Program Information
- ISBN
- 9781761191947
- 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, Addition & Subtraction
Supplemental Math (English) Grade 2
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 2 | 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 clarifies the concepts covered and demonstrates how the math content is interconnected and sequenced to reinforce skills through 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. Collectively, the pathways provide a comprehensive progression for learning addition and subtraction and show where the resource’s focus on computational fluency fits within that broader progression.
Evaluation for 1.1b
The materials suggest using contextual situations, concrete materials, and pictorial representations to help students make sense of the math presented.
The Teacher Book, video resources, and implementation support in the “Program Introduction” explain how educators introduce, reinforce, practice, and extend the program’s main fact strategies, including “Count On,” “Use Doubles,” and “Make Ten,” for addition and subtraction.
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.
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 understand and prepare to teach each concept or strategy before beginning instruction. For example, the “Addition: Count On” strategy contains a video that explains how to teach and model it.
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 addition and subtraction strategy outlines which pages, resources, and/or materials will be needed and who will use them. For example, the “Resource Overview” for the “Addition: Count On” strategy lists one paper cup and 10 counters for the group.
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” section in the “Use Doubles” strategy contains a QR code that links to a one-minute video explaining how to use doubles and counting on to help students learn addition facts in which the two addends are the same or nearly the same.
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. Collectively, the pathways provide a comprehensive progression for learning addition and subtraction and show where the resource’s focus on computational fluency fits within that broader 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, video resources, and implementation support in the “Program Introduction” explain how educators introduce, reinforce, practice, and extend the program’s main fact strategies, including “Count On,” “Use Doubles,” and “Make Ten,” for addition and subtraction.
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 understand and prepare to teach each concept or strategy before beginning instruction. For example, the “Addition: Count On” strategy contains a video that explains how to teach and model it.
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” section in the “Use Doubles” strategy contains a QR code that links to a one-minute video explaining how to use doubles and counting on to help students learn addition facts in which the two addends are the same or nearly the same.
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 allow students to show their understanding of the content through a variety of question types, the assessments include only numeric response item types.
Evaluation for 2.1e
Formative assessment check-ins guide educators in assessing student mastery and identifying instructional needs at each learning phase. Educators collect evidence from a wide range of activities that students complete such as hands-on tasks, written challenges, puzzles, games, and discussions about strategies.
The diagnostic “Progress Monitoring” checklist contains questions that assess skills from basic fact recall to strategy application, including representing facts and applying the “Count On” strategy. These questions align with TEKS-based addition and subtraction concepts and provide educators with evidence of students’ conceptual understanding, strategy use, and computational fluency.
Evaluation for 2.2a
The formative assessment check-ins contain targeted questioning guidance and intervention supports that help educators interpret student performance and monitor progress over time. Educators are provided with recording tools to track mastery.
The materials provide automatically generated assessment reports for individual students and classes based on the diagnostic fact fluency assessments as well as downloadable spreadsheets organized by fact fluency strategy. These reporting tools help educators interpret student performance data, identify instructional needs, and form targeted instructional groups. The “Solution Pathway and Error Analysis Support” resource provides examples of strategy-based solution pathways that students may use to reach the correct answer, allowing 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 their fact fluency growth. Students color in a fact table as they master facts, providing a visual representation of their progress and helping them recognize their developing fluency over time.
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 “Count On” strategy provide additional guidance to encourage student thinking. The materials contain questions that the educator can ask at different points in the activity and encourage students to look for patterns.
The materials contain prompts to help educators conduct frequent checks for understanding. For example, the margin notes for the “Count On” strategy provide support for students who have limited conceptual understanding of zero. Some activities contain highlighted questions, while others provide educator guidance for helping students use a strategy more efficiently.
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 allow students to show their understanding of the content through a variety of question types, 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 diagnostic “Progress Monitoring” checklist contains questions that assess skills from basic fact recall to strategy application, including representing facts and applying the “Count On” strategy. These questions align with TEKS-based addition and subtraction concepts and provide educators with evidence of students’ conceptual understanding, strategy use, and computational fluency.
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 diagnostic fact fluency assessments as well as downloadable spreadsheets organized by fact fluency strategy. These reporting tools help educators interpret student performance data, identify instructional needs, and form targeted instructional groups. The “Solution Pathway and Error Analysis Support” resource provides examples of strategy-based solution pathways that students may use to reach the correct answer, allowing 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 their fact fluency growth. Students color in a fact table as they master facts, providing a visual representation of their progress and helping them recognize their developing fluency over time.
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, the margin notes for the “Count On” strategy provide support for students who have limited conceptual understanding of zero. Some activities contain highlighted questions, while others provide educator guidance for helping students use a strategy more efficiently.
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 “Extend” phase for the “Addition: Count On” strategy includes multiple scaffolded supports to meet varying student needs. Students use concrete models (hundreds charts with counters), visual/virtual representations (a virtual chart beyond 100), and strategy supports (pattern recognition and number lines) in order to extend their understanding.
The additional support section of each check-in provides guidance about next steps for students who struggle. For example, the “Addition: Count On” strategy includes “Check-in 1” to help educators support students who are struggling to understand addition by engaging them in joining groups of five or fewer connecting cubes and describing what is happening using words such as joined, added, put together, connected, and stacked. Guidance indicates that educators should include the addition words on a word wall for students to reference as needed.
Evaluation for 3.1b
The visual representations in practice activities help students build academic vocabulary. Activity 6 for the “Addition: Count On” strategy uses a visual model to help students connect verbal representations with numbers in a fact family, reinforcing their 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 “Subtraction: Make Ten” strategy allow students to extend their learning of basic facts to greater whole number values. For example, activity 2 asks students to observe patterns in subtraction problems, which helps develop fluency with two-digit values. In activity 6, students solve one- and two-step problems within 1,000 fluently.
The materials provide extension activities in the “Extend” section of each strategy. For example, for the “Addition: Count On” strategy, toward the end of the lesson, students explore and apply the strategy to numbers 101 to 120. These enrichment tasks are designed to extend students’ learning beyond grade-level expectations.
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 help individual students. The materials contain digital assessments that students can complete online, but do not include digital accommodations for either whole-group or individual student needs.
The materials do not provide text-to-speech, content and language supports, or calculators that students can use during instruction or assessment. Educators must provide these accommodations outside of the materials in order to meet individual student needs.
