Program Information
- ISBN
- 9781101934029
- Technical Specifications: Checklist
- Tech Specs: Checklist (pdf 1.01 MB)
- Technical Specifications: Professional Development
- Tech Specs: Professional Development (pdf 190.61 KB)
The Times Machine! Supplemental Math Curriculum
Supplemental Math (English) Grade 3
IMRA 2026
Publisher: Ohana Solutions
Copyright: 2024
Rubric: Supplemental Mathematics K–5 (English) | 2025 (Download Not Available)
* Some programs submit evidence for only part of a standard, while others submit all sections. A 100% score means this program met all the expectations it submitted.
Quality Review
Standards Alignment
Rubric Section
| Grade | TEKS % | ELPS % |
|---|---|---|
| Grade 3 | 100% | N/A |
Criteria for Quality
Rubric Section 1
Intentional Instructional Design
Materials support educators in effective implementation through intentional course, unit, and lesson-level design.
Total
91% (21 out of 23 points)
Evaluation for 1.1a
The TEKS Alignment & Navigation Guide identifies the grade 3 mathematics Texas Essential Knowledge and Skills (TEKS) and the mathematical concepts addressed throughout the curriculum, and it provides a rationale for how mathematical understanding develops within grade 3 and across grade levels.
The TEKS Alignment & Navigation Guide provides chapter-by-chapter learning progressions, vertical and horizontal alignment, detailed TEKS implementation and crosswalk guidance, and a TEKS Finder that identifies key instructional locations for supported student expectations. The guide also connects grade 3 English Language Proficiency Standards (ELPS) across listening, speaking, reading, and writing and provides guidance for integrating language development with mathematics instruction. Together, these resources clarify the TEKS, ELPS, concepts, and intended learning progression across grades and within grade 3.
Evaluation for 1.1b
The Curriculum Operations Manual provides implementation guidance, usage suggestions, and recommendations for effective use of the instructional materials. It outlines best practices for classroom organization, integrates video resources to support instruction, and offers guidance for implementing reading lesson plans with fidelity.
The Times Machine! 3rd Grade Curriculum Introduction includes recommendations for using the program to adapt to student needs across contexts, including differentiated instruction and enrichment project-based learning activities.
Evaluation for 1.1c
The TEKS Finder document aligns each TEKS with the corresponding lesson, instructional location, and lesson type. It includes a lesson-type key that helps educators quickly identify and navigate curriculum components.
The Lesson Internalization Protocol directs educators to review prerequisite knowledge and use diagnostic results, classroom observations, Systems Check activities, Facts Are Fuel progress checks, previous assessments, and mathematical discussions to determine the appropriate instructional starting point for each student. Educators may begin chapter instruction as designed for students who demonstrate readiness or provide targeted prerequisite review through Facts Are Fuel, Mission Control, educator-guided instruction, or additional practice before introducing new learning.
Evaluation for 1.1d
The TEKS Alignment & Navigation Guide provides a repeatable Lesson Internalization Protocol that guides educators through identifying the mathematical purpose and TEKS, reviewing prerequisite knowledge, examining lesson components and representations, anticipating student thinking and misconceptions, reviewing assessment evidence, determining instructional entry points, and planning differentiation before instruction.
The materials do not provide steps or expectations for how educators should internalize units. Instead, the materials offer only general advice, such as familiarizing themselves with the chapter.
Evaluation for 1.1e
Chapter 0 establishes a centralized implementation hub for educators and instructional leaders and provides a recommended sequence for familiarizing themselves with the curriculum, resource alignment, lesson structure, professional resources, the assessment system, and instructional supports.
The chapter 0 Implementation Guide identifies instructional coaches, campus administrators, curriculum specialists, and professional learning facilitators as key users. It guides these leaders in using chapter 0 resources for educator onboarding, collaborative planning, lesson internalization, instructional coaching, classroom observations, data-informed decisions, and ongoing professional learning.
Evaluation for 1.2a
Suggested time allocations for lesson components appear throughout each lesson. The materials suggest spending 5 to 10 minutes on Suit Up!, 25 minutes on the Mini-Lesson, 15 minutes on the Exploration, flexible time for Independent Tasks, and 5 minutes for Closure/Elaboration.
The materials include detailed lesson plans with learning objectives aligned to the ELPS. The TEKS Alignment & Navigation Guide embeds language development throughout the instructional sequence rather than teaching it separately from mathematics.
Evaluation for 1.2b
This guidance is not applicable because the program is not designed to be adaptive.
Evaluation for 1.2c
The materials include English-language support for families in each unit, with suggestions for supporting their students’ progress. The materials include suggestions for supporting a student’s progress at home, such as “posting printed multiplication facts around the house for easier memorization.” The family resources include extra practice with multiplication and division problems, as well as explanations for the lattice method, Big 7 method, area/array method, and equal groupings method.
The materials do not include Spanish-language support for families for each unit, with suggestions for supporting students’ progress. No family letter or overview video is available in Spanish.
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
The TEKS Alignment & Navigation Guide provides chapter-by-chapter learning progressions, vertical and horizontal alignment, detailed TEKS implementation and crosswalk guidance, and a TEKS Finder that identifies key instructional locations for supported student expectations. The guide also connects grade 3 English Language Proficiency Standards (ELPS) across listening, speaking, reading, and writing and provides guidance for integrating language development with mathematics instruction. Together, these resources clarify the TEKS, ELPS, concepts, and intended learning progression across grades and within grade 3.
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
The Times Machine! 3rd Grade Curriculum Introduction includes recommendations for using the program to adapt to student needs across contexts, including differentiated instruction and enrichment project-based learning activities.
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
The Lesson Internalization Protocol directs educators to review prerequisite knowledge and use diagnostic results, classroom observations, Systems Check activities, Facts Are Fuel progress checks, previous assessments, and mathematical discussions to determine the appropriate instructional starting point for each student. Educators may begin chapter instruction as designed for students who demonstrate readiness or provide targeted prerequisite review through Facts Are Fuel, Mission Control, educator-guided instruction, or additional practice before introducing new learning.
1.1d
Materials include protocols with corresponding guidance for unit and lesson internalization.
Materials include protocols with corresponding guidance for unit and lesson internalization.
1 out of 2 points
Evaluation for 1.1d
Evaluation for 1.1d
Materials include protocols with corresponding guidance for unit and lesson internalization.
1 out of 2 points
The materials do not provide steps or expectations for how educators should internalize units. Instead, the materials offer only general advice, such as familiarizing themselves with the chapter.
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
The chapter 0 Implementation Guide identifies instructional coaches, campus administrators, curriculum specialists, and professional learning facilitators as key users. It guides these leaders in using chapter 0 resources for educator onboarding, collaborative planning, lesson internalization, instructional coaching, classroom observations, data-informed decisions, and ongoing professional learning.
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.
7 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.
7 out of 7 points
The materials include detailed lesson plans with learning objectives aligned to the ELPS. The TEKS Alignment & Navigation Guide embeds language development throughout the instructional sequence rather than teaching it separately from mathematics.
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 applicable.
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.
Not applicable.
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).
1 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).
1 out of 2 points
The materials do not include Spanish-language support for families for each unit, with suggestions for supporting students’ progress. No family letter or overview video is available in Spanish.
Rubric Section 2
Progress Monitoring
Materials support educators in effective implementation through frequent, strategic opportunities to monitor and respond to student progress.
Total
80% (16 out of 20 points)
Evaluation for 2.1a
The materials clearly define the different types of instructional assessments and explain the purpose of each, providing teachers with guidance on how assessments are intended to support instructional planning, monitor student progress, and inform instructional decisions. Through formative and chapter review lessons and assessments, the checkpoints provide insight into student comprehension, allowing for informed adjustments to teaching strategies.
