Program Information
- ISBN
- 9781761191954
- Technical Specifications: Checklist
- Tech Specs: Checklist (pdf 849.77 KB)
- Technical Specifications: Professional Development
- Tech Specs: Professional Development (pdf 187.45 KB)
Book and Box of Fact Strategies, Multiplication & Division
Supplemental Math (English) Grade 3
IMRA 2026
Publisher: ORIGO Education, Inc
Copyright: 2021
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 Standards and Learning Progression resource for multiplication and division explains the concepts covered and demonstrates how the math content is interconnected and sequenced to reinforce skills across the phases of “Prepare,” “Introduce,” “Reinforce,” “Practice,” and “Extend.”
The materials explicitly address learning pathways across grade levels by identifying relevant standards from previous and subsequent grades and connect them to related standards within the specified grade level. This alignment gives educators a clear view of how multiplication and division develop over time and where the resource’s focus on computational fluency fits within the broader learning progression.
Evaluation for 1.1b
The materials suggest using contextual situations, concrete materials, and pictorial representations to help students make sense of the mathematics presented.
The Teacher Book outlines explicit strategies focused on in the program: “Use Doubling,” “Use Tens,” “Use a Rule,” and “Build Down and Build Up.” The instruction helps students master the strategies by engaging with them across five distinct phases: “Prepare,” “Introduce,” “Reinforce,” “Practice,” and “Extend.”
Evaluation for 1.1c
The data-driven approach in the Texas Essential Skills and Knowledge (TEKS) correlation guide helps educators monitor and record student progress across the instructional phases for each strategy in the multiplication and division program.
The “How to Use Fact Fluency Assessments” document helps students fill gaps in their learning. Educators can identify knowledge gaps early and address them, supporting the development of a strong foundation for student learning.
Evaluation for 1.1d
The strategy overview pages in the Teacher Book provide an overview of the strategy, relevant facts, prerequisite skills, and formative as well as summative assessments.
The materials contain supports, including videos, that help educators thoroughly understand and prepare to teach a concept. For example, the video in the “Multiplication” strategy covers the doubling strategy for multiplication.
Evaluation for 1.1e
The “Resource Overview” provides a comprehensive list of materials educators need to successfully implement all lessons for each fluency strategy.
The professional development resources and training modules help instructional leaders support effective curriculum implementation. These resources provide a classroom walkthrough tool and a support video that guides leaders in using the curriculum effectively.
Evaluation for 1.2a
The “Resource Overview” document for each multiplication and division strategy outlines which page, resources, and/or materials will be needed and who will use them. For example, the “Resource Overview” for the “Multiplication: Use Doubling” strategy lists two small transparent bags and 18 counters for the pair.
The lesson plans contain lesson components across the “Prepare,” “Introduce,” “Reinforce,” “Practice,” and “Extend” phases. However, the materials do not contain detailed lesson plans with suggested timeframes or assessment resources aligned to the ELPS.
Evaluation for 1.2b
This guidance is not applicable because the program is not designed to be adaptive.
Evaluation for 1.2c
The materials include activities that support learning at home and contain key vocabulary terms and QR codes that link to helpful educational videos about each strategy.
The “Learning to Use a Rule” section contains a QR code that links to a video explaining that when multiplying by one, the product will be the other factor, and when multiplying by zero, the product will be zero.
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 materials explicitly address learning pathways across grade levels by identifying relevant standards from previous and subsequent grades and connect them to related standards within the specified grade level. This alignment gives educators a clear view of how multiplication and division develop over time and where the resource’s focus on computational fluency fits within the broader learning progression.
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 Teacher Book outlines explicit strategies focused on in the program: “Use Doubling,” “Use Tens,” “Use a Rule,” and “Build Down and Build Up.” The instruction helps students master the strategies by engaging with them across five distinct phases: “Prepare,” “Introduce,” “Reinforce,” “Practice,” and “Extend.”
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 “How to Use Fact Fluency Assessments” document helps students fill gaps in their learning. Educators can identify knowledge gaps early and address them, supporting the development of a strong foundation for student 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.
2 out of 2 points
Evaluation for 1.1d
Evaluation for 1.1d
Materials include protocols with corresponding guidance for unit and lesson internalization.
2 out of 2 points
The materials contain supports, including videos, that help educators thoroughly understand and prepare to teach a concept. For example, the video in the “Multiplication” strategy covers the doubling strategy for multiplication.
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 professional development resources and training modules help instructional leaders support effective curriculum implementation. These resources provide a classroom walkthrough tool and a support video that guides leaders in using the curriculum effectively.
1.2 Lesson-Level Design
1.2a
If designed to be static, materials include detailed lesson plans with learning objectives, teacher and student materials, lesson components with suggested timeframes, and assessment resources aligned with the TEKS and ELPS.
If designed to be static, materials include detailed lesson plans with learning objectives, teacher and student materials, lesson components with suggested timeframes, and assessment resources aligned with the TEKS and ELPS.
5 out of 7 points
Evaluation for 1.2a
Evaluation for 1.2a
If designed to be static, materials include detailed lesson plans with learning objectives, teacher and student materials, lesson components with suggested timeframes, and assessment resources aligned with the TEKS and ELPS.
5 out of 7 points
The lesson plans contain lesson components across the “Prepare,” “Introduce,” “Reinforce,” “Practice,” and “Extend” phases. However, the materials do not contain detailed lesson plans with suggested timeframes or assessment resources aligned to the ELPS.
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).
2 out of 2 points
Evaluation for 1.2c
Evaluation for 1.2c
Materials contain support for families in Spanish and English for each unit, with suggestions on supporting the progress of their student(s).
2 out of 2 points
The “Learning to Use a Rule” section contains a QR code that links to a video explaining that when multiplying by one, the product will be the other factor, and when multiplying by zero, the product will be zero.
Rubric Section 2
Progress Monitoring
Materials support educators in effective implementation through frequent, strategic opportunities to monitor and respond to student progress.
Total
75% (15 out of 20 points)
Evaluation for 2.1a
The materials describe the formative and summative assessment tools available throughout the program. The “Check-in” pages provide suggested activities for students who need additional support.
The materials include fact fluency assessments as diagnostic evaluations to provide baseline data regarding students’ foundational knowledge or proficiency. The “How to Use Fact Fluency Assessments” resource provides practical examples for implementing diagnostic evaluations.
Evaluation for 2.1b
The materials explain how to administer the summative assessment interviews and include suggested time allotments for student responses and scripted questions to ensure consistent, standardized administration across examiners.
The materials help educators efficiently administer the fact fluency assessments through suggestions about the anticipated time needed to complete an assessment based on student mastery. The fact fluency assessments are not timed, and the materials break down suggested timing for navigation to two to three minutes and approximately five seconds per fact.
Evaluation for 2.1c
The digital assessments are composed of a new collection of items on the digital platform each time a student completes an assessment. The materials also include three printable forms that follow the same structure as the digital randomized assessments.
The materials do not contain digital assessments with accommodations such as text-to-speech, content and language supports, or calculators that educators can enable or disable to support individual students. However, students can customize the learning environment as needed with accessibility tools and aspects such as color scheme, font size, and zoom.
Evaluation for 2.1d
While the diagnostic assessments are TEKS-aligned, the questions do not include at least two levels of complexity. The diagnostic assessments contain one level of complexity, which is recall.
While interactive item types on assessments give educators detailed data on student performance, the assessments include only numeric response item types.
Evaluation for 2.1e
Multiple formative assessment check-ins guide educators in assessing student mastery and identifying instructional needs at each learning phase. Educators collect evidence of student understanding through a variety of activities, including hands-on tasks, written challenges, puzzles, games, and discussions about strategies. These diverse assessment opportunities support ongoing progress monitoring and help educators make informed instructional decisions.