Evaluation for 3.1e
In the “Reinforce” phase of the “Subtraction: Use Doubles” strategy, students use dot cards for visual support in activities 1 and 2 and engage with more abstract representations in activities 3 and 5, where they verbally describe their reasoning. Emergent bilingual (EB) learner supports such as sentence stems further help students express 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 on how to enable students to demonstrate their understanding through various formats, such as by giving written explanations and drawing models.
Evaluation for 3.2a
For each operation and strategy, the “Prepare” phases connect to and activate prior knowledge to ensure that students are prepared to learn a given strategy successfully. The introduction to each strategy lists key prior aspects of learning as prerequisite skills and suggests activities to support each one.
For the “Use Doubles” 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 compose and decompose numbers 6 to 9?”
Evaluation for 3.2b
Across the phases of learning, students engage in direct instruction through strategy cards, small-group tasks that support collaboration and application, writing real-world problems, and game-based practice to reinforce their 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. For example, the “Progress Monitoring” checklist includes an “Additional Support” section with suggested activities and scaffolds for intervention.
When used as interventions, the materials include opportunities for guided, independent, and collaborative practice. Intervention supports can be provided in whole-group, small-group, or individual settings. For the “Addition: Doubles” strategy, activity 2 contains guided practice in a whole-group structure. Activity 5 involves collaborative practice in a small-group setting, and activity 8 provides independent practice in an individual setting.
Evaluation for 3.2d
The materials contain “Enrich” and “Extend” activities that support various forms of engagement, in addition to guidance to help educators implement them effectively. For example, in the “Enrich” section of the “Addition: Doubles + 2” strategy, students use tactile linking cubes in pairs to represent totals. Then, students use number lines to represent facts. Finally, the class plays a game of bingo during which students practice doubling plus 2.
For the “Subtraction: Count On” strategy, the “Extend” activities provide educators with targeted questions and suggestions for support such as, “What other equations can you write to keep the pattern going?”
Evaluation for 3.2e
For the “Addition: Doubles” strategy, activities 2 and 4 of the “Reinforce” phase use the highlighted questions to help educators check for understanding by asking, “How do you know?” or “Why is…”
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 provide an “Additional Support” section for educators to use in addressing student misconceptions identified during the formative assessment.
Evaluation for 3.3a
The “Standards and Learning Progression” resource contains charts that show how the program provides opportunities for students to become proficient in using academic language. Student language proficiency can improve from one to four levels based on the strategies incorporated into the program. A student who is at the pre-production level when starting the “Addition: Count On” strategy (the first strategy) could progress to a beginner level by the end of that strategy and continue progressing throughout the remainder of the program.
The “Emergent Bilingual Learner Support” resources help educators group and scaffold instruction based on language needs. Key vocabulary and sentence stems help students use increasingly academic mathematical language during instruction.
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 educators with embedded guidance to help EB students develop their academic vocabulary, increase their comprehension, build background knowledge, and make cross-linguistic connections through oral discourse. The materials also include embedded guidance to help EB students develop their academic vocabulary, increase their comprehension, and build background knowledge through written discourse. In the “Addition: Doubles + 1” strategy, activity 7 asks students to collaborate to solve a multi-step word problem using the strategy, use available resources to support their thinking, and explain their solution orally to the class, reinforcing academic vocabulary and understanding through discussion.
The materials include explicit explanations of word origins, such as connecting the term double to its Latin roots duo and duplus as well as related vocabulary like duplex and duplicate. This helps students make connections between language structures, word meanings, and academic vocabulary development.
The materials do not contain embedded guidance for educators to support EB students in making cross-linguistic connections through written discourse. There is no evidence of instructional strategies, scaffolds, or opportunities for students to draw on their home languages in order to strengthen their comprehension, develop their academic vocabulary, or communicate their understanding in writing.
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 “Addition: Count On” strategy includes “Check-in 1” to help educators support students who are struggling to understand addition by engaging them in joining groups of five or fewer connecting cubes and describing what is happening using words such as joined, added, put together, connected, and stacked. Guidance indicates that educators should include the addition words 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 in the “Extend” section of each strategy. For example, for the “Addition: Count On” strategy, toward the end of the lesson, students explore and apply the strategy to numbers 101 to 120. These enrichment tasks are designed to extend students’ learning beyond grade-level expectations.
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 that students can use during instruction or assessment. Educators must provide these accommodations outside of the materials in order to meet 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 on how to enable students to demonstrate their understanding through various formats, such as by giving written explanations and drawing models.
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 “Use Doubles” 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 compose and decompose numbers 6 to 9?”
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
When used as interventions, the materials include opportunities for guided, independent, and collaborative practice. Intervention supports can be provided in whole-group, small-group, or individual settings. For the “Addition: Doubles” strategy, activity 2 contains guided practice in a whole-group structure. Activity 5 involves collaborative practice in a small-group setting, and activity 8 provides 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 “Subtraction: Count On” strategy, the “Extend” activities provide educators with targeted questions and suggestions for support such as, “What other equations can you write to keep the pattern going?”
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 provide 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
The “Emergent Bilingual Learner Support” resources help educators group and scaffold instruction based on language needs. Key vocabulary and sentence stems help students use increasingly academic mathematical language during instruction.
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
The materials include explicit explanations of word origins, such as connecting the term double to its Latin roots duo and duplus as well as related vocabulary like duplex and duplicate. This helps students make connections between language structures, word meanings, and academic vocabulary development.
The materials do not contain embedded guidance for educators to support EB students in making cross-linguistic connections through written discourse. There is no evidence of instructional strategies, scaffolds, or opportunities for students to draw on their home languages in order to strengthen their comprehension, develop their academic vocabulary, or communicate their understanding in writing.
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
In the activities for the “Addition: Count On” strategy, students work through a scaffolded progression of opportunities to practice addition. Activities start with single-digit operations and gradually expand to two-digit numbers, each increasing in quantity as well as in the complexity of strategies that use manipulatives, pictures, numbers, equations, hundreds charts, patterns, and number lines.
The check-ins embedded in the “Addition: Count On” strategy require students to show a depth of understanding aligned with grade 2 TEKS by counting forward to 20, subitizing quantities from one to nine, and explaining foundational number concepts such as the meaning of zero and the meaning of addition. These instructional assessments require students to move beyond procedural counting by demonstrating a conceptual understanding of number quantity, cardinality, and number relationships in the context of early addition.