The assessment defines exit tickets and explains their intended purpose. For example, independent practice sheets integrate exit tickets at the conclusion of a lesson. These align with the topic learning objectives, and educators can use them to evaluate student comprehension and track progress.
Evaluation for 2.1b
In Chapter 1, the materials direct educators to set a five-minute timer for students to complete each progress check. This establishes a consistent time frame for assessment administration, allowing students to complete the assessments under the same timed conditions.
Before completing the Facts Are Fuel Progress Checks, students watch preparatory videos and complete a Flight Check-In activity to review expectations and ensure they are ready for the assessment process.
Evaluation for 2.1c
The materials do not provide assessments that students can complete digitally. Instead, educators access assessments digitally, but must download and print the PDF before students can complete each assessment on paper.
Educators must provide any needed accommodations outside of the assessment platform. As a result, the materials do not offer built-in digital tools to support accessibility or individualized assessment administration.
Evaluation for 2.1d
Facts Are Fuel Reasoning Extensions complement fluency measures with TEKS-aligned tasks requiring students to apply, represent, connect, analyze, and justify mathematical thinking. Across chapters 1–10, students encounter varied response formats including multi-select, matching, constructed mathematical models, contextual application, multipart responses, error analysis, strategy comparison, student-created representations, and written mathematical explanations.
The recurring fluency measures and Reasoning Extensions provide educators with multiple forms of diagnostic evidence. Educators can use this evidence to identify fact-fluency needs, assess conceptual understanding and strategy use, and determine readiness for targeted support or enrichment.
Evaluation for 2.1e
The materials include a variety of formative assessments with TEKS-aligned tasks or questions with varying levels of complexity (i.e., more than two levels of complexity). These include Systems Check exit tickets and real-world problem-solving questions where students create their own math problems.
The materials include a variety of TEKS-aligned formative assessments such as quick checks, exit tickets, and embedded tasks within lessons. The Game Time resource gives students opportunities to write a multiplication sentence from an array, then decompose the numbers and apply the distributive property to solve multiplication problems. While tasks are scaffolded with supports such as sentence stems, arrows, and guided structures, they require students to apply mathematical reasoning at multiple levels of cognitive demand.
Evaluation for 2.2a
Instructional assessments include scoring information and guidance for interpreting student performance. The Assessment, Progress Monitoring & Instructional Decision Guide establishes consistent processes for scoring and interpreting diagnostic, formative, progress-monitoring, and summative assessment evidence.
Instructional assessments do not include rationales for each correct and incorrect response. The materials provide guidance to support educators in analyzing performance by TEKS and mathematical concept, and in identifying patterns in correct and incorrect responses. However, each response does not include a rationale.
Evaluation for 2.2b
The Assessment, Progress Monitoring & Instructional Decision Guide establishes a continuous evidence cycle in which educators collect assessment evidence, identify patterns by student, TEKS, concept, and type of error, and use those findings to determine instructional next steps. Guidance supports educators in distinguishing individual needs from class-wide or group trends and determining whether students require targeted reteaching, additional modeling, scaffolded practice, continued distributed practice, or enrichment.
The Individual Student Assessment & Instructional Planning Record supports analysis and planning for individual learners, while the Chapter Assessment Analysis & Instructional Planning Record supports class and group-level analysis of TEKS performance, misconceptions, trends, and planned instructional response. Facts Are Fuel diagnostic and progress-monitoring evidence further supports flexible instructional placement and targeted fact-family practice.
Evaluation for 2.2c
The materials provide tools for both teachers and students to monitor and document student progress and growth over time. The Assessment, Progress Monitoring & Instructional Decision Guide includes chapter-level and individual student tracking records that allow teachers to document assessment evidence, identify instructional needs, develop progress-monitoring plans, and establish review dates to evaluate student growth. Additionally, the Mission Progress Tracker empowers students to take ownership of their learning by setting chapter goals, self-assessing their progress, recording evidence of learning, and reflecting on areas needing additional practice and improvement.
The materials include tools that help educators track student progress and growth. The Assessment, Progress Monitoring & Instructional Decision Guide includes educator-facing progress-monitoring and instructional-planning records that support systematic documentation of assessment evidence, TEKS performance, identified strengths and needs, instructional responses, and subsequent progress.
Evaluation for 2.2d
The materials include System Check questions throughout the lessons that provide opportunities to check for understanding. For example, the Game Time activity directs students to write fact families as they develop fluency with multiplication and division facts.
The Assessment, Progress Monitoring & Instructional Decision Guide helps educators interpret student evidence and identify misconceptions and patterns of need. It guides educators in determining whether to provide immediate clarification, additional modeling, scaffolded practice, targeted reteaching, continued application, or enrichment.
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.
1 out of 1 points
Evaluation for 2.1a
Evaluation for 2.1a
Materials include the definition and intended purpose for the types of instructional assessments.
1 out of 1 points
The assessment defines exit tickets and explains their intended purpose. For example, independent practice sheets integrate exit tickets at the conclusion of a lesson. These align with the topic learning objectives, and educators can use them to evaluate student comprehension and track progress.
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.
1 out of 1 points
Evaluation for 2.1b
Evaluation for 2.1b
Materials include guidance to ensure consistent and accurate administration of instructional assessments.
1 out of 1 points
Before completing the Facts Are Fuel Progress Checks, students watch preparatory videos and complete a Flight Check-In activity to review expectations and ensure they are ready for the assessment process.
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.
0 out of 2 points
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 2 points
Educators must provide any needed accommodations outside of the assessment platform. As a result, the materials do not offer built-in digital tools to support accessibility or individualized assessment administration.
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
The recurring fluency measures and Reasoning Extensions provide educators with multiple forms of diagnostic evidence. Educators can use this evidence to identify fact-fluency needs, assess conceptual understanding and strategy use, and determine readiness for targeted support or enrichment.
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
The materials include a variety of TEKS-aligned formative assessments such as quick checks, exit tickets, and embedded tasks within lessons. The Game Time resource gives students opportunities to write a multiplication sentence from an array, then decompose the numbers and apply the distributive property to solve multiplication problems. While tasks are scaffolded with supports such as sentence stems, arrows, and guided structures, they require students to apply mathematical reasoning at multiple levels of cognitive demand.
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
Instructional assessments do not include rationales for each correct and incorrect response. The materials provide guidance to support educators in analyzing performance by TEKS and mathematical concept, and in identifying patterns in correct and incorrect responses. However, each response does not include a rationale.
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
The Individual Student Assessment & Instructional Planning Record supports analysis and planning for individual learners, while the Chapter Assessment Analysis & Instructional Planning Record supports class and group-level analysis of TEKS performance, misconceptions, trends, and planned instructional response. Facts Are Fuel diagnostic and progress-monitoring evidence further supports flexible instructional placement and targeted fact-family practice.
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
The materials include tools that help educators track student progress and growth. The Assessment, Progress Monitoring & Instructional Decision Guide includes educator-facing progress-monitoring and instructional-planning records that support systematic documentation of assessment evidence, TEKS performance, identified strengths and needs, instructional responses, and subsequent progress.
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
The Assessment, Progress Monitoring & Instructional Decision Guide helps educators interpret student evidence and identify misconceptions and patterns of need. It guides educators in determining whether to provide immediate clarification, additional modeling, scaffolded practice, targeted reteaching, continued application, or enrichment.
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 applicable.
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.
Not applicable.
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
87% (34 out of 39 points)
Evaluation for 3.1a
The TEKS Alignment & Navigation Guide identifies prerequisite knowledge within the learning progression and provides a Lesson Internalization Protocol that directs educators to review prerequisite concepts, diagnostic evidence, prior assessments, classroom observations, Systems Check evidence, and mathematical discussions before instruction. Educators use this evidence to determine whether students can begin instruction as designed or need targeted support with prerequisite concepts.