The materials contain questions that rely on response formats such as hands-on tasks, written challenges, puzzles, games, and discussions about strategies to represent a variety of interactive item types. This promotes student engagement and allows educators to gather comprehensive data on student learning, identify misconceptions, and adjust instruction based on diverse evidence of understanding.
Evaluation for 2.2a
The formative assessment check-ins contain guidance for targeted questions as well as intervention supports that help educators interpret student performance and monitor progress over time. Educators have access to recording tools to track mastery using classroom or school scoring systems.
The materials provide automatically generated assessment reports for individual students and classes based on the fact fluency assessments as well as downloadable spreadsheets organized by fact fluency strategy. These tools help educators interpret student performance data, identify instructional needs, and form targeted instructional groups. In addition, the “Solution Pathway and Error Analysis Support” resource provides examples of strategy-based solution pathways that students may use to reach the correct answer, enabling educators to examine students’ thinking and address any misconceptions they may have.
Evaluation for 2.2b
The materials include formative assessment check-ins with suggested activities to use when students do not demonstrate mastery of the essential ideas in a given phase. Educators can implement these supports individually or in small-group settings based on instructional context and student needs.
The materials contain reporting spreadsheets for the fact fluency assessments. Students complete the assessments, and the educator uploads the data. The class summary worksheet generates students’ scores for each strategy and substrategy, enabling the educator to identify specific needs and form instructional groups.
Evaluation for 2.2c
The downloadable “Recording Spreadsheet” enables educators to enter student data and track mastery of individual questions across formative assessments. By consolidating assessment results in a single location, the spreadsheet supports ongoing progress monitoring, streamlines data analysis, and helps educators identify trends and make informed instructional decisions.
The “Program Introduction” includes a progress tracker that students use to monitor and take ownership of their fact fluency development. Students color in a fact table as they master individual facts, creating a visual record of their progress and allowing them to see their growth over time. The tracker also helps students identify facts they have mastered and those they still need to practice, supporting goal-setting and encouraging continued development of computational fluency.
Evaluation for 2.2d
The materials contain guidance to help educators conduct frequent checks for understanding at key points throughout each lesson or activity. The “Extend” activities for the “Use Doubling” strategy provide additional guidance to encourage student thinking. The materials include questions that educators can ask at different points in the work and encourage students to look for patterns.
The materials contain prompts to help educators conduct frequent checks for understanding. For example, in the “Use Doubling” strategy, the margin notes provide support for the language of doubling in a variety of contexts. Some activities contain highlighted questions, while others represent a given strategy in different forms.
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 materials include fact fluency assessments as diagnostic evaluations to provide baseline data regarding students’ foundational knowledge or proficiency. The “How to Use Fact Fluency Assessments” resource provides practical examples for implementing diagnostic evaluations.
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
The materials help educators efficiently administer the fact fluency assessments through suggestions about the anticipated time needed to complete an assessment based on student mastery. The fact fluency assessments are not timed, and the materials break down suggested timing for navigation to two to three minutes and approximately five seconds per fact.
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.
1 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.
1 out of 2 points
The materials do not contain digital assessments with accommodations such as text-to-speech, content and language supports, or calculators that educators can enable or disable to support individual students. However, students can customize the learning environment as needed with accessibility tools and aspects such as color scheme, font size, and zoom.
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.
0 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.
0 out of 4 points
While interactive item types on assessments give educators detailed data on student performance, the assessments include only numeric response item types.
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 contain questions that rely on response formats such as hands-on tasks, written challenges, puzzles, games, and discussions about strategies to represent a variety of interactive item types. This promotes student engagement and allows educators to gather comprehensive data on student learning, identify misconceptions, and adjust instruction based on diverse evidence of understanding.
2.2 Data Analysis and Progress Monitoring
2.2a
Instructional assessments include scoring information and guidance for interpreting student performance, including rationale for each correct and incorrect response.
Instructional assessments include scoring information and guidance for interpreting student performance, including rationale for each correct and incorrect response.
3 out of 3 points
Evaluation for 2.2a
Evaluation for 2.2a
Instructional assessments include scoring information and guidance for interpreting student performance, including rationale for each correct and incorrect response.
3 out of 3 points
The materials provide automatically generated assessment reports for individual students and classes based on the fact fluency assessments as well as downloadable spreadsheets organized by fact fluency strategy. These tools help educators interpret student performance data, identify instructional needs, and form targeted instructional groups. In addition, the “Solution Pathway and Error Analysis Support” resource provides examples of strategy-based solution pathways that students may use to reach the correct answer, enabling educators to examine students’ thinking and address any misconceptions they may have.
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 materials contain reporting spreadsheets for the fact fluency assessments. Students complete the assessments, and the educator uploads the data. The class summary worksheet generates students’ scores for each strategy and substrategy, enabling the educator to identify specific needs and form instructional groups.
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 “Program Introduction” includes a progress tracker that students use to monitor and take ownership of their fact fluency development. Students color in a fact table as they master individual facts, creating a visual record of their progress and allowing them to see their growth over time. The tracker also helps students identify facts they have mastered and those they still need to practice, supporting goal-setting and encouraging continued development of computational fluency.
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 materials contain prompts to help educators conduct frequent checks for understanding. For example, in the “Use Doubling” strategy, the margin notes provide support for the language of doubling in a variety of contexts. Some activities contain highlighted questions, while others represent a given strategy in different forms.
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
90% (35 out of 39 points)
Evaluation for 3.1a
The “Introduce” phase of the “Multiplication: Use Doubling” strategy includes scaffolded supports ranging from concrete models (craft sticks, cups, counters, bags) and visual representations (folded paper with paint blobs) to more abstract work with array to enable a gradual progression in understanding.
The additional support section of each check-in provides guidance about next steps for students who struggle. For example, the “Reinforce” phase for the “Division: Use Doubling” strategy suggests scaffolding to help students understand division by having them equally share 40 or fewer counters and describe what is happening. Students use terms such as sharing, groups of, equal groups, grouping, and division. The materials also recommend displaying the terms of division on a word wall for students to reference as needed.
Evaluation for 3.1b
Embedded supports for developing academic vocabulary are incorporated through visual representations. In activity 1 for the “Multiplication: Use Doubling” strategy, students use visual models to connect verbal representations with numbers in a set of related doubling facts, supporting understanding of mathematical language in context.
The “Emergent Bilingual Learner Support Resources” page provides structured vocabulary lists, sentence frames, and instructional strategies to help students build academic vocabulary. This page also includes guidance for promoting discourse, modeling language, and using multiple representations, which serve as embedded supports during instruction. Additionally, grouping strategies and scaffolds within instructional routines help students engage with academic language in context.
Evaluation for 3.1c
The “Extend” activities for the “Multiplication: Use Tens” strategy enable students to extend their basic facts learning to greater whole number values. For instance, activity 5 provides an opportunity to multiply a two-digit number by a one-digit number. Activity 10 builds the language of doubling and halving, which supports the multiplication of two-digit numbers.
The materials provide extension activities for students in the “Extend” section of each strategy. For example, for the “Division: Use Tens” strategy, students are given a real-world problem that involves figuring out how many bundles of bricks are needed for a job and how many bricks are left over. This activity takes the lesson taught previously and enriches learning by requiring deeper reasoning and critical thinking.
Evaluation for 3.1d
The digital materials do not provide accommodations such as text-to-speech, content and language supports, or calculators that educators can enable or disable to support individual students. Although the materials include digital assessments that students can complete online, they do not offer built-in digital accommodations to address whole-group or individual student needs.
The materials do not provide text-to-speech, content and language supports, or calculators for students to use during instruction or assessment. Educators must use external tools or provide separate accommodations to address individual student needs.