Evaluation for 4.1b
Each strategy includes “Extend” phases for extension and enrichment. In the “Subtraction: Make Ten” strategy, students extend their learning of basic facts to greater whole number values. For example, activity 11 provides an opportunity to add two two-digit numbers (another grade 2 standard). Activity 13 has students solve one- and two-step problems within 1,000 fluently (a grade 3 standard).
In the “Subtraction: Count On” strategy, students start by physically moving counters to represent subtraction. They then progress to a pictorial representation of adding and subtracting by one on a number track. Next, students connect the concrete models and pictorial representations to standard algorithms.
Evaluation for 4.2a
The “Introduction” for the Addition: Doubles strategy shows coherence across concepts through activities 2 and 5 by connecting doubles facts, addition, and number decomposition. In activity 2, students relate real-world examples of equal groups to doubles facts and addition expressions. In activity 5, students use ten frames to analyze relationships among doubles facts and recognize that double 5 plus double 2 results in the same total as double 7. These activities teach patterns and relationships among numbers as well as connect composing and decomposing numbers to fact fluency in addition.
The “Addition: Doubles” strategy requires students to use ten frames in order to visually see how to calculate when adding doubles. Educator prompts (such as, “What do you notice about the counters on these ten frames? What doubles can you see?”) enable them to examine how understanding doubles will help students use other strategies such as “Doubles + 1” and “Doubles + 2.”
Evaluation for 4.2b
The “Prerequisite Skills” section in the overview of the “Addition: Count On” strategy demonstrates coherence vertically across grade bands by connecting grade 2 learning to foundational concepts from grade K and grade 1. The materials identify counting forward to 20, subitizing quantities from one to nine, understanding zero, and understanding addition as prerequisite skills for applying the “Count On” strategy. The table listing the prerequisite skills helps educators identify specific activities that review and strengthen each concept, connecting prior learning to grade 2 addition strategies and supporting a coherent progression of mathematical understanding across grade levels.
In the “Addition: Count On” strategy, the “Extend” phase makes an explicit connection to the “Count On” strategy as well as student investigations into patterns for adding 10 or 20 to two-digit numbers. Students use the “Support 13” hundreds chart as a bridge pictorial and a hands-on strategy for making connections with place value and algorithms in higher grades.
Evaluation for 4.2c
The “Prepare” phase for each strategy reviews learning from an earlier grade or earlier learning in the current grade, depending on the strategy. This helps students connect concepts (e.g., counting or place value), procedures, strategies, and/or physical and visual representations (e.g., counters, ten frames, or number lines).
The materials demonstrate coherence across lessons through the structured progression of the “Prepare,” “Introduce,” “Reinforce,” “Practice,” and “Extend” phases. Students build on previously learned concepts and representations during the “Prepare” phase; develop an understanding of new strategies through concrete and pictorial models during the “Introduce,” “Reinforce,” and “Practice” phases; and finally apply the strategies to greater whole numbers during the “Extend” phase. This progression connects prior knowledge to current learning while preparing students for future mathematical concepts and procedures.
Evaluation for 4.3a
The materials provide opportunities to practice spaced retrieval with previously learned skills and concepts across the learning pathways. For example, for the Addition: Doubles strategy in the “Prepare” phase, students review composing and decomposing numbers six to nine. Students then repeat the activity in reverse order to practice composing a number from six to nine. Eventually, students split doubles into more manageable parts.
In the “Addition: Doubles + 1” strategy, the “Introduce” phase provides opportunities to practice spaced retrieval with previously learned skills and concepts across the learning pathways. In activities 1–6, students repeatedly retrieve doubles facts learned through the “Use Doubles” strategy and apply them to determine “Doubles + 1” facts. Students use known doubles facts to represent quantities, solve addition facts, model relationships with cubes and ten frames, and identify unknown facts. These activities require students to recall and apply previously learned doubles concepts and procedures while developing the “Doubles + 1” strategy.
Evaluation for 4.3b
In the “Addition: Make Ten” strategy “Extend” phase, activity 11 organizes students into small groups and presents a two-digit plus two-digit problem. Students are prompted to investigate the different ways they have learned to calculate the total (such as make ten or place value thinking) in combination with the “Make Ten” strategy. Students are encouraged to use resources to support their thinking. When each group has identified at least one strategy, different students present and demonstrate their methods to the class.
For all strategies in the “Practice” phase, students have opportunities to engage in interleaved practices. Students practice the full range of addition facts while selecting and applying previously learned strategies, including “Count On,” “Doubles,” “Doubles + 1,” and “Make Ten.” Rather than focusing on a single strategy, this section requires students to analyze expressions, determine efficient methods for solving problems, and apply concepts and procedures based on multiple strategies.
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
The check-ins embedded in the “Addition: Count On” strategy require students to show a depth of understanding aligned with grade 2 TEKS by counting forward to 20, subitizing quantities from one to nine, and explaining foundational number concepts such as the meaning of zero and the meaning of addition. These instructional assessments require students to move beyond procedural counting by demonstrating a conceptual understanding of number quantity, cardinality, and number relationships in the context of early addition.
4.1b
Questions and tasks, including enrichment and extension materials, increase in rigor and complexity, leading to grade-level and above grade-level proficiency in the mathematics TEKS.
Questions and tasks, including enrichment and extension materials, increase in rigor and complexity, leading to grade-level and above grade-level proficiency in the mathematics TEKS.
4 out of 4 points
Evaluation for 4.1b
Evaluation for 4.1b
Questions and tasks, including enrichment and extension materials, increase in rigor and complexity, leading to grade-level and above grade-level proficiency in the mathematics TEKS.
4 out of 4 points
In the “Subtraction: Count On” strategy, students start by physically moving counters to represent subtraction. They then progress to a pictorial representation of adding and subtracting by one on a number track. Next, students connect the concrete models and pictorial representations to standard algorithms.
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 “Addition: Doubles” strategy requires students to use ten frames in order to visually see how to calculate when adding doubles. Educator prompts (such as, “What do you notice about the counters on these ten frames? What doubles can you see?”) enable them to examine how understanding doubles will help students use other strategies such as “Doubles + 1” and “Doubles + 2.”
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
In the “Addition: Count On” strategy, the “Extend” phase makes an explicit connection to the “Count On” strategy as well as student investigations into patterns for adding 10 or 20 to two-digit numbers. Students use the “Support 13” hundreds chart as a bridge pictorial and a hands-on strategy for making connections with place value and algorithms in higher grades.