The Assessment, Progress Monitoring & Instructional Decision Guide provides instructional-response guidance for students who demonstrate unfinished learning. Educators can use additional modeling, concrete and visual representations, educator-guided practice, targeted Facts Are Fuel review, Mission Control support, flexible Pit Crew placement, additional practice, and progress monitoring before or during continued grade-level instruction.
Evaluation for 3.1b
The Professional Resource Guide includes Language Supports and Academic Vocabulary guidance that helps educators identify essential mathematical language, preteach vocabulary when needed, connect words to visuals, gestures, manipulatives, models, and student-friendly explanations, and support students in using increasingly precise mathematical language during instruction and discourse.
Historical Adventures at a Glance provides chapter-specific background on the historical and real-world settings in chapters 1–10. This background helps educators anticipate references that students may find unfamiliar before instruction. The guide also provides an explicit sequence for supporting students with unfamiliar references: “show, name, briefly explain, connect, use, and return students to the mathematics.”
Evaluation for 3.1c
The materials include explicit educator guidance for enrichment and extension activities for students who have demonstrated proficiency in grade-level content and skills. For example, in the Problem-Based Learning unit Operation Lift-Off, students can explore historical applications of multiplication and division and deepen their understanding of these mathematical concepts through hands-on engineering projects and problem-solving activities.
While the problem-based learning unit includes enrichment activities, the materials do not identify or provide guidance for activities intended for students who have demonstrated proficiency in above-grade-level content and skills.
Evaluation for 3.1d
The materials use a mixed-media format but lack built-in accessibility features for their digital resources. Educators must rely on external tools or accommodations to meet individual students’ accessibility needs.
The materials do not provide adjustable accommodations, such as text-to-speech, content and language supports, or calculators, for students. Students cannot access these supports directly within the materials during instruction or assessment. Educators must implement any needed accommodations separately to ensure students receive appropriate support.
Evaluation for 3.1e
In the Problem-Based Learning unit, “Mission 1” asks students to sketch their design, write down questions as they go, and make connections between counting an array and multiplying.
The materials provide educator guidance on multiple ways students can demonstrate understanding of multiplication concepts, including kinesthetic modeling of arrays (rows and columns), discourse to identify unknown factors within arrays and complete multiplication equations, and gestures to represent mathematical vocabulary. Students engage with interactive supports, such as “Facts are Fuel” videos, written or verbal explanations, and visual representations, allowing students to express understanding through perform, express, and represent formats.
Evaluation for 3.2a
The materials introduce and reinforce academic vocabulary within the context of instruction, allowing students to connect mathematical language to visual models and problem-solving situations. Lessons consistently embed vocabulary rather than requiring educators to teach the vocabulary in isolation. Vocabulary supports, including flashcards and student-facing materials, provide repeated exposure to key terms. These resources reinforce understanding through visual representation and repeated use across instructional contexts.
Following instruction on skip counting and the multiplication chart, the materials direct educators to facilitate discussion that connects multiplication by two to the concept of doubling. This guidance emphasizes the overarching idea that multiplication represents repeated equal groups and helps students develop a conceptual understanding of twos facts as doubles.
Evaluation for 3.2b
The materials suggest using a combination of direct instruction to introduce concepts, independent activities for practice, and real-world applications in the Problem-Based Learning units to connect the content to students’ lives.
The Teacher’s Guide provides explicit direction for effective lesson delivery by including detailed lesson plans with step-by-step instructions, suggested pacing, and general differentiation strategies for each lesson. These resources help educators implement instruction consistently while adapting lessons to meet diverse student needs.
Evaluation for 3.2c
The materials include multi-tiered intervention methods for various practices and structures. For example, lesson plans include a differentiation list for whole groups to watch a video and discuss, collaborative groups to work on Game Time, and independent practice during class or for homework. The materials state that the lists “represent a few broad examples.”
The materials do not provide guidance for implementing multi-tiered intervention methods, including processes for identifying student needs, delivering targeted interventions, or monitoring student progress across tiers.
Evaluation for 3.2d
In the Problem-Based Learning unit, the materials provide students with project-based learning missions that incorporate hands-on engineering design challenges and authentic problem-solving activities. These experiences extend learning beyond routine practice, encouraging students to apply mathematical concepts in meaningful real-world contexts while fostering critical thinking, collaboration, and deeper conceptual understanding.
In the Problem-Based Learning unit, the “Mission 4” guidance gives the educator questions to ask; for example, “Ask students to share ways they have learned to use multiplication and division to solve real-world problems from the lessons so far.” Support continues by providing examples such as dividing a container of strawberries with a sibling or using multiplication to determine how much three $5 bags of popcorn will cost at the movies.
Evaluation for 3.2e
The chapter 6 Game Time activity prompts educators to respond to groups that arrive at different answers by reviewing and reiterating that following the steps in the correct order yields the correct answer. Additionally, materials prompt educators to monitor groups’ understanding and note misconceptions.
Embedded checks for understanding occur throughout the materials, providing questioning that supports educators in monitoring student learning during lesson delivery. The materials note when educators should monitor groups for understanding and identify misconceptions. In addition, the materials provide examples educators can use to address and clarify misconceptions, supporting timely, targeted feedback as students engage with the lesson content.
Evaluation for 3.3a
The materials emphasize ways educators can build academic vocabulary as the unit progresses, such as modeling mathematical vocabulary in short sentences and using practiced mathematical vocabulary.
The materials guide educators in incorporating multiple levels of language support to help students build academic language, including sentence stems, graphic organizers, and word banks. Supports align with the new ELPS proficiency levels to promote access and participation in mathematical discourse. For example, educators may ask intermediate learners to connect a model to an equation or rehearse with a partner before sharing with the whole group.
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 TEKS Alignment & Navigation Guide explains that it integrates mathematical models, visual representations, academic vocabulary, graphic-novel contexts, educator modeling, partner discourse, sentence supports, manipulatives, oral explanations, written responses, and multiple entry points for developing both mathematical understanding and academic language.
The materials include a section in the TEKS Alignment & Navigation Guide dedicated to specifically addressing bilingual/ESL implementation. This section outlines the purpose and instructional framework, including a briefing, System Check, Game Time and Independent Practice, and debriefing.
Evaluation for 3.3d
Oral discourse builds background knowledge by using contextual analogies to support conceptual understanding before and during instruction. For example, a “factory” analogy introduces factors and multiples, where the educator explains how a factory produces multiples of a toy. This analogy engages students in discussions about how multiple productions of a product at a factory relate to grouping and multiplication. Through oral explanation and guided discussion, students connect the real-world context to mathematical relationships, strengthening their conceptual understanding of multiplication equation structures.
The materials provide strategies for leveraging students’ home languages and supporting cross-linguistic connections through oral or written discourse. These strategies build upon students’ existing linguistic knowledge to increase comprehension of academic vocabulary and content concepts while strengthening their ability to understand, communicate, and demonstrate learning through increasingly complex oral and written discourse.
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
The Assessment, Progress Monitoring & Instructional Decision Guide provides instructional-response guidance for students who demonstrate unfinished learning. Educators can use additional modeling, concrete and visual representations, educator-guided practice, targeted Facts Are Fuel review, Mission Control support, flexible Pit Crew placement, additional practice, and progress monitoring before or during continued grade-level instruction.
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
Historical Adventures at a Glance provides chapter-specific background on the historical and real-world settings in chapters 1–10. This background helps educators anticipate references that students may find unfamiliar before instruction. The guide also provides an explicit sequence for supporting students with unfamiliar references: “show, name, briefly explain, connect, use, and return students to the mathematics.”
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.
1 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.
1 out of 2 points
While the problem-based learning unit includes enrichment activities, the materials do not identify or provide guidance for activities intended for students who have demonstrated proficiency in above-grade-level content and skills.