Evaluation for 3.1e
In the “Reinforce” phase of the “Multiplication: Use a Rule” strategy, students create physical models using classroom resources, draw pictures to match descriptions, and write number sentences to represent pictures while verbally explaining their reasoning. Emergent bilingual (EB) learner supports such as sentence stems further help students express their mathematical thinking.
A range of problem-solving options in the units, such as worked examples, video excerpts, and real-world applications, help students make meaningful connections to the content. The materials also include guidance for educators to help students show their understanding through multiple formats, such as written and verbal explanations as well as visual representations and drawing models. These varied approaches support diverse learning preferences and provide multiple pathways for students to demonstrate their understanding.
Evaluation for 3.2a
For each operation and strategy, the lessons illustrate patterns, features, and relationships through multiple representations. For example, activity 1 of the “Multiplication: Use a Rule” strategy involves real-world situations to illustrate key features of the strategy. Activity 3 contains colored arrays on a grid alongside verbal and equation representations, and activity 5 uses counters on plates. The activities of the “Extend” phase often include patterning work to show how the strategy extends to greater whole number values.
For the “Division: Build Down and Build Up” strategy, the educator is provided with the prerequisite skills and prior knowledge students will need. The materials give specific look-fors to help the educator elicit what students already know about a topic before introducing new information. For example, the educator could ask, “Can the student identify and describe turnaround facts (the commutative property)?”
Evaluation for 3.2b
Across the phases of learning, students engage in direct instruction using a sharing mat to model strategies, small-group tasks, and game-based practice to reinforce understanding.
The Teacher Book lists the supports as references in the side notes to show educators the exact supplies needed during lesson delivery in order to support instructional approaches. These supports are available for the educator to download.
Evaluation for 3.2c
Each check-in provides a structure for monitoring progress and identifying gaps in student learning. The “Additional Support” section (located in the middle of the page) suggests activities and scaffolds for intervention.
The materials offer opportunities for guided, independent, and collaborative practice when used for intervention. Intervention supports can be provided in whole-group, small-group, or individual settings. Activity 2 of the “Multiplication: Build Down and Build Up” strategy involves collaborative practice in a small-group setting. Activity 3 includes guided practice in a whole-group structure, and activity 10 allows for independent practice in an individual setting.
Evaluation for 3.2d
In the “Enrich” section of the “Multiplication: Build Down” strategy, students cut out a 20-by-2 array and determine the equation to match. The lesson moves into a whole-group discussion and then to group work playing the game “Use a Tens Lens.” After playing the game in groups, the students complete workbook pages with multiplication problems.
For the “Division: Use Doubling” strategy, the “Extension” activities provide educators with targeted questions and suggestions for support such as, “I think (Anna’s) strategy would be easier if...”
Evaluation for 3.2e
Activity 2 of the “Multiplication: Use Tens” strategy uses the highlighted questions to help educators check for understanding by asking, “How can you prove it?” or “What do you notice…”
Formative assessments are embedded within each sequence of a strategy lesson and include prompts and questions that help educators assess student understanding in the moment. These check-ins also offer an “Additional Support” section for educators to use in addressing student misconceptions identified during the formative assessment.
Evaluation for 3.3a
The materials include accommodations designed to engage students in using increasingly more academic language. For example, in activity 2 of the “Multiplication: Build Down” strategy, students “model the strategy using bags of counters. A student at the pre-production level may write an equation or select the appropriate equation for the situation. The student may also be able to say or repeat the number names in their primary language or in English.”
A dedicated section in the “Standards and Learning Progression” resource addresses speaking, listening, reading, and writing for all proficiency levels as defined by the ELPS. For example, in activity 5 of the “Division: Use Doubling” strategy, students “create fact family equations with an array illustrating the relationships among the facts. Students at this level can follow the directions and respond appropriately to comments from their partner.”
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 “Program Introduction” resource is dedicated to supporting EB learners and contains implementation guidance (such as grouping practices) that provides deliberate opportunities for students to engage in listening, speaking, reading, and writing. Students are assigned specific roles in group activities, which ensures that they actively participate in multiple language domains while collaborating with their peers.
The “ELPS Learning Progression” and “Emergent Bilingual Learner Support” resources provide structured guidance across proficiency levels and the five phases of learning, with explicit strategies for speaking, listening, reading, and writing. The supports include scaffolding, vocabulary development, and sentence stems aligned with ELPS expectations to ensure access to grade-level mathematics while supporting language development within ESL and bilingual instructional settings.
Evaluation for 3.3d
The materials provide embedded guidance to help EB students develop academic vocabulary, increase comprehension, build background knowledge, and make cross-linguistic connections through oral discourse. The materials also contain embedded guidance to help EB students develop academic vocabulary, increase comprehension, and build background knowledge through written discourse. In addition, the materials provide educators with resources to help students connect new information to prior knowledge. For example, the “Prepare” phase of each strategy involves activities that confirm students have the necessary prerequisite skills and establish a foundation for the understanding students acquire when learning a given strategy.
In activity 5 of the “Division: Use Doubling” strategy, students collaborate to solve a multi-step word problem that highlights the relationships relevant to this strategy. Students are encouraged to choose resources to support their thinking and then explain their solution to the class.
The materials do not contain embedded guidance for educators to help EB students make cross-linguistic connections through written discourse. With no evidence of intentional supports for translanguaging and language transfer, educators may have difficulty helping students leverage their existing linguistic knowledge to build proficiency in English.
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 additional support section of each check-in provides guidance about next steps for students who struggle. For example, the “Reinforce” phase for the “Division: Use Doubling” strategy suggests scaffolding to help students understand division by having them equally share 40 or fewer counters and describe what is happening. Students use terms such as sharing, groups of, equal groups, grouping, and division. The materials also recommend displaying the terms of division on a word wall for students to reference as needed.
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
The “Emergent Bilingual Learner Support Resources” page provides structured vocabulary lists, sentence frames, and instructional strategies to help students build academic vocabulary. This page also includes guidance for promoting discourse, modeling language, and using multiple representations, which serve as embedded supports during instruction. Additionally, grouping strategies and scaffolds within instructional routines help students engage with academic language in context.
3.1c
Materials include explicit educator guidance for enrichment and extension activities for students who have demonstrated proficiency in grade-level and above grade-level content and skills.
Materials include explicit educator guidance for enrichment and extension activities for students who have demonstrated proficiency in grade-level and above grade-level content and skills.
2 out of 2 points
Evaluation for 3.1c
Evaluation for 3.1c
Materials include explicit educator guidance for enrichment and extension activities for students who have demonstrated proficiency in grade-level and above grade-level content and skills.
2 out of 2 points
The materials provide extension activities for students in the “Extend” section of each strategy. For example, for the “Division: Use Tens” strategy, students are given a real-world problem that involves figuring out how many bundles of bricks are needed for a job and how many bricks are left over. This activity takes the lesson taught previously and enriches learning by requiring deeper reasoning and critical thinking.
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 text-to-speech, content and language supports, or calculators for students to use during instruction or assessment. Educators must use external tools or provide separate accommodations to address individual student needs.
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
A range of problem-solving options in the units, such as worked examples, video excerpts, and real-world applications, help students make meaningful connections to the content. The materials also include guidance for educators to help students show their understanding through multiple formats, such as written and verbal explanations as well as visual representations and drawing models. These varied approaches support diverse learning preferences and provide multiple pathways for students to demonstrate their understanding.
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
For the “Division: Build Down and Build Up” strategy, the educator is provided with the prerequisite skills and prior knowledge students will need. The materials give specific look-fors to help the educator elicit what students already know about a topic before introducing new information. For example, the educator could ask, “Can the student identify and describe turnaround facts (the commutative property)?”
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 Book lists the supports as references in the side notes to show educators the exact supplies needed during lesson delivery in order to support instructional approaches. These supports are available for the educator to download.
3.2c
Materials include multi-tiered intervention methods for various types of practice and structures and educator guidance to support effective implementation.