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 demonstrate coherence across lessons through the structured progression of the “Prepare,” “Introduce,” “Reinforce,” “Practice,” and “Extend” phases. Students build on previously learned concepts and representations during the “Prepare” phase; develop an understanding of new strategies through concrete and pictorial models during the “Introduce,” “Reinforce,” and “Practice” phases; and finally apply the strategies to greater whole numbers during the “Extend” phase. This progression connects prior knowledge to current learning while preparing students for future mathematical concepts and procedures.
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 the “Addition: Doubles + 1” strategy, the “Introduce” phase provides opportunities to practice spaced retrieval with previously learned skills and concepts across the learning pathways. In activities 1–6, students repeatedly retrieve doubles facts learned through the “Use Doubles” strategy and apply them to determine “Doubles + 1” facts. Students use known doubles facts to represent quantities, solve addition facts, model relationships with cubes and ten frames, and identify unknown facts. These activities require students to recall and apply previously learned doubles concepts and procedures while developing the “Doubles + 1” strategy.
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
For all strategies in the “Practice” phase, students have opportunities to engage in interleaved practices. Students practice the full range of addition facts while selecting and applying previously learned strategies, including “Count On,” “Doubles,” “Doubles + 1,” and “Make Ten.” Rather than focusing on a single strategy, this section requires students to analyze expressions, determine efficient methods for solving problems, and apply concepts and procedures based on multiple strategies.
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 “Make Ten: Subtraction” strategy, students explore connections among multiple representations such as egg cartons and connect cubes, counters, and ten frames. Questions such as, “How could you figure out the number of counters that are covered?” prompt students to analyze the relationships within the models. Students engage in partner discussions to explain how they would determine a missing part, deepening their understanding of mathematical concepts.
For the “Addition: Doubles + 1” strategy in the “Reinforce” phase, activity 4 asks students to join connecting cubes to represent the doubles facts for one to nine. Students join one more cube to each stack to represent the “Doubles + 1” facts and are then prompted to compare representations and talk about the patterns they see.
Evaluation for 5.1b
In the “Prepare” phase of the “Addition: Count On” strategy, students use egg cartons and cubes to develop the idea of zero. Students model a story the educator reads using the cubes to eventually represent zero eggs in the carton.
In the “Extend” phase of the “Addition: Count On” strategy, students create pictorial representations related to each strategy. In activity 11, students sketch on number lines and are prompted to verbalize their thinking strategy. For example, “I started at 98 and I jumped 10 to 108, then another 10 to 118. Then I added one more: 98 plus 21 is 119.”
Evaluation for 5.1c
In the “Extend” phase of the “Addition: Count On” strategy, activities 4–6 engage students to apply their understanding of the “Count On” strategy to new situations involving two-digit numbers. Students use hundreds charts and equation patterns to add 10 and 20 to numbers within 120 as well as generate additional equations that follow the pattern.
In the “Extend” phase of the “Subtraction: Count On” strategy, students use a hundreds chart to solve subtraction expressions with larger numbers, including numbers within 100 and examples that bridge 100. Students determine whether it is more efficient to use “Count Back” or “Count On,” such as “Count Back for 119–22” or “Count On for 106–85.”
Evaluation for 5.2a
In the practice activity of the “Addition: Doubles + 2” strategy, students work with a partner to develop fluency in the relevant set of facts. Students play a mix-and-match game using dominoes and addition cards. Students match both items and then find the sum. This builds automaticity and fluency with a pictorial representation, an abstract representation, and the solution.
For the activities in the “Practice” phase of the Addition: Doubles + 2 strategy, students play partner and small-group games to develop automaticity and fluency in the “Doubles + 2” strategy. Students match pictorial representations, abstract equations, and solutions (e.g., a domino showing 7 + 9, the equation 7 + 9, and the total 16), while additional games require students to repeatedly verbalize and apply “Doubles + 2” facts. These repeated opportunities support automatic recall of addition facts and build the fluency needed to complete grade-level mathematical tasks.
Evaluation for 5.2b
In the “Extend” phase of the “Addition: Make Ten” strategy, students work on an open number line. This activity is more efficient than using base 10 materials or counters. Both tools support accuracy as they are used for reference (e.g., filling a ten frame or reaching a benchmark value on a number line). This activity involves a variety of efficient and flexible strategies for using open number lines near 100.
Students come up with different ways to count counters while using the “Addition: Count On” strategy in the “Prepare” phase. Students encourage each other to count the same group of counters in other ways, moving the counters as they count. As the students become more fluent, they are prompted to say the greatest number of counters they can see, without counting, and then count on from that number to figure out the total number of counters. When the students become fluent, the count can be extended to 15 and then to 20.
Evaluation for 5.2c
As students learn various strategies and representations, they are encouraged to select the strategy that is most efficient for them when solving a mixed set of problems. In the “Extend” phase of the “Subtraction: Use Doubles” strategy, suggested questions for educators to ask support the evaluative process. For example, educators may ask, “Who used a strategy like (Vishaya’s)? Do you think (Jacob’s) strategy is easier to use than (Morgan’s) strategy? Why?”
In the “Extend” phase of the “Subtraction: Count On” strategy, students use number lines to compare solving 15 – 2 through “Count Back” and solving 15 – 13 through “Thinking Addition” and “Count On.” The educator prompts students to explain where the difference is shown on each number line and helps students consider when “Count Back” is more efficient and when “Thinking Addition” is more efficient.
Evaluation for 5.2d
For all strategies in the “Reinforce” phase, a domino is used to represent 7 + 8. The educator asks, “What is a quick way to figure out the total number of dots? Would you use the Count On strategy?” This involves considering all strategies learned and determining which one would be the most efficient to solve the problem.
The activities provide guidance for selecting increasingly efficient strategies by prompting students to compare doubles facts and “Doubles + 2” facts on a number track for the “Addition: Doubles + 2” strategy. Students are encouraged to recognize that finding the double of the number between the addends is more efficient than using “Count On,” and students test whether this relationship holds with other numbers.
Evaluation for 5.3a
In the “Practice” phase of all strategies, students think conceptually when they connect facts with possible strategies. Students think more procedurally in a follow-up activity when they work to complete fact family diagrams.
