "select and print the version that is appropriate for your students" and to consider laminating it for repeated use throughout the year.Embedded support for students is found in "Concept Mini Lessons" in the "Language Support" section. For example, in grade 1, "Place Value: Compose, Decompose, and Represent Numbers to 120," the "Language Support" inObjective2states, "Consider creating a chart to support students with new terms." The "Language Support" provides a visual representation of place, value, and digit as terms related to the place value cards of the lesson.Support for student application of appropriate mathematical language and academic vocabulary in discourse is found in the "Concept Mini Lessons." For example, in grade 1, "Addition: Add Within 100 by Using Mental Strategies," teachers guide students to review their work by restating the learning of the day with, "We needed to find the total of 32 and 7. We broke apart 32 so we could add the ones first. After we added the ones, we had a simpler problem, 30 + 9." Students are then invited to turn and talk to their peers about how they can break apart one addend to make a simpler problem using the terms from the lesson.
Evaluation for 5.4d
The materials include embedded guidance to facilitate mathematical conversations, allowing students to hear, refine, and use math language with peers in "Concept Mini Lessons." For example, in grade 1, "Subtract: Subtract Within 100 by Using Mental Strategies," students review the use of subtracting like units using a number line. The materials state, "We subtracted like units to find 67 − 23. We subtracted the tens, and then we subtracted the ones. We took away 20 first, and then took away 3 more to get 44." Students are then invited to turn and talk with a partner about how they can use the number line to help them subtract like units using mathematical language from the lesson.The materials include "Teacher Tips" and "Language Support" in the "Concept Mini Lessons" to facilitate mathematical conversations. For example, in grade 1, "Addition: Add Within 100 by Using Mental Strategies," the "Teacher Tip" offers tips to support students in understanding the quantity versus the value of ten-sticks and cubes. The materials state, "Support students by emphasizing the value of each cube stick or cube and counting by tens and ones to find the total." The "Language Support" offers support for homonyms of mathematical terms. The materials state, "Consider intentionally pairing the term sum with total orally and in writing so students understand the mathematical meaning of the word."In the "Application" section, students hear, refine, and use math language with peers. For example, in grade 1, "Place Value: Compose, Decompose, and Represent Numbers to 120," students work with a partner to solve a multi-part task involving composing, decomposing, and representing numbers to 120. Students use contextual information to support their understanding and apply critical thinking along with mathematical language to solve three related problems.
Evaluation for 5.4e
The 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 through structured teacher guidance. For example, the "Concept Mini Lessons" in each unit include crafted sample dialogues with anticipated student responses, exemplar answers, and strategies for refining or redirecting student thinking.The materials include visual and analytical tools to support educators with various student responses. For example, lessons provide visual examples of proficient student work and include "Questions to Advance Student Thinking" at the end of each "Concept Mini Lesson" to help teachers identify misconceptions and scaffold guidance based on student responses.Each "Concept Guide"contains a "Student Misconceptions" section, which includes explicit strategies for addressing common misunderstandings, enabling educators to give timely, targeted feedback that fosters accurate learning.
Evaluation for 5.5a
The materials include TEKS process standards integrated appropriately into the materials. The "Family Math" page for each unit contains visual representations of the concepts to be taught, along with information for families. For example, in grade 1, "Place Value: Compose, Decompose, and Represent Numbers to 120," students use objects, place value charts, and their own drawings to represent numbers up to 120 and show the value of the digits by writing the number in expanded form. Students use an image of ten-sticks, linking cubes, a number bond, and a blank expanded form sentence to represent the number 86.Each "Concept Mini Lesson" includes a "Progression of Mini Lesson Objectives" that outlines the concept, tools, and representations used. For example, in the grade 1, "Place Value: Compose, Decompose, and Represent Numbers to 120," the "Progression of Mini Lesson Objectives" lists ten-sticks, linking cubes, number bonds, place value cards, and place value drawings to support composing and decomposing numbers to 120. Students select appropriate tools, solve problems using manipulatives, and explain their thinking through symbols, diagrams, and precise language both verbally and in writing.In "Application," students access the integrated TEKS process standards by using appropriate tools and techniques to solve problems, and communicating and justifying their mathematical thinking using various representations. For example, in grade 1, "Place Value: Compose, Decompose, and Represent Numbers to 120," students collaborate in pairs to solve a multi-part task involving composing, decomposing, and representing numbers up to 120. They use contextual information to support their understanding and apply critical thinking to solve three related problems with the use of a place value chart and linking cubes to build a model of their solution.
Evaluation for 5.5b
The materials include a description of how process standards are incorporated and connected throughout the learning pathways. For example, theImplementation Guidestates, "The TEKS Mathematical Process Standards (MPS) are seamlessly woven into different components of the program." Integration of the process standards includes students communicating mathematical ideas using various representations and precise language, choosing appropriate tools and methods to solve problems in "Application," and exploring relationships between past and current concepts to deepen understanding in "Concept Mini Lessons."The "Alignment Guide"for each strand lists the TEKS and the process standards for each concept. For example, the "Place Value" strand lists process standards 1.C, 1.D, 1.E, 1.G for grade K, "Compose, Decompose, and Represent Teen Numbers," process standards 1.A, 1.C, 1.D, 1.E, 1.G for grade 1, "Compose, Decompose, and Represent Numbers to 120," and process standards 1.A–1.G for grade 2, "Compose, Decompose, and Represent Numbers to 1,200."The "Strand by Grade: Scope and Sequence," states "Math Catalyst Texasprovides a mathematical progression of concepts unbound by the constraints of grade-level standards. Although the Texas Essential Knowledge and Skills (TEKS) are provided as a useful reference for teachers, the "Concepts" and "Objectives" within each strand build upon each other to form a ladder of mathematical understanding." Teachers use the objectives and current student data to determine a starting point for the student based on the strand versus the specific TEKS.