Materials include multi-tiered intervention methods for various types of practice and structures and educator guidance to support effective implementation.
3 out of 3 points
Evaluation for 3.2c
Evaluation for 3.2c
Materials include multi-tiered intervention methods for various types of practice and structures and educator guidance to support effective implementation.
3 out of 3 points
The materials offer opportunities for guided, independent, and collaborative practice when used for intervention. Intervention supports can be provided in whole-group, small-group, or individual settings. Activity 2 of the “Multiplication: Build Down and Build Up” strategy involves collaborative practice in a small-group setting. Activity 3 includes guided practice in a whole-group structure, and activity 10 allows for independent practice in an individual setting.
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
For the “Division: Use Doubling” strategy, the “Extension” activities provide educators with targeted questions and suggestions for support such as, “I think (Anna’s) strategy would be easier if...”
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
Formative assessments are embedded within each sequence of a strategy lesson and include prompts and questions that help educators assess student understanding in the moment. These check-ins also offer an “Additional Support” section for educators to use in addressing student misconceptions identified during the formative assessment.
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
A dedicated section in the “Standards and Learning Progression” resource addresses speaking, listening, reading, and writing for all proficiency levels as defined by the ELPS. For example, in activity 5 of the “Division: Use Doubling” strategy, students “create fact family equations with an array illustrating the relationships among the facts. Students at this level can follow the directions and respond appropriately to comments from their partner.”
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 “ELPS Learning Progression” and “Emergent Bilingual Learner Support” resources provide structured guidance across proficiency levels and the five phases of learning, with explicit strategies for speaking, listening, reading, and writing. The supports include scaffolding, vocabulary development, and sentence stems aligned with ELPS expectations to ensure access to grade-level mathematics while supporting language development within ESL and bilingual instructional settings.
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.
7 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.
7 out of 8 points
In activity 5 of the “Division: Use Doubling” strategy, students collaborate to solve a multi-step word problem that highlights the relationships relevant to this strategy. Students are encouraged to choose resources to support their thinking and then explain their solution to the class.
The materials do not contain embedded guidance for educators to help EB students make cross-linguistic connections through written discourse. With no evidence of intentional supports for translanguaging and language transfer, educators may have difficulty helping students leverage their existing linguistic knowledge to build proficiency in English.
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
100% (16 out of 16 points)
Evaluation for 4.1a
The materials indicate that the “program addresses all components of grade 3 TEKS 4(F): recall facts to multiply up to 10 by 10 with automaticity and recall the corresponding division facts.” The digital version of a fact fluency assessment includes randomized samples of items drawn from facts such as 3 x 5 and 9 x 6.
Educators can periodically administer the paper-based fact fluency assessments throughout the learning progression, either to assess mastery or to use as diagnostic evaluations for students who are struggling with basic facts. This enables educators to assess student knowledge of multiplication facts within 100 and provide appropriate instruction to help fill gaps in student learning. For example, “Form A, Multiplication within 100” contains 35 multiplication facts, including up to 10 x 10.
Evaluation for 4.1b
In the “Extend” phase of the “Division: Use Tens” strategy, students progress from dividing multiples of 5 using base 10 blocks and equal groups to analyzing division patterns, decomposing numbers to find quotients, and applying multiplication strategies to solve division problems. Students move from concrete representations to explaining relationships among dividends, divisors, and quotients; identifying patterns in quotient changes; and justifying the strategies they used to find a solution.
The “Doubling” strategy provides practice opportunities across the “Prepare,” “Introduce,” “Reinforce,” “Practice,” and “Extend” phases. In these phases, students repeatedly apply a given strategy in multiple formats such as fact card analysis, partner and group games, and structured problem-solving activities. Across the phases, students engage in tasks that require them to use the “Doubling” strategy to determine products, compare expressions, and justify their thinking during gameplay and collaborative practice, allowing them to deepen their understanding of multiplication facts through repeated application, reasoning, and strategy selection rather than isolated skill practice.
Evaluation for 4.2a
In grade 3, the materials show coherence across concepts within the grade level by connecting the “Count On,” “Doubles,” and “Near Doubles” strategies throughout the progression of fact instruction. Students first develop an understanding of “Count On” and “Count Back” and then apply these strategies to solve near-doubles problems using known doubles facts and related number relationships. The “Extend” phase connects these strategies to larger whole numbers, allowing students to apply the same relationships and patterns across increasingly complex number sets.
The “Multiplication: Use Doubles” strategy directs educators to check student understanding of prior concepts. The check-in instructs the educator to ask, “Can the student represent doubles addition facts using different models? Does the student understand and apply the commutative property of addition?” This questioning lays the foundation for students to move forward toward multiplication.
Evaluation for 4.2b
In the “Multiplication: Use Doubling” strategy, the “Introduce” phase connects how repeated addition and finding the total relate to multiplication and finding the product. Activity 1 gives students manipulatives and prompts them to place five craft sticks into two cups, write the addition equation to match, and then use multiplication to describe adding equal groups recording the multiplication equation. This activity is repeated for groups of four and groups of eight. Students are encouraged to compare the equations and describe any relationships they notice.
The materials show vertical coherence by connecting previously learned addition concepts to new learning of multiplication. Students build on prerequisite skills, including doubles addition facts, extending doubles to two-digit numbers, and the commutative property of addition, before applying such understanding to the “Multiplication: Use Doubling” strategy. This progression links foundational number relationships from earlier grades to multiplication concepts developed in the current grade.
Evaluation for 4.2c
In the “Prepare” phase of the “Division: Build Down and Build Up” strategy, students review prior learning from earlier grades and earlier lessons. In activities 1–4, students revisit arrays, multiplication facts, turnaround facts, and partitioning strategies to connect equal groups and arrays to the commutative, distributive, and associative properties of multiplication.
The materials introduce new concepts and procedures while connecting students’ previous knowledge of related mathematical concepts. Each strategy includes the “Prepare” phase, which lists required background knowledge. In the “Prepare” phase for the “Division: Use Tens” strategy, the materials ask, “Does the student know the tens multiplication facts?”
Evaluation for 4.3a
The “Multiplication: Use Doubling” strategy reinforces mental computation based on the doubles facts for addition. The “Use Doubling” strategy reviews the twos facts and then encourages students to think “double double” to figure out the fours facts and their turnarounds. Finally, students are encouraged to think “double double double” to figure out the eights facts and their turnarounds.
In grade 3, the lessons provide opportunities for spaced practice as students progress across representations when learning the strategy. While fluency practice happens in the “Practice” phase, students have been practicing informally as well as over time in the “Introduce” and “Reinforce” phases. In a broader sense, spaced practice also happens as students use known facts and strategies in other periods of learning math, beyond the scope of the supplemental learning described here.
Evaluation for 4.3b
Students apply various multiplication strategies to solve products beyond basic facts, including decomposing factors, using tens facts, halving and doubling, and applying distributive reasoning based on the “Multiplication: Use Tens” strategy in the “Extend” phase. For example, in activity 10, students solve 48 × 5 using different strategies and compare methods for solution. Students select and apply efficient strategies while making connections among previously learned multiplication concepts and procedures rather than relying on a single approach.
In the “Multiplication: Build Down and Build Up” strategy, the “Prepare” phase includes activities where students create different arrays using dot grids and manipulatives. Students are prompted to create new or smaller arrays, identify the total, and write the corresponding equations. This understanding of content is reiterated in subsequent activities with increasing complexity using knowledge of the distributive property (where students partition an array into two smaller arrays) and the associative property (where students can rearrange an array to make multiplication easier).
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
Educators can periodically administer the paper-based fact fluency assessments throughout the learning progression, either to assess mastery or to use as diagnostic evaluations for students who are struggling with basic facts. This enables educators to assess student knowledge of multiplication facts within 100 and provide appropriate instruction to help fill gaps in student learning. For example, “Form A, Multiplication within 100” contains 35 multiplication facts, including up to 10 x 10.