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.
0 out of 3 points
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 3 points
The materials do not provide adjustable accommodations, such as text-to-speech, content and language supports, or calculators, for students. Students cannot access these supports directly within the materials during instruction or assessment. Educators must implement any needed accommodations separately to ensure students receive appropriate support.
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
The materials provide educator guidance on multiple ways students can demonstrate understanding of multiplication concepts, including kinesthetic modeling of arrays (rows and columns), discourse to identify unknown factors within arrays and complete multiplication equations, and gestures to represent mathematical vocabulary. Students engage with interactive supports, such as “Facts are Fuel” videos, written or verbal explanations, and visual representations, allowing students to express understanding through perform, express, and represent formats.
3.2 Instructional Methods
3.2a
Materials include explicit (direct) prompts and guidance for educators to build knowledge by activating prior knowledge, anchoring big ideas, and highlighting and connecting key patterns, features, and relationships through multiple means of representation.
Materials include explicit (direct) prompts and guidance for educators to build knowledge by activating prior knowledge, anchoring big ideas, and highlighting and connecting key patterns, features, and relationships through multiple means of representation.
5 out of 5 points
Evaluation for 3.2a
Evaluation for 3.2a
Materials include explicit (direct) prompts and guidance for educators to build knowledge by activating prior knowledge, anchoring big ideas, and highlighting and connecting key patterns, features, and relationships through multiple means of representation.
5 out of 5 points
Following instruction on skip counting and the multiplication chart, the materials direct educators to facilitate discussion that connects multiplication by two to the concept of doubling. This guidance emphasizes the overarching idea that multiplication represents repeated equal groups and helps students develop a conceptual understanding of twos facts as doubles.
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
The Teacher’s Guide provides explicit direction for effective lesson delivery by including detailed lesson plans with step-by-step instructions, suggested pacing, and general differentiation strategies for each lesson. These resources help educators implement instruction consistently while adapting lessons to meet diverse student needs.
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.
2 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.
2 out of 3 points
The materials do not provide guidance for implementing multi-tiered intervention methods, including processes for identifying student needs, delivering targeted interventions, or monitoring student progress across tiers.
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
In the Problem-Based Learning unit, the “Mission 4” guidance gives the educator questions to ask; for example, “Ask students to share ways they have learned to use multiplication and division to solve real-world problems from the lessons so far.” Support continues by providing examples such as dividing a container of strawberries with a sibling or using multiplication to determine how much three $5 bags of popcorn will cost at the movies.
3.2e
Materials include prompts and guidance to support educators in providing timely feedback during lesson delivery.
Materials include prompts and guidance to support educators in providing timely feedback during lesson delivery.
2 out of 2 points
Evaluation for 3.2e
Evaluation for 3.2e
Materials include prompts and guidance to support educators in providing timely feedback during lesson delivery.
2 out of 2 points
Embedded checks for understanding occur throughout the materials, providing questioning that supports educators in monitoring student learning during lesson delivery. The materials note when educators should monitor groups for understanding and identify misconceptions. In addition, the materials provide examples educators can use to address and clarify misconceptions, supporting timely, targeted feedback as students engage with the lesson content.
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
The materials guide educators in incorporating multiple levels of language support to help students build academic language, including sentence stems, graphic organizers, and word banks. Supports align with the new ELPS proficiency levels to promote access and participation in mathematical discourse. For example, educators may ask intermediate learners to connect a model to an equation or rehearse with a partner before sharing with the whole group.
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 applicable.
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.
Not applicable.
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
The materials include a section in the TEKS Alignment & Navigation Guide dedicated to specifically addressing bilingual/ESL implementation. This section outlines the purpose and instructional framework, including a briefing, System Check, Game Time and Independent Practice, and debriefing.
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
The materials provide strategies for leveraging students’ home languages and supporting cross-linguistic connections through oral or written discourse. These strategies build upon students’ existing linguistic knowledge to increase comprehension of academic vocabulary and content concepts while strengthening their ability to understand, communicate, and demonstrate learning through increasingly complex oral and written discourse.
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 applicable.
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.
Not applicable.
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
88% (14 out of 16 points)
Evaluation for 4.1a
In Chapter 3, “Bagels and Hammers (Distributive Property),” Game Time Independent Practice asks students to solve two-digit-by-one-digit multiplication problems using mental math, partial products, or the distributive property. Students apply place-value understanding to decompose factors and determine products using different approaches. This develops conceptual understanding of multiplication beyond memorizing procedures.
In Chapter 9, the “Big Bars of Chocolate” kinesthetic performance task asks students to calculate the area of a floor, wall, or window in a real-world design scenario. Students create a model, label its dimensions and area, and explain how they determined their solution. The task provides an opportunity to demonstrate mathematical understanding through representations and justification, not computation alone.
Evaluation for 4.1b
Chapter 9 introduces two-digit-by-two-digit multiplication through a progression of strategies. Students begin with arrays, area models, and the box/grid method before moving to stacking, expanded form, and the traditional algorithm. The progression connects concrete and visual representations to more abstract procedures, allowing students to apply earlier multiplication concepts to increasingly complex computations.
In the Problem-Based Learning unit, “Mission 2 Systems Check” reviews concepts from previous chapters before students complete a Showtime exit ticket. The lesson concludes with a Debrief connecting multiplication and division in real-world situations. Students revisit previously learned concepts and apply their understanding to problems involving related operations.
Evaluation for 4.2a
In “The Fours,” students use known twos facts to derive fours facts by doubling, connecting multiplication equations to arrays and square numbers, and examining related fact family relationships. These connections help students recognize mathematical patterns and see multiplication concepts as interconnected rather than isolated facts.
The student book demonstrates coherence across concepts. For example, in chapter 1, “Magic Marching Ants and Ancient Rome” emphasizes the importance of arranging objects in rows and columns, known as “arrays,” to see what multiplication looks like with equal groups. In chapter 2, “Pirates and Shiny Coins: Skip Counting and the Multiplication Chart” connects the previous multiplication concept to the columns (and rows) of a multiplication chart to skip count easily.
Evaluation for 4.2b
Chapter 10, “Fashion Models and Halloween Candy: Methods for Long Division,” demonstrates vertical coherence across grade bands by connecting students’ prior understanding of place value concepts and regrouping procedures to the development of long division with multi-digit dividends. Students apply knowledge of hundreds, tens, and ones to model equal-group division, regroup place-value units, and solve division problems, linking foundational concepts from earlier grades to a more advanced division concept typically developed in later grades.
The materials develop mathematical connections by linking skip counting, repeated addition, multiplication, and number-line representations. In chapter 2, students use number lines to model skip counting and connect each jump to repeated addition and multiplication facts. Students apply prior knowledge of counting patterns to determine multiples and represent multiplication situations symbolically and visually. These experiences connect concepts, procedures, and representations while building a deeper understanding of multiplication.
Evaluation for 4.2c
In Unit 4, "Division as Fair Sharing,", educator guidance explains how students' understanding of the division symbol and equal groups supports their later learning about fractions. The lesson compares fair-sharing and measurement interpretations of division, helping students connect their understanding of equal groups to future fraction concepts.
In Chapter 4, the materials connect division instruction to previously introduced addition and subtraction concepts. These connections build on students' prior mathematical learning and support their understanding of the inverse relationship between multiplication and division. The guidance demonstrates how mathematical concepts develop across lessons and prepares students for related concepts in later grade levels.
Evaluation for 4.3a
Throughout the multiplication learning pathway, students revisit arrays and repeated addition as they develop multiplication fluency. Lessons initially use visual models to establish the meaning of multiplication before incorporating skip counting and number-line representations in subsequent activities. Returning to these foundational concepts allows students to retrieve earlier learning while applying it to increasingly complex multiplication problems.