In the “Introduce” phase of the “Addition: Make Ten” strategy, students use concrete and pictorial representations to recognize that different models can show the same total, supporting conceptual understanding of how numbers can be decomposed and recomposed to make ten. In the “Reinforce” phase, students connect equivalent equations and use one equation to help solve another, shifting toward a procedural emphasis as they apply the “Make Ten” strategy both accurately and efficiently.
Evaluation for 5.3b
The “Addition: Doubles” strategy includes concrete and pictorial representations in the “Introduce” and “Reinforce” phases. The “Reinforce” and “Practice” phases focus on pictorial and abstract representations, while the “Extend” phase uses a combination of all three. Students move from using paint and beads to ten frames and dominoes to equations.
The activities in the “Introduce” phase of the “Addition: Doubles + 1” strategy provide opportunities for students to use concrete models such as connecting cubes, counters, and double ten frames to model “Doubles + 1” facts. Students use pictorial representations such as drawings, dot patterns, or ten frame representations to visualize the strategy. The activities help students connect these representations to abstract models as they write and discuss equations like 4 + 4 = 8 and 4 + 5 = 9 and use known doubles facts to determine unknown sums.
Evaluation for 5.3c
Lessons are designed using a concrete-to-representational-to-abstract approach in which students first use hands-on manipulatives like base 10 blocks, counters, ten frames, and place value materials to model situations involving addition and subtraction. Students then transition to representational models (including drawings and number lines) to visualize their thinking and demonstrate relationships between numbers. Finally, students connect these models to abstract representations by writing equations, using mathematical symbols, and applying efficient computational strategies.
In the activities of the “Reinforce” phase of the “Addition: Doubles + 2” strategy, students build cube trains and write matching “Doubles + 2” equations. Students use cube models to identify patterns and connect them to symbolic expressions. Throughout the sequence, the educator prompts students to describe patterns, explain their thinking, and justify how the models represent the corresponding equations.
Evaluation for 5.4a
In activity 4 of the “Reinforce” phase of the “Subtraction: Use Doubles” strategy, students build academic mathematical language through visual representations and mathematical discourse. Students use pictures of dominoes to write turnaround facts, record both related equations, and justify their thinking by sharing their responses aloud. For example, a student might explain, “Double six is 12. The turnaround fact is the same,” reinforcing the relationship between doubles facts and turnaround facts while using precise mathematical vocabulary.
The materials teach mathematical vocabulary and encourage students to use formal mathematical language as they learn terms such as addends, sum, commutative property, and turnarounds in relation to the “Addition: Count On” strategy. The educator notes define key vocabulary by explaining that “the parts…being joined together are called addends” and “the total they form is called the sum.” During the check-in, the materials direct educators to create a mathematical word wall and reinforce terms such as joined, added, put together, connected, and stacked to support students’ use of mathematical language during instruction.
Evaluation for 5.4b
In activity 2 of the “Extend” phase in the “Subtraction: Use Doubles” strategy, educator-directed questions support and extend students’ use of academic mathematical vocabulary. The educator prompts students to explain their thinking using terms such as double and half, encouraging them to accurately apply this vocabulary as they solve problems and discuss strategies with classmates.
The lesson in the “Extend” phase of the “Addition: Use Doubles” strategy includes guidance for educators to scaffold and support students’ use of academic mathematical vocabulary as they communicate with peers. During activity 8, students write five IN numbers and five corresponding OUT numbers between 25 and 60 on the “Input/Output Machine.” The educator uses guiding questions to help students describe the mathematical rule that changes each IN number into its corresponding OUT number, reinforcing mathematical vocabulary throughout the activity. Students then exchange their input/output machines with a partner, calculate each other’s OUT numbers, explain their reasoning, and check one another’s work, providing additional opportunities to use mathematical language in context.
Evaluation for 5.4c
Embedded collaborative structures require students to communicate mathematically with their peers for the “Addition: Count On” strategy. For example, students work with partners on activities where they explain and discuss efficient strategies, such as using “the number tracks to help debate the efficiency of each strategy.”
For the “Addition: Use Doubles” strategy, students use counters and a T-chart to sort numbers into odd and even categories. As they complete the activity, they identify patterns, explain why each number belongs in its category, and use the terms odd and even to justify their classifications. The educator facilitates discussion by prompting students to compare patterns and describe their reasoning, encouraging them to communicate using precise mathematical vocabulary.
Evaluation for 5.4d
In the “Prepare” phase of the “Subtraction: Count On” strategy, students participate in a whole-class activity in which they read addition facts aloud while their classmates identify and state the corresponding turnaround facts. The educator directs each standing student to read an equation (including the total) and then invites another student to share the matching turnaround fact. This structure encourages students to listen carefully, make mathematical connections, and communicate using appropriate mathematical language.
In the “Extend” phase of the “Doubles + 2” strategy, activity 6 prompts students to determine totals, explain how they found each answer, discuss number patterns with a partner, and then share their observations with the class. Questions such as “Tell me how you know each total,” “Turn to the student beside you and talk about the patterns you see,” and “How do you know the totals?” encourage students to explain and justify their reasoning while listening to and building on the ideas of others.
Evaluation for 5.4e
In the “Introduce” phase of the “Subtraction: Count On” strategy, students model “six take away one” with counting cubes in order to build a conceptual understanding of subtraction. Educators address inaccurate or incomplete responses by introducing the term subtraction, if needed, and asking, “How is subtraction different from addition?” This helps educators identify misconceptions, connect students’ prior knowledge to the new concept, and redirect their thinking through purposeful questioning and mathematical discussion.
The educator uses example responses such as “Six and four make ten,” and prompts students to explain how they know that two quantities make ten, encouraging them to justify their reasoning when using the “Subtraction: Make Ten” strategy in the “Prepare” phase. The materials help educators identify and address misconceptions by advising, “Watch for students who have difficulty identifying the numbers. They may need more subitizing practice. Also, notice whether students can easily identify the greater of the two numbers.” This guidance enables educators to recognize misconceptions, provide targeted instructional support, and redirect inaccurate thinking while reinforcing students’ mathematical reasoning and vocabulary.
Evaluation for 5.5a
In the “Introduce” phase of the “Subtraction: Count On” strategy, students solve subtraction problems that reflect everyday situations. For example, students solve the problem, “Six people are in a store. Two walk out. How many people are in the store now?” The educator uses this real-world context to help students model subtraction and connect math to everyday experiences.