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
The “Doubling” strategy provides practice opportunities across the “Prepare,” “Introduce,” “Reinforce,” “Practice,” and “Extend” phases. In these phases, students repeatedly apply a given strategy in multiple formats such as fact card analysis, partner and group games, and structured problem-solving activities. Across the phases, students engage in tasks that require them to use the “Doubling” strategy to determine products, compare expressions, and justify their thinking during gameplay and collaborative practice, allowing them to deepen their understanding of multiplication facts through repeated application, reasoning, and strategy selection rather than isolated skill practice.
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 “Multiplication: Use Doubles” strategy directs educators to check student understanding of prior concepts. The check-in instructs the educator to ask, “Can the student represent doubles addition facts using different models? Does the student understand and apply the commutative property of addition?” This questioning lays the foundation for students to move forward toward multiplication.
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 show vertical coherence by connecting previously learned addition concepts to new learning of multiplication. Students build on prerequisite skills, including doubles addition facts, extending doubles to two-digit numbers, and the commutative property of addition, before applying such understanding to the “Multiplication: Use Doubling” strategy. This progression links foundational number relationships from earlier grades to multiplication concepts developed in the current grade.
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
The materials introduce new concepts and procedures while connecting students’ previous knowledge of related mathematical concepts. Each strategy includes the “Prepare” phase, which lists required background knowledge. In the “Prepare” phase for the “Division: Use Tens” strategy, the materials ask, “Does the student know the tens multiplication facts?”
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 grade 3, the lessons provide opportunities for spaced practice as students progress across representations when learning the strategy. While fluency practice happens in the “Practice” phase, students have been practicing informally as well as over time in the “Introduce” and “Reinforce” phases. In a broader sense, spaced practice also happens as students use known facts and strategies in other periods of learning math, beyond the scope of the supplemental learning described here.
4.3b
Materials provide interleaved practice opportunities with previously learned skills and concepts across learning pathways.
Materials provide interleaved practice opportunities with previously learned skills and concepts across learning pathways.
2 out of 2 points
Evaluation for 4.3b
Evaluation for 4.3b
Materials provide interleaved practice opportunities with previously learned skills and concepts across learning pathways.
2 out of 2 points
In the “Multiplication: Build Down and Build Up” strategy, the “Prepare” phase includes activities where students create different arrays using dot grids and manipulatives. Students are prompted to create new or smaller arrays, identify the total, and write the corresponding equations. This understanding of content is reiterated in subsequent activities with increasing complexity using knowledge of the distributive property (where students partition an array into two smaller arrays) and the associative property (where students can rearrange an array to make multiplication easier).
Rubric Section 5
Balance of Conceptual and Procedural Understanding
Materials are designed to balance conceptual understanding, procedural skills, and fluency.
Total
100% (38 out of 38 points)
Evaluation for 5.1a
In the “Introduce” phase of the “Use a Rule” strategy, students engage in linking real-world contexts, arrays, connecting cubes, equations, and base 10 block models to represent multiplication by one and zero. Students compare representations, explain the relationships among the models, and justify how each representation supports the multiplication presented.
In grade 3, the materials require students to interpret, analyze, and compare multiple representations of fives multiplication facts. Students choose a fives fact and its turnaround fact based on the “Multiplication: Use Tens” strategy in the “Reinforce” phase. Students then represent the fact using jumps on a number line, a picture with equal groups, an array, and words. Students compare their representations and discuss how the models are the same as well as different.
Evaluation for 5.1b
In activity 6 of the “Division: Use Doubling” strategy, students represent division situations by sharing pictures, grouping pictures, and connecting cube models. Students connect division facts to related multiplication facts as they model and explain each situation.
Students choose a division fact they know that relates to a twos, fours, or eights multiplication fact that they think is difficult to remember in the “Reinforce” phase of the “Division: Use Doubling” strategy. Students then represent the fact as a sharing picture, as a grouping picture, and in words. Next, they use resources (such as connecting cubes) to act out the division problem.
Evaluation for 5.1c
In the “Extend” phase of the “Multiplication: Build Up” strategy, students apply their conceptual understanding of multiplication patterns and relationships to new problem situations. Students use known multiplication facts, arrays, and build-up strategies to determine unknown products, extend patterns to larger factors, and solve multiplication problems involving one- and two-digit numbers.
The materials ask students to analyze an ancient Egyptian doubling method to solve 28 × 13 by creating a table of doubles, identifying which numbers combine to make 13, and adding the corresponding doubled values in the “Extend” phase of the “Multiplication: Use Doubling” strategy. Students then apply the same method with a partner to calculate 31 × 12.
Evaluation for 5.2a
A fact fluency assessment is untimed and contains 35 multiplication facts on the digital platform. The assessment can be administered numerous times in order to build and track student automaticity as well as fluency over time.
The tasks of the “Introduce” phase of the “Division: Use Tens” strategy build the automaticity and fluency students need to complete grade-level mathematical tasks. In activity 3, students play partner and small-group games to develop fluency with the relevant set of facts. Students play a mix-and-match game with a pictorial representation, an abstract representation, and the solution.
Evaluation for 5.2b
The “Introduce” phase of the “Multiplication: Use a Rule” strategy supports efficient and accurate mathematical procedures by having students model multiplication by one and zero using real-world situations, arrays, and concrete models before writing matching equations. Understanding these rules allows students to efficiently determine products involving one or zero while accurately connecting models and equations.
In the “Practice” phase of the “Multiplication: Use a Rule” strategy, students create and use a rule to figure out the product of facts. For example, students are given the fact 1 × 5, with the product covered. The educator asks, “What rule can you use to figure out the product?” and “What is the turnaround fact?” Students explain the rules they would use. Next, the class either agrees or disagrees with students’ thinking.
Evaluation for 5.2c
During the “Extend” phase of the “Multiplication: Use a Rule” strategy, students read each expression displayed and then identify the expression with the greatest product. Students are grouped into pairs to share their reasoning. Educators are prompted to listen to the students’ discussions and then invite individuals to share their ideas with the class. Students test their predictions with a calculator and discuss the outcomes.
For all strategies, an activity in the “Reinforce” phase asks students to sort multiplication facts by strategy and explain why a particular strategy should be used to find the product. Students compare approaches and respond to prompts such as, “How would a different strategy work for this product?” This supports the evaluation of efficient strategies, flexible strategy selection, and the accurate use of multiplication facts.
Evaluation for 5.2d
Across the phases of learning, students progress from using concrete objects and contextual situations to more abstract representations and thinking. Educator questions support this development by encouraging students to connect representations. For example, students can connect base 10 representations with oral and written equations in the “Extend” phase of the “Multiplication: Use Doubling” strategy.
In grade 3, educator guidance helps students select increasingly efficient approaches for division. In the “Extend” phase of the “Division: Build Down and Build Up” strategy, students solve 360 ÷ 18 by discussing possible strategies with a partner. The educator listens for efficient strategies, records multiple methods on the board, and prompts students to interpret each strategy and explain why it works.
Evaluation for 5.3a
Grade 3 activities of the “Multiplication: Build Down” strategy highlight a conceptual focus, while others underscore a procedural emphasis. In the “Introduce” phase, activities encourage students to see that different representations show the same total, focusing on conceptual understanding. Activities in the “Reinforce” phase highlight the equivalence of different equations or other more abstract representations, connecting to a greater procedural emphasis.
The “Multiplication: Use Tens” strategy includes a practice activity that addresses the conceptual emphasis of the TEKS by asking students to use known tens facts and turnaround facts to reason about unknown products and explain their thinking. The procedural emphasis is addressed during activities 3–7, where students repeatedly apply the “Use Tens” strategy to determine products, solve puzzles, and match multiplication expressions to solutions.