In Game Time: Mission 7.1 Independent Practice, students revisit multiplication and division relationships by writing multiplication sentences to represent pictorial models. Students then use the same representations to write corresponding division sentences. This activity requires students to recall previously introduced multiplication concepts and apply their understanding of related operations in a later learning pathway.
Evaluation for 4.3b
The materials organize instruction around individual mathematical concepts, with practice activities primarily reinforcing the skill addressed in the current lesson or chapter. Although students revisit previously introduced strategies, the identified activities do not demonstrate how different skills and concepts are intentionally mixed within practice opportunities to reinforce connections across learning pathways.
In Unit 9, Game Time Independent Practice asks students to solve two-digit-by-two-digit multiplication problems using the traditional algorithm, partial products, or the window method. While students revisit previously learned multiplication strategies, the activity focuses on solving the same type of problem through different methods. It does not incorporate a combination of previously learned third-grade skills, such as multiplication and division relationships, within the practice sequence. As a result, the example demonstrates strategy review rather than interleaved practice that reinforces connections across the third-grade learning pathways.
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
In Chapter 9, the “Big Bars of Chocolate” kinesthetic performance task asks students to calculate the area of a floor, wall, or window in a real-world design scenario. Students create a model, label its dimensions and area, and explain how they determined their solution. The task provides an opportunity to demonstrate mathematical understanding through representations and justification, not computation alone.
4.1b
Questions and tasks, including enrichment and extension materials, increase in rigor and complexity, leading to grade-level and above grade-level proficiency in the mathematics TEKS.
Questions and tasks, including enrichment and extension materials, increase in rigor and complexity, leading to grade-level and above grade-level proficiency in the mathematics TEKS.
4 out of 4 points
Evaluation for 4.1b
Evaluation for 4.1b
Questions and tasks, including enrichment and extension materials, increase in rigor and complexity, leading to grade-level and above grade-level proficiency in the mathematics TEKS.
4 out of 4 points
In the Problem-Based Learning unit, “Mission 2 Systems Check” reviews concepts from previous chapters before students complete a Showtime exit ticket. The lesson concludes with a Debrief connecting multiplication and division in real-world situations. Students revisit previously learned concepts and apply their understanding to problems involving related operations.
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
The student book demonstrates coherence across concepts. For example, in chapter 1, “Magic Marching Ants and Ancient Rome” emphasizes the importance of arranging objects in rows and columns, known as “arrays,” to see what multiplication looks like with equal groups. In chapter 2, “Pirates and Shiny Coins: Skip Counting and the Multiplication Chart” connects the previous multiplication concept to the columns (and rows) of a multiplication chart to skip count easily.
4.2b
Materials demonstrate coherence vertically across concepts and grade bands, including connections from grade K–6, by connecting patterns, big ideas, and relationships.
Materials demonstrate coherence vertically across concepts and grade bands, including connections from grade K–6, by connecting patterns, big ideas, and relationships.
1 out of 1 points
Evaluation for 4.2b
Evaluation for 4.2b
Materials demonstrate coherence vertically across concepts and grade bands, including connections from grade K–6, by connecting patterns, big ideas, and relationships.
1 out of 1 points
The materials develop mathematical connections by linking skip counting, repeated addition, multiplication, and number-line representations. In chapter 2, students use number lines to model skip counting and connect each jump to repeated addition and multiplication facts. Students apply prior knowledge of counting patterns to determine multiples and represent multiplication situations symbolically and visually. These experiences connect concepts, procedures, and representations while building a deeper understanding of multiplication.
4.2c
Materials demonstrate coherence across lessons or activities by connecting students’ prior knowledge of concepts and procedures to the mathematical concepts to be learned in the current grade level and future grade levels.
Materials demonstrate coherence across lessons or activities by connecting students’ prior knowledge of concepts and procedures to the mathematical concepts to be learned in the current grade level and future grade levels.
4 out of 4 points
Evaluation for 4.2c
Evaluation for 4.2c
Materials demonstrate coherence across lessons or activities by connecting students’ prior knowledge of concepts and procedures to the mathematical concepts to be learned in the current grade level and future grade levels.
4 out of 4 points
In Chapter 4, the materials connect division instruction to previously introduced addition and subtraction concepts. These connections build on students' prior mathematical learning and support their understanding of the inverse relationship between multiplication and division. The guidance demonstrates how mathematical concepts develop across lessons and prepares students for related concepts in later grade levels.
4.3 Coherence and Variety of Practice
4.3a
Materials provide spaced retrieval opportunities with previously learned skills and concepts across learning pathways.
Materials provide spaced retrieval opportunities with previously learned skills and concepts across learning pathways.
2 out of 2 points
Evaluation for 4.3a
Evaluation for 4.3a
Materials provide spaced retrieval opportunities with previously learned skills and concepts across learning pathways.
2 out of 2 points
In Game Time: Mission 7.1 Independent Practice, students revisit multiplication and division relationships by writing multiplication sentences to represent pictorial models. Students then use the same representations to write corresponding division sentences. This activity requires students to recall previously introduced multiplication concepts and apply their understanding of related operations in a later learning pathway.
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
In Unit 9, Game Time Independent Practice asks students to solve two-digit-by-two-digit multiplication problems using the traditional algorithm, partial products, or the window method. While students revisit previously learned multiplication strategies, the activity focuses on solving the same type of problem through different methods. It does not incorporate a combination of previously learned third-grade skills, such as multiplication and division relationships, within the practice sequence. As a result, the example demonstrates strategy review rather than interleaved practice that reinforces connections across the third-grade learning pathways.
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
Chapter 7 materials include a Game Time independent practice where students analyze visual grouping models and connect multiplication and division equations to conceptual representations involving equal groups and arrays. For example, questions show equal groups of various models and include prompts such as “What multiplication sentence does the picture show?” and “What division sentence does the picture show?” The materials include questions in which students draw a picture of the given math equation. Collectively, these activities require students to interpret, analyze, and evaluate representations for math concepts and situations.
In unit 1, lesson 2, students evaluate array representations by comparing a three-by-four array and a four-by-three array. The materials include an educator prompt, “Are the two problems on the board the same?” Students justify their conclusions by discussing the commutative property and comparing the arrays and multiplication expressions.
Evaluation for 5.1b
In chapter 1, the Magic Marching Ants and Ancient Rome kinesthetic activity directs students to use pictures of dice with three dots to combine multiples of three and match them with the total to connect repeated addition and multiples to multiplication.
In the grade 3, chapter 5, The Fives activity, students use their fingers as physical representations while skip counting by fives to model multiplication facts, such as using four fingers to represent 5 × 4. Students use a tangible model to represent a multiplication situation before connecting the model to the corresponding multiplication fact.
Evaluation for 5.1c
In chapter 2, students use the multiplication chart to locate products, identify patterns, and connect rows and columns to multiplication facts. The materials explain how students use two factors to find the corresponding product within the chart. In the chapter 2 Game Time practice, students interpret the multiplication chart and use it to solve multiplication problems and verify answers.
In the Problem-Based Learning unit “Mission 2,” students apply their understanding of arrays and multiplication to a new context by designing a remote control using a rectangular array and determining its area. Students record the multiplication fact represented by their design and compare the total number of squares in their array to the total area of the 144-square grid, applying multiplication concepts to a design and measurement task.
Evaluation for 5.2a
The chapter 1 Game Time practice allows students to build automaticity and fluency necessary to meet grade-level TEKS. The chapter 1 Let’s Play activity guides students to identify “factors” and “products” and provides examples showing that the order of these in multiplication does not matter. The materials give students a variety of multiplication equations to identify factors and products and rewrite them to show a matching fact.