The “Standards and Learning Progression” resource integrates the TEKS mathematical process standards throughout each phase of instruction. During the “Prepare” phase, students analyze relationships and connect mathematical ideas to build conceptual understanding. In the “Introduce” phase, they select and use appropriate tools, representations, and strategies to solve problems. During the “Reinforce” and “Practice” phases, students communicate their mathematical reasoning and solutions using multiple representations and mathematical language. In the “Extend” phase, students apply their learning to new problem situations, explain and justify their reasoning, and use precise mathematical vocabulary. Together, these instructional phases embed the TEKS process standards within grade-level content for addition and subtraction in order to support the development of conceptual understanding, problem-solving, and mathematical communication.
Evaluation for 5.5b
The “Standards and Learning Progression” resource explicitly identifies the mathematical process standard emphasized during the “Prepare,” “Introduce,” “Reinforce,” “Practice,” and “Extend” phases. The materials clarify how each phase develops a different aspect of mathematical thinking, showing how students build conceptual understanding, apply problem-solving strategies, communicate mathematical reasoning, and extend their learning across the broader instructional pathway.
The grade 2 materials identify a TEKS mathematical process standard for each phase of learning and explain how that standard connects to the instructional pathway. For example, the “Prepare” phase of the “Addition: Use Doubles” strategy emphasizes Process Standard 1F by engaging students in connecting the concept of doubling to their prior understanding of odd and even numbers while analyzing the relationship between a base number and its double or near double.
Evaluation for 5.5c
The “Standards and Learning Progression” resource supports educators by explicitly connecting individual lesson activities to the TEKS mathematical process standards and explaining how each activity reinforces the targeted process skills. This guidance helps educators recognize how students build conceptual understanding and apply the process standards across the learning pathway.
Each lesson phase includes “Check-In” questions that help educators monitor students’ understanding of the TEKS mathematical process standards. The questions prompt educators to determine whether students recognize relationships among operations or strategies and explain their mathematical thinking. For example, the materials ask questions such as, “Can the student explain their thinking strategy?” These embedded prompts encourage students to communicate their reasoning, make mathematical connections, and demonstrate the process skills identified in the TEKS.
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
For the “Addition: Doubles + 1” strategy in the “Reinforce” phase, activity 4 asks students to join connecting cubes to represent the doubles facts for one to nine. Students join one more cube to each stack to represent the “Doubles + 1” facts and are then prompted to compare representations and talk about the patterns they see.
5.1b
Questions and tasks provide opportunities for students to create concrete models and pictorial representations to represent mathematical situations.
Questions and tasks provide opportunities for students to create concrete models and pictorial representations to represent mathematical situations.
2 out of 2 points
Evaluation for 5.1b
Evaluation for 5.1b
Questions and tasks provide opportunities for students to create concrete models and pictorial representations to represent mathematical situations.
2 out of 2 points
In the “Extend” phase of the “Addition: Count On” strategy, students create pictorial representations related to each strategy. In activity 11, students sketch on number lines and are prompted to verbalize their thinking strategy. For example, “I started at 98 and I jumped 10 to 108, then another 10 to 118. Then I added one more: 98 plus 21 is 119.”
5.1c
Questions and tasks provide opportunities for students to apply conceptual understanding to new problem situations and contexts.
Questions and tasks provide opportunities for students to apply conceptual understanding to new problem situations and contexts.
1 out of 1 points
Evaluation for 5.1c
Evaluation for 5.1c
Questions and tasks provide opportunities for students to apply conceptual understanding to new problem situations and contexts.
1 out of 1 points
In the “Extend” phase of the “Subtraction: Count On” strategy, students use a hundreds chart to solve subtraction expressions with larger numbers, including numbers within 100 and examples that bridge 100. Students determine whether it is more efficient to use “Count Back” or “Count On,” such as “Count Back for 119–22” or “Count On for 106–85.”
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
For the activities in the “Practice” phase of the Addition: Doubles + 2 strategy, students play partner and small-group games to develop automaticity and fluency in the “Doubles + 2” strategy. Students match pictorial representations, abstract equations, and solutions (e.g., a domino showing 7 + 9, the equation 7 + 9, and the total 16), while additional games require students to repeatedly verbalize and apply “Doubles + 2” facts. These repeated opportunities support automatic recall of addition facts and build the fluency needed to complete grade-level mathematical tasks.
5.2b
Materials provide opportunities for students to practice the application of efficient, flexible, and accurate mathematical procedures throughout learning pathways.
Materials provide opportunities for students to practice the application of efficient, flexible, and accurate mathematical procedures throughout learning pathways.
3 out of 3 points
Evaluation for 5.2b
Evaluation for 5.2b
Materials provide opportunities for students to practice the application of efficient, flexible, and accurate mathematical procedures throughout learning pathways.
3 out of 3 points
Students come up with different ways to count counters while using the “Addition: Count On” strategy in the “Prepare” phase. Students encourage each other to count the same group of counters in other ways, moving the counters as they count. As the students become more fluent, they are prompted to say the greatest number of counters they can see, without counting, and then count on from that number to figure out the total number of counters. When the students become fluent, the count can be extended to 15 and then to 20.
5.2c
Materials provide opportunities for students to evaluate mathematical representations, models, strategies, and solutions for efficiency, flexibility, and accuracy throughout learning pathways.
Materials provide opportunities for students to evaluate mathematical representations, models, strategies, and solutions for efficiency, flexibility, and accuracy throughout learning pathways.
3 out of 3 points
Evaluation for 5.2c
Evaluation for 5.2c
Materials provide opportunities for students to evaluate mathematical representations, models, strategies, and solutions for efficiency, flexibility, and accuracy throughout learning pathways.
3 out of 3 points
In the “Extend” phase of the “Subtraction: Count On” strategy, students use number lines to compare solving 15 – 2 through “Count Back” and solving 15 – 13 through “Thinking Addition” and “Count On.” The educator prompts students to explain where the difference is shown on each number line and helps students consider when “Count Back” is more efficient and when “Thinking Addition” is more efficient.
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
The activities provide guidance for selecting increasingly efficient strategies by prompting students to compare doubles facts and “Doubles + 2” facts on a number track for the “Addition: Doubles + 2” strategy. Students are encouraged to recognize that finding the double of the number between the addends is more efficient than using “Count On,” and students test whether this relationship holds with other numbers.
5.3 Balance of Conceptual Understanding and Procedural Fluency
5.3a
Materials explicitly state how the conceptual and procedural emphasis of the TEKS are addressed.