Evaluation for 5.3b
In the “Reinforce” phase of all strategies, students select a word problem, choose a math tool to act it out, and then draw a picture to represent it. Students write the matching division fact and a related multiplication fact.
Students use concrete, pictorial, and abstract models with multiplication facts in the “Reinforce” phase of the “Multiplication: Use Doubling” strategy. Students record the twos, fours, and eights multiplication facts they know and then select a difficult fact to represent with concrete materials through illustration, pictorial representation, and abstract models. Students write, in words, how they used the strategy. At the end of the activity, students share and explain their representations.
Evaluation for 5.3c
In the “Prepare” phase of the “Division: Build Down and Build Up” strategy, the activities establish supports for students by modeling appropriate representations and drawing connections between drawings for essential prior knowledge. In combination with the learning in the “Introduce” phase, students are supported to connect two physical and visual models to abstract symbols, and to create concrete or pictorial models related to abstract symbols.
In the “Reinforce” phase of the “Multiplication: Use Doubling” strategy, students create a pictorial representation of a division word problem and connect that representation to matching division and related multiplication equations. The educator asks students to explain their representations and solutions to their peers, helping students create, connect, and explain representational models and abstract mathematical concepts.
Evaluation for 5.4a
In activity 1 of the “Extend” phase of the “Division: Use Tens” strategy, the educator organizes students into pairs and provides each pair with a sharing mat and base 10 blocks. Students work together to determine how to share 100 across five equal groups, model the solution with the manipulatives, and describe the strategy they used to represent equal sharing.
In the “Introduce” phase of the “Division: Use Doubling” strategy, students identify words in word problems that signal multiplication or division and add these terms to a classroom word wall. The activity strengthens students’ academic mathematical language by helping them connect vocabulary to problem situations and encouraging them to use the word wall as a reference when discussing multiplication and division concepts with their peers and educators.
Evaluation for 5.4b
For the “Division: Use Tens” strategy, students use sharing mats and base 10 blocks to explore the relationship between multiplication and division through hands-on problem-solving. The educator prompts students to explain their thinking by asking, “How can you describe the relationship between multiplication and division?” Students use academic mathematical terms such as equal groups, factors, products, dividends, and quotients as they describe the connections between the two operations.
Activities 4 and 5 of the “Extend” phase in the “Division: Build Down and Build Up” strategy provide educators with embedded guidance to scaffold and support students’ use of academic mathematical vocabulary during mathematical discourse. The educator prompts students to discuss strategies for finding quotients and uses sentence frames such as “I chose this strategy because…”, “I like your strategy, but I wonder…”, and “Did you think about…” to encourage meaningful mathematical conversations. These structured prompts help students explain and compare multiple methods for solution, interpret equations, describe why their strategies work, and justify their reasoning using precise mathematical language.
Evaluation for 5.4c
In activity 5 of the “Introduce” phase in the “Division: Build Down and Build Up” strategy, students use strategy cards that show the total number of dots, the number of equal rows, and the number in each row. The educator prompts students to connect each division problem to a related multiplication fact, and encourages them to explain their reasoning using precise mathematical language. Students share statements such as, “I know 9 × 3 is 27, so 27 ÷ 9 must be 3,” reinforcing the relationship between multiplication and division while developing their ability to communicate mathematical thinking using appropriate academic vocabulary.
Activity 4 in the “Introduce” phase of the “Multiplication: Use a Rule” strategy asks students to generate other words for zero. The educator records students’ responses on the board and helps them create multiplication stories that involve zero. Students share real-world examples, such as “the number of empty rows of seats at a football game,” and then help create a wall chart that organizes situations involving a factor of zero. For example, students place “six empty nests” under __ × 0 and “no bags of five apples” under 0 × __. The educator encourages students to contribute a variety of examples and explain how each situation matches the corresponding multiplication expression, reinforcing precise mathematical vocabulary and reasoning.
Evaluation for 5.4d
In activity 3 of the “Prepare” phase of the “Build Down and Build Up” strategy, the educator organizes students into small groups to discuss their investigations of arrays. The educator prompts students to refer to their arrays as they explain and justify their reasoning, encouraging them to use mathematical evidence to support their conclusions. These collaborative discussions give students opportunities to compare strategies, respond to their classmates’ ideas, and strengthen their mathematical communication.
The “Reinforce” phase of the “Subtraction: Use Doubles” strategy provides educators with embedded guidance to help students hear, refine, and use mathematical language with their peers. The educator uses sentence frames to support respectful mathematical discourse and encourage students to evaluate and build on one another’s strategies. For example, students use prompts such as “I like [student’s] strategy because...” and “I think [student’s] strategy would be easier if...” to explain their thinking, provide constructive feedback, and communicate using appropriate mathematical vocabulary.
Evaluation for 5.4e
Activity 5 in the “Prepare” phase of the “Multiplication: Build Down and Build Up” strategy alerts educators that some students may rely only on addition and miss opportunities to solve problems more efficiently by using subtraction. The educator monitors students’ strategies, identifies those who avoid subtraction, and encourages them to broaden their approach by considering subtraction as an alternative strategy. This embedded guidance helps educators recognize limited reasoning, address misconceptions about strategy selection, and promote more flexible mathematical thinking.
The “Reinforce” phase for all strategies provides embedded guidance for educators to anticipate a variety of student responses by including exemplar answers for discussion tasks. In activity 13, students illustrate and act out a word problem with manipulatives, write the corresponding division equation and related multiplication fact, and explain how their representation matches the problem. Students then share their work with the class and describe their mathematical reasoning. The materials support educators by providing five sample student responses, including examples such as, “A group of 49 people attend a sports game. They sit in rows of seven. How many people sit in each row?”
Evaluation for 5.5a
The “Standards and Learning Progression” resource identifies some of the TEKS mathematical process standards and provides educators with an instructional example for each one. For example, the resource highlights how students extend their understanding to larger whole numbers by applying problem-solving strategies in new situations, reasoning through unfamiliar tasks, and explaining how previously learned strategies support their solutions.
In activity 6 in the “Reinforce” phase of the “Division: Use Tens” strategy, students solve real-world word problems by selecting a problem, choosing a mathematical tool to model it, drawing a representation, and writing the corresponding division equation and related multiplication fact. Students collaborate with a peer when they select the same problem and then share their work with the class and explain how each representation models the situation. This sequence engages students in problem-solving, selecting appropriate tools, using multiple representations, communicating mathematical ideas, and making connections between multiplication and division, demonstrating how the process standards support grade-level content throughout instruction.
Evaluation for 5.5b
The “Standards and Learning Progression” resource clearly identifies the mathematical process standard emphasized during the “Prepare,” “Introduce,” “Reinforce,” “Practice,” and “Extend” phases. The resource also describes how each phase builds students’ mathematical thinking by developing conceptual understanding, strengthening problem-solving skills, encouraging mathematical communication, and extending learning across the broader instructional pathway.
The grade 3 materials identify a TEKS mathematical process standard for each phase of learning and explain how that standard links to the instructional pathway. For example, the “Prepare” phase of the “Multiplication: Use Doubling” strategy emphasizes Process Standard 1F by engaging students in analyzing relationships among multiple representations of multiplication facts as they match the appropriate cards during activity 2. This activity helps students connect mathematical ideas and build conceptual understanding through pattern recognition and discussion.
Evaluation for 5.5c
The materials embed the TEKS mathematical process standards throughout instruction by identifying the targeted process standard for each lesson. The “Standards and Learning Progression” resource explains how lesson activities develop problem-solving, reasoning, communication, and representation, helping educators connect daily instruction to the TEKS process standards.