In chapter 5, “Tricks and Stories for Memorizing the Multiplication Facts—The Threes,” students engage in a fluency bingo game in which they take turns drawing a card and calling out the correct answers to multiplication and division equations for the threes facts. Students will check the winner’s answers, engaging all students in the activity.
Evaluation for 5.2b
Chapter 2 presents skip counting as repeatedly adding the same number (skip counting by 4 gives 4, 8, 12, and 16 because 4 is added each time), and the materials teach skip counting as a strategy connected to multiplication and repeated addition, stating, “Skip counting and repeated addition are really the same thing, and they are both great ways to find multiples!” Students apply skip counting as an efficient procedure for finding products and multiples.
Students practice efficient mathematical procedures by applying the commutative and associative properties to rewrite multiplication expressions to simplify computation. For example, in chapter 6, students compare 5 × (2 × 7) and (5 × 2) × 7 and recognize that regrouping the factors creates the easier multiplication fact 10 × 7 while maintaining the same product.
In chapter 2, students apply accurate procedures when using multiplication charts. The materials state, "we could put one finger on the left 8, and another finger on the top 3. Then we slide our fingers in straight lines (staying inside the “8” row and the “3” column) until they run into each other at the answer: 24!" Students repeatedly practice this procedure to accurately determine products.
Evaluation for 5.2c
In chapter 8, “More Bagels and Royal Kitties: Multi-Digit Multiplication,” students compare the partial products method with the traditional multiplication method. The materials explain that partial products help students see what is happening mathematically but also note that place value can be “tricky” and that the traditional method avoids adding partial products at the end of the computation.
In chapter 5, the Game Time practice prompts students to evaluate the visual grouping model (hands) and solve nines facts. For example, the Let’s Play section shows 7 × 9 = 63 with a model and a written explanation. Students use this to memorize facts (accuracy) while also staying flexible in their strategy (efficient and accurate). The materials include the statement, “It’s great to do it both ways to make sure we get the same answer,” which supports students’ flexibility with learning facts. Additional practice lets students decide how to solve problems, building all of these skills.
Evaluation for 5.2d
In chapter 3, students learn to decompose numbers into more compatible values. The materials demonstrate how students can break apart a factor into easier numbers, such as decomposing 12 into 10 and 2. The lesson models why choosing 10 as part of a decomposition can make calculations easier and more efficient, stating, “Multiplication by 10 is super easy—we just add a zero!”
In chapter 2, “Pirates and Shiny Coins: Skip Counting and the Multiplication Chart,” the materials prompt the educator to ask students questions as they debrief the skip counting and multiples in the Pirate Ship Race game and the Game Time activity. For example, the educator can ask, “What observations did you make about getting to the number the fastest?” “Was it faster to count the treasure using nickels or dimes?” and “What is the fastest way to reach 100? Nickels, dimes, or quarters?”
Evaluation for 5.3a
In chapter 4, the materials develop the concept of division before connecting multiplication and division through repeated addition, repeated subtraction, inverse operations, and number-line models. First, students explore how multiplication is like repeated addition, and then they examine division as repeated subtraction on a number line before relating the two operations as inverses. This progression emphasizes why division works conceptually before students apply division procedures.
In chapter 3, the lessons explicitly address procedural understanding by guiding students to use the distributive property to decompose multiplication problems into more manageable parts. Students practice breaking apart factors, solving partial products, and combining results to determine products efficiently. Educator guidance repeatedly directs students to apply the procedure, using additional examples to support procedural fluency with multiplication strategies.
Evaluation for 5.3b
The materials rely on visual models, including arrays, dot models, and multiplication charts. For example, in chapter 3, students use arrays to represent multiplication facts and analyze decomposed arrays to understand the distributive property. The materials explicitly show how a 3 × 7 array can be split into smaller arrays (3 × 2 and 3 × 5) while maintaining the same total.
In chapter 3, students explore distributive property tasks using base-ten blocks (concrete) to build and split arrays (pictorial) before solving abstract equations. Students use a knife (popsicle stick) to show different ways to split the same expressions and facts. The educator reminds students that there are multiple ways to split the larger number in each problem. The materials provide examples to reference, as needed.
Evaluation for 5.3c
In chapter 1, “Magic Marching Ants and Ancient Rome: Intro to Multiplication,” the text explains that a great way to see what multiplication looks like is to arrange objects in rows and columns, like an array. The materials provide an image of an array with three columns and four rows, along with the definition. It describes the array, saying, “This array has 4 rows and 3 columns. It could be called a ‘4 by 3 array.’”
In chapter 3, students create concrete models by building 3 × 7 and 3 × 9 arrays with unit cubes, and then they physically separate the arrays using a “bagel splitter” to represent the distributive property. Students connect these concrete models to abstract multiplication expressions by recording equations, such as 3 × 2 + 3 × 5, and determine the total product, demonstrating how decomposing factors can simplify multiplication.
Evaluation for 5.4a
In chapter 3, “The Distributive Property” includes a kinesthetic activity that gives students opportunities to “split” or decompose cubes into arrays. Students explore and discuss multiple examples by writing their thinking on the board and explaining how their strategies connect to the distributive property. Students decide how to split the arrays and then determine how to split the numbers, comparing and justifying different approaches.
In chapter 1, “A Trip to the Toy Factory: Factors and Products” builds students’ academic mathematical language through contextual storytelling, visual array models, and explicit vocabulary instruction. Students use labeled arrays and multiplication equations to define and apply the terms “factor” and “product,” strengthening their conceptual understanding of multiplication.
Evaluation for 5.4b
Lesson assessments reinforce key mathematical vocabulary by engaging students in meaningful language activities. For example, the chapter 2 “Pirates and Shiny Coins” lesson includes the What’s It Called? activity, where students select two vocabulary words, explain each term in their own words, and draw a picture to illustrate its meaning.
The grade 3 materials support students’ use of academic vocabulary by encouraging them to use terms such as distributive property, factors, products, and partial products when explaining their strategies to peers and the educator. The materials include embedded educator guidance that extends students’ use of this vocabulary beyond the lesson and into increasingly complex mathematical discussions and contexts.
Evaluation for 5.4c
In chapter 3, “The Distributive Property,” students build cube arrays and actively split, or decompose, the arrays into smaller parts. The educator guides students in deciding how to split the arrays, then splits the numbers while students write their strategies on the board, explain the connections among rows, columns, and the distributive property, and discuss multiple solution methods with the class.
In “PBL Mission 1,” the educator facilitates mathematical discourse by asking students to make connections between arrays and explain their reasoning with prompts such as “What connections can you make between the theater chair array and the array on the board?” “How can we determine the number of squares?” and “Is there a faster way?” Students also present a question or problem their squadron encountered during brainstorming and explain how they plan to solve it, strengthening their ability to communicate mathematical reasoning with peers and the educator using appropriate mathematical language.
Evaluation for 5.4d
In the chapter 1 Arrays for Multiplication kinesthetic activity, students physically arrange themselves into rows and columns to create arrays. The educator prompts students to share different strategies for determining the total number of students and encourages them to compare and discuss their approaches. As students explain their thinking, they connect the structure of arrays to the number of rows and columns and use skip counting to determine the total. Students count aloud together, reinforcing mathematical vocabulary while building their conceptual understanding of multiplication.
In chapter 3, the materials engage students in small-group problem-solving involving multiplication and the distributive property, allowing them to collaborate as they decompose factors, represent multiplication with arrays, and solve problems using the distributive property. The materials’ educator guidance helps facilitate these discussions to refine and extend students’ mathematical language during peer interactions. As students communicate their thinking, educators support students in building academic vocabulary through purposeful questioning, sentence stems, and discussion prompts.
Evaluation for 5.4e
The materials provide worked examples, sample responses, and step-by-step solution models that demonstrate mathematical reasoning and correct procedures. These examples help educators model effective problem-solving strategies and support students’ understanding of the mathematical concepts. The materials include multiple exemplar responses that reflect different solution strategies or levels of understanding.