Evaluation for 5.5c
The materials do not include an overview of the TEKS process standards incorporated into each lesson. The "Alignment Guide"for each unit lists the TEKS process standards incorporated into the unit, but the full process standard is not defined. The TEKS process standards are not included in any other overviews. TheImplementation Guidestates, "Although all components provide space for TEKS MPS by design, the "Alignment Guides" help teachers track which TEKS MPS are emphasized in each concept. More than one TEKS MPS may be identified per concept."
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
The materials provide opportunities for students to think mathematically during "Concept Mini Lessons" and "Questions to Advance Student Thinking." For example, in grade 1, "Concept Mini Lesson: Addition: Add Within 100 by Using Mental Strategies," students build their understanding of addition of ones and tens using drawings, linking cubes, number paths, and number sentences to represent their thinking. The "Questions to Advance Student Thinking" further support students by asking, "What can you add together first? Why does that work? How can breaking apart a two-digit addend help you make a simpler problem?"The materials provide opportunities for students to persevere through solving problems using the "Read-Draw-Write Tool" from theImplementation Guide, which "provides visuals, prompts, and questions to remind students how they can approach solving a variety of problems." Students persevere by reading parts of the problem, asking questions to themselves about the problem, creating drawings and representations, labeling the known and unknown, and finally adding number sentences and statements to their solutions.The materials provide opportunities for students to make sense of mathematics by providing "Application" sessions. For example, in the grade 1, "Addition: Add Within 100 by Using Mental Strategies," students work independently or with a partner to play games and complete tasks to develop an understanding of addition by adding units in various ways using the "Read-Draw-Write Tool," decks of cards, number mats, and number paths.
Evaluation for 6.1b
The materials support students in understanding that there can be multiple ways to solve problems and complete tasks. For example, in grade 1, "Concept Mini Lesson: Addition: Add Within 100 by Using Mental Strategies," the "Questions to Advance Student Thinking" asks, "How can you represent the number sentence with cubes or quick tens and ones? Does the total change if you start with the ones first?"The materials support students in explaining that there can be multiple ways to solve problems and complete tasks. For example, in grade 1, "Application" for "Addition: Add Within 100 by Using Mental Strategies," students explore mental math strategies for addition using number paths, number mats, decks of cards, whiteboards, and markers. In each task, students are invited to share their work with a partner to "share solution paths and make connections between different representations."The materials support students in justifying that there can be multiple ways to solve problems and complete tasks. For example, in the grade 1, "Concept Mini Lesson: Early Numeracy: Conceptual Subitizing Within 10," students determine the parts of a number using their own fingers before moving to dots on cards. The teacher guides the students to determine other ways to show the number four. The materials state, "I see some of you showed 4 by using 2 fingers and 2 fingers. Is there another way to show 4?"
Evaluation for 6.1c
The materials are designed to require students to make sense of mathematics through multiple opportunities for students to do math with peers and/or educators using "Application." For example, in grade 1, "Subtraction: Subtract Within 100 by Using Mental Strategies," students work in pairs to practice subtraction within 100 by using the "Read-Draw-Write Tool," playing a game about compensation, and solving tasks, all while sharing their thinking and problem-solving strategies with their peers.The materials are designed to require students to make sense of mathematics through multiple opportunities for students to write about math with peers and/or educators by using the "Read-Draw-Write Tool" from theImplementation Guide, which "provides visuals, prompts, and questions to remind students how they can approach solving a variety of problems." Students read parts of the problem, ask questions to themselves about the problem, create drawings and representations,andlabel the known and unknown. Finally, students add number sentences and written statements to their solutions.The materials are designed to require students to make sense of mathematics through multiple opportunities for students to discuss math with peers and/or educators using "Questions to Advance Student Thinking." For example, in grade 1, "Concept Mini Lesson: Subtract Within 100 by Using Mental Strategies," questions include, "What benchmark number can help you subtract? What are the parts if you take the benchmark number from the total? How do the parts help you find the difference?"
Evaluation for 6.2a
The materials support educators in guiding students to share their problem-solving approaches, including explanations, arguments, and justifications. For example, in grade 1, "Concept Mini Lesson: Addition: Add Within 100 by Using Mental Strategies," students use linking cubes and whiteboards to practice decomposing a two-digit number into tens and ones to add the ones first. Students are encouraged to "turn and talk about how they can break apart one addend to make a simpler problem" while using their linking cubes.The materials support educators in guiding students to reflect on their problem-solving approaches, including explanations and justifications through the use of "Questions to Advance Student Thinking." For example, in grade 1, "Concept Mini Lesson: Addition: Add Within 100 by Using Mental Strategies," questions include, "How can you break apart a two-digit addend? How is that helpful?. . .How can breaking apart a two-digit addend help you make a simpler problem?" Students use the tools available to them to justify their explanation.
Evaluation for 6.2b
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.The materials do include prompts and guidance to support educators in providing explanatory feedback based on anticipated misconceptions; however, the guidance is found at the beginning of the unit and not in the lessons. For example, in the "Concept Guide"of grade 1, "Subtraction: Subtract Within 100 by Using Mental Strategies," the common misconception among students is to "subtract the subtrahend from the benchmark number but then subtract the result from the other part instead of adding." Teachers are prompted to use number bonds to show the parts under the minuend and use the linking cubes to subtract the subtrahend from the decomposed minuend.
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