Each lesson phase includes “Check-In” questions that help educators monitor students’ mastery of the TEKS mathematical process standards. The questions prompt educators to determine whether students recognize relationships among operations or strategies and whether they can solve increasingly complex problems. For example, the materials ask, “Can the student solve one- and two-step word problems involving division with two- and three-digit numbers?” This question aligns with TEKS Process Standard 1B by requiring students to analyze the problem, develop a solution strategy, and apply mathematical reasoning to solve multi-step tasks.
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 grade 3, the materials require students to interpret, analyze, and compare multiple representations of fives multiplication facts. Students choose a fives fact and its turnaround fact based on the “Multiplication: Use Tens” strategy in the “Reinforce” phase. Students then represent the fact using jumps on a number line, a picture with equal groups, an array, and words. Students compare their representations and discuss how the models are the same as well as different.
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
Students choose a division fact they know that relates to a twos, fours, or eights multiplication fact that they think is difficult to remember in the “Reinforce” phase of the “Division: Use Doubling” strategy. Students then represent the fact as a sharing picture, as a grouping picture, and in words. Next, they use resources (such as connecting cubes) to act out the division problem.
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
The materials ask students to analyze an ancient Egyptian doubling method to solve 28 × 13 by creating a table of doubles, identifying which numbers combine to make 13, and adding the corresponding doubled values in the “Extend” phase of the “Multiplication: Use Doubling” strategy. Students then apply the same method with a partner to calculate 31 × 12.
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
The tasks of the “Introduce” phase of the “Division: Use Tens” strategy build the automaticity and fluency students need to complete grade-level mathematical tasks. In activity 3, students play partner and small-group games to develop fluency with the relevant set of facts. Students play a mix-and-match game with a pictorial representation, an abstract representation, and the solution.
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
In the “Practice” phase of the “Multiplication: Use a Rule” strategy, students create and use a rule to figure out the product of facts. For example, students are given the fact 1 × 5, with the product covered. The educator asks, “What rule can you use to figure out the product?” and “What is the turnaround fact?” Students explain the rules they would use. Next, the class either agrees or disagrees with students’ thinking.
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
For all strategies, an activity in the “Reinforce” phase asks students to sort multiplication facts by strategy and explain why a particular strategy should be used to find the product. Students compare approaches and respond to prompts such as, “How would a different strategy work for this product?” This supports the evaluation of efficient strategies, flexible strategy selection, and the accurate use of multiplication facts.
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 grade 3, educator guidance helps students select increasingly efficient approaches for division. In the “Extend” phase of the “Division: Build Down and Build Up” strategy, students solve 360 ÷ 18 by discussing possible strategies with a partner. The educator listens for efficient strategies, records multiple methods on the board, and prompts students to interpret each strategy and explain why it works.
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
The “Multiplication: Use Tens” strategy includes a practice activity that addresses the conceptual emphasis of the TEKS by asking students to use known tens facts and turnaround facts to reason about unknown products and explain their thinking. The procedural emphasis is addressed during activities 3–7, where students repeatedly apply the “Use Tens” strategy to determine products, solve puzzles, and match multiplication expressions to solutions.
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
Students use concrete, pictorial, and abstract models with multiplication facts in the “Reinforce” phase of the “Multiplication: Use Doubling” strategy. Students record the twos, fours, and eights multiplication facts they know and then select a difficult fact to represent with concrete materials through illustration, pictorial representation, and abstract models. Students write, in words, how they used the strategy. At the end of the activity, students share and explain their representations.
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 the “Reinforce” phase of the “Multiplication: Use Doubling” strategy, students create a pictorial representation of a division word problem and connect that representation to matching division and related multiplication equations. The educator asks students to explain their representations and solutions to their peers, helping students create, connect, and explain representational models and abstract mathematical concepts.
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 the “Introduce” phase of the “Division: Use Doubling” strategy, students identify words in word problems that signal multiplication or division and add these terms to a classroom word wall. The activity strengthens students’ academic mathematical language by helping them connect vocabulary to problem situations and encouraging them to use the word wall as a reference when discussing multiplication and division concepts with their peers and educators.
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
Activities 4 and 5 of the “Extend” phase in the “Division: Build Down and Build Up” strategy provide educators with embedded guidance to scaffold and support students’ use of academic mathematical vocabulary during mathematical discourse. The educator prompts students to discuss strategies for finding quotients and uses sentence frames such as “I chose this strategy because…”, “I like your strategy, but I wonder…”, and “Did you think about…” to encourage meaningful mathematical conversations. These structured prompts help students explain and compare multiple methods for solution, interpret equations, describe why their strategies work, and justify their reasoning using precise mathematical language.
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
Activity 4 in the “Introduce” phase of the “Multiplication: Use a Rule” strategy asks students to generate other words for zero. The educator records students’ responses on the board and helps them create multiplication stories that involve zero. Students share real-world examples, such as “the number of empty rows of seats at a football game,” and then help create a wall chart that organizes situations involving a factor of zero. For example, students place “six empty nests” under __ × 0 and “no bags of five apples” under 0 × __. The educator encourages students to contribute a variety of examples and explain how each situation matches the corresponding multiplication expression, reinforcing precise mathematical vocabulary and reasoning.
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
The “Reinforce” phase of the “Subtraction: Use Doubles” strategy provides educators with embedded guidance to help students hear, refine, and use mathematical language with their peers. The educator uses sentence frames to support respectful mathematical discourse and encourage students to evaluate and build on one another’s strategies. For example, students use prompts such as “I like [student’s] strategy because...” and “I think [student’s] strategy would be easier if...” to explain their thinking, provide constructive feedback, and communicate using appropriate mathematical vocabulary.
5.4e
Materials include embedded guidance to anticipate a variety of student answers including exemplar responses to questions and tasks, including guidance to support and/or redirect inaccurate student responses.
Materials include embedded guidance to anticipate a variety of student answers including exemplar responses to questions and tasks, including guidance to support and/or redirect inaccurate student responses.
2 out of 2 points
Evaluation for 5.4e
Evaluation for 5.4e
Materials include embedded guidance to anticipate a variety of student answers including exemplar responses to questions and tasks, including guidance to support and/or redirect inaccurate student responses.
2 out of 2 points
The “Reinforce” phase for all strategies provides embedded guidance for educators to anticipate a variety of student responses by including exemplar answers for discussion tasks. In activity 13, students illustrate and act out a word problem with manipulatives, write the corresponding division equation and related multiplication fact, and explain how their representation matches the problem. Students then share their work with the class and describe their mathematical reasoning. The materials support educators by providing five sample student responses, including examples such as, “A group of 49 people attend a sports game. They sit in rows of seven. How many people sit in each row?”
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 activity 6 in the “Reinforce” phase of the “Division: Use Tens” strategy, students solve real-world word problems by selecting a problem, choosing a mathematical tool to model it, drawing a representation, and writing the corresponding division equation and related multiplication fact. Students collaborate with a peer when they select the same problem and then share their work with the class and explain how each representation models the situation. This sequence engages students in problem-solving, selecting appropriate tools, using multiple representations, communicating mathematical ideas, and making connections between multiplication and division, demonstrating how the process standards support grade-level content throughout instruction.
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 grade 3 materials identify a TEKS mathematical process standard for each phase of learning and explain how that standard links to the instructional pathway. For example, the “Prepare” phase of the “Multiplication: Use Doubling” strategy emphasizes Process Standard 1F by engaging students in analyzing relationships among multiple representations of multiplication facts as they match the appropriate cards during activity 2. This activity helps students connect mathematical ideas and build conceptual understanding through pattern recognition and discussion.
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
Each lesson phase includes “Check-In” questions that help educators monitor students’ mastery of the TEKS mathematical process standards. The questions prompt educators to determine whether students recognize relationships among operations or strategies and whether they can solve increasingly complex problems. For example, the materials ask, “Can the student solve one- and two-step word problems involving division with two- and three-digit numbers?” This question aligns with TEKS Process Standard 1B by requiring students to analyze the problem, develop a solution strategy, and apply mathematical reasoning to solve multi-step tasks.