The materials do not include embedded guidance to support and/or redirect inaccurate student responses. The student edition includes “Watch Out” examples that present both correct and incorrect worked solutions, allowing students to compare reasoning and identify common mistakes. For example, the chapter 6 lesson uses modeled examples and misconception guidance to help students recognize and correct errors related to the order of operations. However, these examples focus on PEMDAS and the order of operations, which are not included in the grade 3 TEKS. As a result, although the materials demonstrate how to address misconceptions, they do not include comparable embedded instructional support for anticipating or redirecting misconceptions aligned to grade 3 mathematics standards.
Evaluation for 5.5a
In chapter 1, “Marching Ants: Arrays for Multiplication,” students use pictorial arrays to model multiplication, identify rows and columns, write the corresponding multiplication equations (e.g., 2 × 5 = 10 and 4 × 3 = 12), and explain the relationship between each representation and its equation. These activities integrate the TEKS mathematical process standards by engaging students in using representations, analyzing mathematical relationships, and communicating mathematical ideas as they develop their understanding of multiplication concepts.
In “PBL Mission 1,” students explain the connections between the theater chair array and the remote design array, identify a more efficient strategy for determining the total number of objects, and reflect on whether their remote design meets the established criteria. These activities encourage students to communicate their mathematical thinking using appropriate vocabulary.
Evaluation for 5.5b
The materials embed mathematical process standards in lessons and activities, and the process standards connect to the content standards. Through intentionally sequenced learning pathways, students apply mathematical processes, including problem-solving, reasoning, communication, and the use of multiple representations, to develop a deeper conceptual understanding of mathematical content.
The materials integrate the TEKS mathematical process standards into individual lessons. For example, the chapter 3 “Distributive Property” lesson engages students in decomposing numbers, applying the distributive property, solving simpler multiplication problems, and combining partial products to build conceptual understanding.
Evaluation for 5.5c
The lessons include activities aligned with the TEKS mathematical process standards. For example, students use arrays, number lines, multiplication charts, and problem-solving strategies to represent mathematical ideas and solve problems. Educator guidance connects the instructional activities to those standards.
The TEKS Alignment & Navigation Guide explains that “rather than being taught as isolated standards, these practices are intentionally embedded within every chapter and every lesson.” The materials elaborate that educators model mathematical thinking, introduce new concepts, activate prior knowledge, and facilitate mathematical discussions that establish conceptual understanding during the “Briefing” section of the lesson.
5.1 Development of Conceptual Understanding
5.1a
Questions and tasks provide opportunities for students to interpret, analyze, and evaluate models and representations for mathematical concepts and situations.
Questions and tasks provide opportunities for students to interpret, analyze, and evaluate models and representations for mathematical concepts and situations.
3 out of 3 points
Evaluation for 5.1a
Evaluation for 5.1a
Questions and tasks provide opportunities for students to interpret, analyze, and evaluate models and representations for mathematical concepts and situations.
3 out of 3 points
In unit 1, lesson 2, students evaluate array representations by comparing a three-by-four array and a four-by-three array. The materials include an educator prompt, “Are the two problems on the board the same?” Students justify their conclusions by discussing the commutative property and comparing the arrays and multiplication expressions.
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
In the grade 3, chapter 5, The Fives activity, students use their fingers as physical representations while skip counting by fives to model multiplication facts, such as using four fingers to represent 5 × 4. Students use a tangible model to represent a multiplication situation before connecting the model to the corresponding multiplication fact.
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
In the Problem-Based Learning unit “Mission 2,” students apply their understanding of arrays and multiplication to a new context by designing a remote control using a rectangular array and determining its area. Students record the multiplication fact represented by their design and compare the total number of squares in their array to the total area of the 144-square grid, applying multiplication concepts to a design and measurement task.
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
In chapter 5, “Tricks and Stories for Memorizing the Multiplication Facts—The Threes,” students engage in a fluency bingo game in which they take turns drawing a card and calling out the correct answers to multiplication and division equations for the threes facts. Students will check the winner’s answers, engaging all students in the activity.
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
Students practice efficient mathematical procedures by applying the commutative and associative properties to rewrite multiplication expressions to simplify computation. For example, in chapter 6, students compare 5 × (2 × 7) and (5 × 2) × 7 and recognize that regrouping the factors creates the easier multiplication fact 10 × 7 while maintaining the same product.
In chapter 2, students apply accurate procedures when using multiplication charts. The materials state, "we could put one finger on the left 8, and another finger on the top 3. Then we slide our fingers in straight lines (staying inside the “8” row and the “3” column) until they run into each other at the answer: 24!" Students repeatedly practice this procedure to accurately determine products.
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
In chapter 5, the Game Time practice prompts students to evaluate the visual grouping model (hands) and solve nines facts. For example, the Let’s Play section shows 7 × 9 = 63 with a model and a written explanation. Students use this to memorize facts (accuracy) while also staying flexible in their strategy (efficient and accurate). The materials include the statement, “It’s great to do it both ways to make sure we get the same answer,” which supports students’ flexibility with learning facts. Additional practice lets students decide how to solve problems, building all of these skills.
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
In chapter 2, “Pirates and Shiny Coins: Skip Counting and the Multiplication Chart,” the materials prompt the educator to ask students questions as they debrief the skip counting and multiples in the Pirate Ship Race game and the Game Time activity. For example, the educator can ask, “What observations did you make about getting to the number the fastest?” “Was it faster to count the treasure using nickels or dimes?” and “What is the fastest way to reach 100? Nickels, dimes, or quarters?”
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
In chapter 3, the lessons explicitly address procedural understanding by guiding students to use the distributive property to decompose multiplication problems into more manageable parts. Students practice breaking apart factors, solving partial products, and combining results to determine products efficiently. Educator guidance repeatedly directs students to apply the procedure, using additional examples to support procedural fluency with multiplication strategies.
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
In chapter 3, students explore distributive property tasks using base-ten blocks (concrete) to build and split arrays (pictorial) before solving abstract equations. Students use a knife (popsicle stick) to show different ways to split the same expressions and facts. The educator reminds students that there are multiple ways to split the larger number in each problem. The materials provide examples to reference, as needed.
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
In chapter 3, students create concrete models by building 3 × 7 and 3 × 9 arrays with unit cubes, and then they physically separate the arrays using a “bagel splitter” to represent the distributive property. Students connect these concrete models to abstract multiplication expressions by recording equations, such as 3 × 2 + 3 × 5, and determine the total product, demonstrating how decomposing factors can simplify multiplication.
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
In chapter 1, “A Trip to the Toy Factory: Factors and Products” builds students’ academic mathematical language through contextual storytelling, visual array models, and explicit vocabulary instruction. Students use labeled arrays and multiplication equations to define and apply the terms “factor” and “product,” strengthening their conceptual understanding of multiplication.
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
The grade 3 materials support students’ use of academic vocabulary by encouraging them to use terms such as distributive property, factors, products, and partial products when explaining their strategies to peers and the educator. The materials include embedded educator guidance that extends students’ use of this vocabulary beyond the lesson and into increasingly complex mathematical discussions and contexts.
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
In “PBL Mission 1,” the educator facilitates mathematical discourse by asking students to make connections between arrays and explain their reasoning with prompts such as “What connections can you make between the theater chair array and the array on the board?” “How can we determine the number of squares?” and “Is there a faster way?” Students also present a question or problem their squadron encountered during brainstorming and explain how they plan to solve it, strengthening their ability to communicate mathematical reasoning with peers and the educator using appropriate mathematical language.