Materials explicitly state how the conceptual and procedural emphasis of the TEKS are addressed.
2 out of 2 points
Evaluation for 5.3a
Evaluation for 5.3a
Materials explicitly state how the conceptual and procedural emphasis of the TEKS are addressed.
2 out of 2 points
In the “Introduce” phase of the “Addition: Make Ten” strategy, students use concrete and pictorial representations to recognize that different models can show the same total, supporting conceptual understanding of how numbers can be decomposed and recomposed to make ten. In the “Reinforce” phase, students connect equivalent equations and use one equation to help solve another, shifting toward a procedural emphasis as they apply the “Make Ten” strategy both accurately and efficiently.
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
The activities in the “Introduce” phase of the “Addition: Doubles + 1” strategy provide opportunities for students to use concrete models such as connecting cubes, counters, and double ten frames to model “Doubles + 1” facts. Students use pictorial representations such as drawings, dot patterns, or ten frame representations to visualize the strategy. The activities help students connect these representations to abstract models as they write and discuss equations like 4 + 4 = 8 and 4 + 5 = 9 and use known doubles facts to determine unknown sums.
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 activities of the “Reinforce” phase of the “Addition: Doubles + 2” strategy, students build cube trains and write matching “Doubles + 2” equations. Students use cube models to identify patterns and connect them to symbolic expressions. Throughout the sequence, the educator prompts students to describe patterns, explain their thinking, and justify how the models represent the corresponding equations.
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
The materials teach mathematical vocabulary and encourage students to use formal mathematical language as they learn terms such as addends, sum, commutative property, and turnarounds in relation to the “Addition: Count On” strategy. The educator notes define key vocabulary by explaining that “the parts…being joined together are called addends” and “the total they form is called the sum.” During the check-in, the materials direct educators to create a mathematical word wall and reinforce terms such as joined, added, put together, connected, and stacked to support students’ use of mathematical language during instruction.
5.4b
Materials include embedded educator guidance to scaffold, support, and extend students’ use of academic mathematical vocabulary in context when communicating with peers and educators.
Materials include embedded educator guidance to scaffold, support, and extend students’ use of academic mathematical vocabulary in context when communicating with peers and educators.
2 out of 2 points
Evaluation for 5.4b
Evaluation for 5.4b
Materials include embedded educator guidance to scaffold, support, and extend students’ use of academic mathematical vocabulary in context when communicating with peers and educators.
2 out of 2 points
The lesson in the “Extend” phase of the “Addition: Use Doubles” strategy includes guidance for educators to scaffold and support students’ use of academic mathematical vocabulary as they communicate with peers. During activity 8, students write five IN numbers and five corresponding OUT numbers between 25 and 60 on the “Input/Output Machine.” The educator uses guiding questions to help students describe the mathematical rule that changes each IN number into its corresponding OUT number, reinforcing mathematical vocabulary throughout the activity. Students then exchange their input/output machines with a partner, calculate each other’s OUT numbers, explain their reasoning, and check one another’s work, providing additional opportunities to use mathematical language in context.
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
For the “Addition: Use Doubles” strategy, students use counters and a T-chart to sort numbers into odd and even categories. As they complete the activity, they identify patterns, explain why each number belongs in its category, and use the terms odd and even to justify their classifications. The educator facilitates discussion by prompting students to compare patterns and describe their reasoning, encouraging them to communicate using precise mathematical vocabulary.
5.4d
Materials include embedded guidance to facilitate mathematical conversations allowing students to hear, refine, and use math language with peers.
Materials include embedded guidance to facilitate mathematical conversations allowing students to hear, refine, and use math language with peers.
2 out of 2 points
Evaluation for 5.4d
Evaluation for 5.4d
Materials include embedded guidance to facilitate mathematical conversations allowing students to hear, refine, and use math language with peers.
2 out of 2 points
In the “Extend” phase of the “Doubles + 2” strategy, activity 6 prompts students to determine totals, explain how they found each answer, discuss number patterns with a partner, and then share their observations with the class. Questions such as “Tell me how you know each total,” “Turn to the student beside you and talk about the patterns you see,” and “How do you know the totals?” encourage students to explain and justify their reasoning while listening to and building on the ideas of others.
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 educator uses example responses such as “Six and four make ten,” and prompts students to explain how they know that two quantities make ten, encouraging them to justify their reasoning when using the “Subtraction: Make Ten” strategy in the “Prepare” phase. The materials help educators identify and address misconceptions by advising, “Watch for students who have difficulty identifying the numbers. They may need more subitizing practice. Also, notice whether students can easily identify the greater of the two numbers.” This guidance enables educators to recognize misconceptions, provide targeted instructional support, and redirect inaccurate thinking while reinforcing students’ mathematical reasoning and vocabulary.
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
The “Standards and Learning Progression” resource integrates the TEKS mathematical process standards throughout each phase of instruction. During the “Prepare” phase, students analyze relationships and connect mathematical ideas to build conceptual understanding. In the “Introduce” phase, they select and use appropriate tools, representations, and strategies to solve problems. During the “Reinforce” and “Practice” phases, students communicate their mathematical reasoning and solutions using multiple representations and mathematical language. In the “Extend” phase, students apply their learning to new problem situations, explain and justify their reasoning, and use precise mathematical vocabulary. Together, these instructional phases embed the TEKS process standards within grade-level content for addition and subtraction in order to support the development of conceptual understanding, problem-solving, and mathematical communication.
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 2 materials identify a TEKS mathematical process standard for each phase of learning and explain how that standard connects to the instructional pathway. For example, the “Prepare” phase of the “Addition: Use Doubles” strategy emphasizes Process Standard 1F by engaging students in connecting the concept of doubling to their prior understanding of odd and even numbers while analyzing the relationship between a base number and its double or near double.
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’ understanding of the TEKS mathematical process standards. The questions prompt educators to determine whether students recognize relationships among operations or strategies and explain their mathematical thinking. For example, the materials ask questions such as, “Can the student explain their thinking strategy?” These embedded prompts encourage students to communicate their reasoning, make mathematical connections, and demonstrate the process skills identified in the TEKS.
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
Grade 2 materials provide opportunities for students to make sense of subtraction by using doubles facts to solve related subtraction problems. Students analyze number relationships, apply a known strategy, and determine whether the number relationships are true. These tasks promote perseverance in problem-solving by requiring students to reason through the relationships and apply efficient strategies rather than simply recall an answer.