Rubric Section 6
Productive Struggle
Materials support students in applying disciplinary practices to productive problem-solving, including explaining and revising their thinking.
Total
100% (19 out of 19 points)
Evaluation for 6.1a
Activity 1 in the “Prepare” phase of the “Multiplication: Use Doubling” strategy presents students with multiple representations of two groups of six. Students work with a partner to determine which images accurately represent 6 + 6 and discuss their reasoning. Students then represent another doubles addition fact in three different ways. Volunteers present and explain their representations to the class while classmates ask clarifying questions to deepen their understanding.
Activity 4 in the “Introduce” phase of the “Division: Use a Rule” strategy engages students in mathematical thinking by asking them to create representations of real-world problems. Across the division and related multiplication thinking strategies, students repeatedly decontextualize situations by representing problems symbolically and connecting them to mathematical relationships. Students discuss previously learned strategies, explain how those strategies support solving division problems, and share their reasoning with their classmates. Students then represent situations that model a division fact and write the related multiplication fact. The educator prompts students to connect multiplication and division by asking, “What multiplication fact can we use to solve this problem (9 divided by 1 = __)?”
Evaluation for 6.1b
The program builds a toolbox of strategies that helps students recognize multiple approaches for solving computation problems. Students gain experience in selecting strategies, explaining when each approach may be useful, and applying their understanding during the activities for all strategies. These activities encourage students to compare methods, justify their choices, and develop flexibility in solving mathematical problems.
For the “Division: Build Down and Build Up” strategy, students investigate multiple ways to calculate multiplication products by drawing pictures or writing equations to support their thinking. After identifying at least two methods for solution, students present and demonstrate different approaches to the class, explain how each method works, and justify the efficiency of their chosen strategy while comparing it with other valid methods for solution.
Evaluation for 6.1c
The lessons frequently organize students into pairs or small groups to model multiplication, use manipulatives, play mathematical games, investigate patterns, and solve problems together. For example, for the “Multiplication: Use a Rule” strategy, students work in pairs to write multiplication situations (e.g., “five baskets of three eggs”) and exchange their work with another pair to write the matching multiplication facts.
Activity 7 in the “Practice” phase of the “Multiplication: Build Down” strategy engages students in collaborative work as they record multiplication facts they find difficult to recall; describe the corresponding build-down strategy in words; and represent each fact using arrays, equal groups, number lines, and the “Build Down” strategy. Students share their representations with the class and explain their mathematical thinking, creating opportunities to solve problems, write about math, and discuss their ideas with their peers and the educator.
Evaluation for 6.2a
For the “Division: Use a Rule” strategy, students investigate whether a given rule applies in all cases, test their generalizations, and actively listen and ask questions using prompts such as “I agree/disagree because...” and “Does your rule work with...?” This allows students to evaluate and refine mathematical arguments by considering evidence and responding to peers’ reasoning.
The “Extend” phase of the “Multiplication: Build Down and Build Up” strategy equips educators with guidance to help students share and reflect on their problem-solving approaches. Students work collaboratively to identify and explain patterns; share and justify solution strategies with their groups; compare multiple methods for solution; discuss why a selected strategy is effective; and reflect on classmates’ approaches using discussion stems such as “I chose this strategy because…,” “I like your strategy, but I wonder…,” and “Did you think about…?” Educators record and compare students’ strategies, prompt students to explain why different methods work, and facilitate discussions that encourage students to explain their reasoning, construct mathematical arguments, and justify their thinking.
Evaluation for 6.2b
The “Introduce” phase of the “Division: Use Doubling” strategy prompts educators to ask questions that reveal students’ thinking and monitor students who repeatedly subtract groups. The materials direct educators to highlight known and unknown values to address misconceptions about the two equal-group structures in division.
The materials provide key questions and prompts that help educators respond to students’ thinking by probing their reasoning, asking students to explain the strategies they used, and extending their understanding. For example, check-in 23 states, “Look carefully at the numbers in each equation. What do you notice about multiplying by one?” and “What rule could you share with a friend to help multiply by one?” These prompts help educators elicit students’ reasoning and provide feedback based on students’ responses.
6.1 Student Self-Efficacy
6.1a
Materials provide opportunities for students to think mathematically, persevere through solving problems, and to make sense of mathematics.
Materials provide opportunities for students to think mathematically, persevere through solving problems, and to make sense of mathematics.
3 out of 3 points
Evaluation for 6.1a
Evaluation for 6.1a
Materials provide opportunities for students to think mathematically, persevere through solving problems, and to make sense of mathematics.
3 out of 3 points
Activity 4 in the “Introduce” phase of the “Division: Use a Rule” strategy engages students in mathematical thinking by asking them to create representations of real-world problems. Across the division and related multiplication thinking strategies, students repeatedly decontextualize situations by representing problems symbolically and connecting them to mathematical relationships. Students discuss previously learned strategies, explain how those strategies support solving division problems, and share their reasoning with their classmates. Students then represent situations that model a division fact and write the related multiplication fact. The educator prompts students to connect multiplication and division by asking, “What multiplication fact can we use to solve this problem (9 divided by 1 = __)?”
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
For the “Division: Build Down and Build Up” strategy, students investigate multiple ways to calculate multiplication products by drawing pictures or writing equations to support their thinking. After identifying at least two methods for solution, students present and demonstrate different approaches to the class, explain how each method works, and justify the efficiency of their chosen strategy while comparing it with other valid methods for solution.
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
Activity 7 in the “Practice” phase of the “Multiplication: Build Down” strategy engages students in collaborative work as they record multiplication facts they find difficult to recall; describe the corresponding build-down strategy in words; and represent each fact using arrays, equal groups, number lines, and the “Build Down” strategy. Students share their representations with the class and explain their mathematical thinking, creating opportunities to solve problems, write about math, and discuss their ideas with their peers and the educator.
6.2 Facilitating Productive Struggle
6.2a
Materials support educators in guiding students to share and reflect on their problem-solving approaches, including explanations, arguments, and justifications.
Materials support educators in guiding students to share and reflect on their problem-solving approaches, including explanations, arguments, and justifications.
6 out of 6 points
Evaluation for 6.2a
Evaluation for 6.2a
Materials support educators in guiding students to share and reflect on their problem-solving approaches, including explanations, arguments, and justifications.
6 out of 6 points
The “Extend” phase of the “Multiplication: Build Down and Build Up” strategy equips educators with guidance to help students share and reflect on their problem-solving approaches. Students work collaboratively to identify and explain patterns; share and justify solution strategies with their groups; compare multiple methods for solution; discuss why a selected strategy is effective; and reflect on classmates’ approaches using discussion stems such as “I chose this strategy because…,” “I like your strategy, but I wonder…,” and “Did you think about…?” Educators record and compare students’ strategies, prompt students to explain why different methods work, and facilitate discussions that encourage students to explain their reasoning, construct mathematical arguments, and justify their thinking.
6.2b
Materials include prompts and guidance to support educators in providing explanatory feedback based on student responses and anticipated misconceptions.
Materials include prompts and guidance to support educators in providing explanatory feedback based on student responses and anticipated misconceptions.
4 out of 4 points
Evaluation for 6.2b
Evaluation for 6.2b
Materials include prompts and guidance to support educators in providing explanatory feedback based on student responses and anticipated misconceptions.
4 out of 4 points
The materials provide key questions and prompts that help educators respond to students’ thinking by probing their reasoning, asking students to explain the strategies they used, and extending their understanding. For example, check-in 23 states, “Look carefully at the numbers in each equation. What do you notice about multiplying by one?” and “What rule could you share with a friend to help multiply by one?” These prompts help educators elicit students’ reasoning and provide feedback based on students’ responses.