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
In chapter 3, the materials engage students in small-group problem-solving involving multiplication and the distributive property, allowing them to collaborate as they decompose factors, represent multiplication with arrays, and solve problems using the distributive property. The materials’ educator guidance helps facilitate these discussions to refine and extend students’ mathematical language during peer interactions. As students communicate their thinking, educators support students in building academic vocabulary through purposeful questioning, sentence stems, and discussion prompts.
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.
1 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.
1 out of 2 points
The materials do not include embedded guidance to support and/or redirect inaccurate student responses. The student edition includes “Watch Out” examples that present both correct and incorrect worked solutions, allowing students to compare reasoning and identify common mistakes. For example, the chapter 6 lesson uses modeled examples and misconception guidance to help students recognize and correct errors related to the order of operations. However, these examples focus on PEMDAS and the order of operations, which are not included in the grade 3 TEKS. As a result, although the materials demonstrate how to address misconceptions, they do not include comparable embedded instructional support for anticipating or redirecting misconceptions aligned to grade 3 mathematics standards.
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
In “PBL Mission 1,” students explain the connections between the theater chair array and the remote design array, identify a more efficient strategy for determining the total number of objects, and reflect on whether their remote design meets the established criteria. These activities encourage students to communicate their mathematical thinking using appropriate vocabulary.
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
The materials integrate the TEKS mathematical process standards into individual lessons. For example, the chapter 3 “Distributive Property” lesson engages students in decomposing numbers, applying the distributive property, solving simpler multiplication problems, and combining partial products to build conceptual understanding.
5.5c
Materials include an overview of the TEKS process standards incorporated into each lesson.
Materials include an overview of the TEKS process standards incorporated into each lesson.
1 out of 1 points
Evaluation for 5.5c
Evaluation for 5.5c
Materials include an overview of the TEKS process standards incorporated into each lesson.
1 out of 1 points
The TEKS Alignment & Navigation Guide explains that “rather than being taught as isolated standards, these practices are intentionally embedded within every chapter and every lesson.” The materials elaborate that educators model mathematical thinking, introduce new concepts, activate prior knowledge, and facilitate mathematical discussions that establish conceptual understanding during the “Briefing” section of the lesson.
Rubric Section 6
Productive Struggle
Materials support students in applying disciplinary practices to productive problem-solving, including explaining and revising their thinking.
Total
79% (15 out of 19 points)
Evaluation for 6.1a
In chapter 2, “Pirates and Shiny Coins: Skip Counting and the Multiplication Chart,” students analyze mathematical relationships using arrays, multiplication charts, number lines, repeated addition, and distributive property models rather than relying solely on memorization. Students explore why multiplication works through arrays and investigate patterns in multiplication charts.
The materials engage students in discovering mathematical principles through guided investigations and exploration. The chapter 1 Arrays for Multiplication kinesthetic activity encourages students to think mathematically and make sense of multiplication concepts. Students physically arrange themselves into rows and columns to create arrays while the educator prompts them to determine the total number of students in different ways. As students share their strategies, they connect the structure of arrays to the number of rows and columns and use skip counting to determine the total. By counting aloud and explaining their reasoning, students build conceptual understanding of multiplication rather than simply memorizing facts.
Evaluation for 6.1b
The chapter 4 Fact Families . . . and Dinosaurs! activity engages students in analyzing and explaining the relationship between multiplication and division. Students sort and connect related multiplication and division equations into fact families and then explain why the equations belong together by identifying the common factors and product or quotient. As students discuss their reasoning, they recognize that multiplication and division are inverse operations and use this relationship to explain how knowing one fact helps determine related facts.
The chapter 8 Game Time: Peer Practice activity helps students understand that there are multiple ways to solve multiplication problems using the distributive property. Students break apart factors in different ways and explain the strategy they used to find a solution. Throughout the lessons, the materials incorporate structured opportunities for students to justify, defend, or compare multiple solution strategies through written or oral mathematical arguments.
Evaluation for 6.1c
Chapter 2, “Pirates and Shiny Coins: Skip Counting and the Multiplication Chart,” suggests using the What’s It Called? handout to help students use the lesson’s mathematical vocabulary. The handout prompts students to select two words from the lesson, explain each word in their own words, and draw a picture to help illustrate their meanings.
In the chapter 3 “Bagels and Hammers (Distribution Property)” lesson, students work with a partner to build and decompose numbers using unit cubes. Students discuss strategies for splitting numbers into groups of tens and leftovers and solve multiple examples together to strengthen their understanding of the distributive property. Models also represent multiplication expressions, and students justify their reasoning using mathematical language.
Evaluation for 6.2a
In the “PBL Mission 1” Ask, Imagine, Plan activity, students solve problems using multiplication and division skills to design a Times Machine! remote to travel to places in history. To explain and make connections, the materials prompt the educator to ask students questions such as “How can we determine the number of squares in the remote base on the board?” and “Is there a faster way?” In this way, the materials support educators in guiding a discussion in which students share and reflect on their problem-solving approaches.
The chapter 8 station activities engage students in solving multiplication problems using three (and possibly four) different methods. After completing the stations, the class reviews each strategy, and the educator prompts students to discuss which method they prefer and explain why. The discussion encourages students to share and reflect on their problem-solving approaches and explanations; however, the materials do not give students opportunities to construct mathematical arguments.
Evaluation for 6.2b
The chapter 1, lesson 1 Game Time peer practice activity requires students to complete a multiplication worksheet using visual representations of arrays to reinforce the relationship between rows, columns, and multiplication equations. During the activity, the materials direct educators to actively monitor student work, observe group discussions, and identify specific misconceptions or errors in students’ understanding. The lesson then instructs educators to address misunderstandings by modeling correct examples, stating, “Be sure to clear up misconceptions about rows and columns by modeling examples on the board.” In this way, the materials guide educators to provide explanatory feedback based on student responses and anticipated misconceptions.
While the materials provide worked examples, modeled reasoning, and character dialogue that demonstrates correct mathematical thinking, they do not include educator prompts that help educators respond to specific student answers with explanatory feedback, prompts that identify common misconceptions, or feedback that addresses inaccurate student thinking.
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
The materials engage students in discovering mathematical principles through guided investigations and exploration. The chapter 1 Arrays for Multiplication kinesthetic activity encourages students to think mathematically and make sense of multiplication concepts. Students physically arrange themselves into rows and columns to create arrays while the educator prompts them to determine the total number of students in different ways. As students share their strategies, they connect the structure of arrays to the number of rows and columns and use skip counting to determine the total. By counting aloud and explaining their reasoning, students build conceptual understanding of multiplication rather than simply memorizing facts.
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
The chapter 8 Game Time: Peer Practice activity helps students understand that there are multiple ways to solve multiplication problems using the distributive property. Students break apart factors in different ways and explain the strategy they used to find a solution. Throughout the lessons, the materials incorporate structured opportunities for students to justify, defend, or compare multiple solution strategies through written or oral mathematical arguments.
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
In the chapter 3 “Bagels and Hammers (Distribution Property)” lesson, students work with a partner to build and decompose numbers using unit cubes. Students discuss strategies for splitting numbers into groups of tens and leftovers and solve multiple examples together to strengthen their understanding of the distributive property. Models also represent multiplication expressions, and students justify their reasoning using mathematical language.
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.
4 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.
4 out of 6 points
The chapter 8 station activities engage students in solving multiplication problems using three (and possibly four) different methods. After completing the stations, the class reviews each strategy, and the educator prompts students to discuss which method they prefer and explain why. The discussion encourages students to share and reflect on their problem-solving approaches and explanations; however, the materials do not give students opportunities to construct mathematical arguments.
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
While the materials provide worked examples, modeled reasoning, and character dialogue that demonstrates correct mathematical thinking, they do not include educator prompts that help educators respond to specific student answers with explanatory feedback, prompts that identify common misconceptions, or feedback that addresses inaccurate student thinking.