Students think mathematically in the “Extend” phase of the “Double Plus” strategy by solving subtraction word problems with the think-addition strategy and representing their thinking on a number line. They persevere as they compare multiple solution strategies, ask clarifying questions, and challenge reasoning they believe is incorrect. They make sense of mathematics by connecting addition and subtraction, explaining their reasoning, and discussing why different strategies effectively solve real-world problems.
Evaluation for 6.1b
In the “Subtraction: Count On” strategy, students discuss whether it is easier or not to start with the greater number and count on, and students verbalize their reasoning while solving addition and subtraction problems. Educators are prompted to ask questions such as “How do you know?”, “What do you notice?”, and “Explain your thinking strategy.”
Grade 2 materials help students explain and justify strategies for solving subtraction problems using doubles. Students make sense of the relationship between addition doubles facts and related subtraction facts, then explain how the relevant strategy helps them solve problems. The activities show that students can solve problems in multiple ways by connecting subtraction to known addition relationships and using mathematical reasoning to justify their methods.
Evaluation for 6.1c
Students engage in collaborative mathematical tasks and work in pairs or small groups to solve problems using number tracks, dominoes, hundreds charts, ten frames, spinners, and game boards. For example, for the “Addition: Make Ten” strategy, students work in pairs to play a mix-and-match game by matching related “Make Ten” representations. For each correct match, students verbalize the addition.
In the “Reinforce” phase of the “Subtraction: Use Doubles” strategy, activity 6 engages students in mathematical writing as they reflect on facts they find challenging to remember. Students discuss and compare the strategies they use to solve problems through prompts such as, “Who used a strategy like [student 1]? Do you think [student 2’s] strategy is easier to use than [student 3’s]? Why?” Students ask clarifying questions and challenge classmates’ reasoning when they believe an idea is incorrect. The lesson repeats this process with three additional word problems, giving students multiple opportunities to explain, evaluate, and refine their problem-solving strategies.
Evaluation for 6.2a
In the “Reinforce” phase of the “Doubles + 1” strategy, the lesson prompts educators to have students explain how they solved problems and describe their thinking. Students write all the “Doubles + 1” facts they know, use connecting cubes to act out the addition, and write the matching turnaround fact. Educators then invite students to share the facts they chose and describe how they added. The materials include an exemplar example for educator support.
In the “Reinforce” phase of the “Subtraction: Count On” strategy, students reflect on their problem-solving approaches. In activity 7, educators help students clarify their thinking about turnaround facts by asking targeted questions. Students use number tracks to represent facts (such as 5 + 1 and 1 + 5) and compare the efficiency of different strategies. The educator asks, “What do you find easier to do: start with the greater number and count on one or start with one and count on the greater number?” Students explain and justify their reasoning. The lesson repeats this process with additional “Count On” strategy cards (such as 8 + 2 and 9 + 1) to reinforce strategic thinking and mathematical discussion.
Evaluation for 6.2b
In the “Reinforce” phase of the “Addition: Make Ten” strategy, students use ten frames and counters to solve addition problems. Students represent the same total in different ways and explain how their arrangements show the solution. Educators invite students to share their representations and justify their thinking. If needed, educators demonstrate how to make 10 by moving two of the four counters to fill the other ten frame.
In the “Introduce” phase of the “Addition: Make Ten” strategy, educators identify students who need additional support counting on from a given number. The materials recommend providing these students with more concrete practice using connecting cubes or ten frames. During the activity, the educator prompts students to represent a number less than 10 using their fingers and explains, “If I say ‘five,’ you would show me five fingers like this to make ten. Ready? Seven.” Students repeat the activity with different starting numbers less than 10 in order to strengthen their understanding of making 10.
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
Students think mathematically in the “Extend” phase of the “Double Plus” strategy by solving subtraction word problems with the think-addition strategy and representing their thinking on a number line. They persevere as they compare multiple solution strategies, ask clarifying questions, and challenge reasoning they believe is incorrect. They make sense of mathematics by connecting addition and subtraction, explaining their reasoning, and discussing why different strategies effectively solve real-world problems.
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
Grade 2 materials help students explain and justify strategies for solving subtraction problems using doubles. Students make sense of the relationship between addition doubles facts and related subtraction facts, then explain how the relevant strategy helps them solve problems. The activities show that students can solve problems in multiple ways by connecting subtraction to known addition relationships and using mathematical reasoning to justify their methods.
6.1c
Materials are designed to require students to make sense of mathematics through multiple opportunities for students to do, write about, and discuss math with peers and/or educators.
Materials are designed to require students to make sense of mathematics through multiple opportunities for students to do, write about, and discuss math with peers and/or educators.
3 out of 3 points
Evaluation for 6.1c
Evaluation for 6.1c
Materials are designed to require students to make sense of mathematics through multiple opportunities for students to do, write about, and discuss math with peers and/or educators.
3 out of 3 points
In the “Reinforce” phase of the “Subtraction: Use Doubles” strategy, activity 6 engages students in mathematical writing as they reflect on facts they find challenging to remember. Students discuss and compare the strategies they use to solve problems through prompts such as, “Who used a strategy like [student 1]? Do you think [student 2’s] strategy is easier to use than [student 3’s]? Why?” Students ask clarifying questions and challenge classmates’ reasoning when they believe an idea is incorrect. The lesson repeats this process with three additional word problems, giving students multiple opportunities to explain, evaluate, and refine their problem-solving strategies.
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
In the “Reinforce” phase of the “Subtraction: Count On” strategy, students reflect on their problem-solving approaches. In activity 7, educators help students clarify their thinking about turnaround facts by asking targeted questions. Students use number tracks to represent facts (such as 5 + 1 and 1 + 5) and compare the efficiency of different strategies. The educator asks, “What do you find easier to do: start with the greater number and count on one or start with one and count on the greater number?” Students explain and justify their reasoning. The lesson repeats this process with additional “Count On” strategy cards (such as 8 + 2 and 9 + 1) to reinforce strategic thinking and mathematical discussion.
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
In the “Introduce” phase of the “Addition: Make Ten” strategy, educators identify students who need additional support counting on from a given number. The materials recommend providing these students with more concrete practice using connecting cubes or ten frames. During the activity, the educator prompts students to represent a number less than 10 using their fingers and explains, “If I say ‘five,’ you would show me five fingers like this to make ten. Ready? Seven.” Students repeat the activity with different starting numbers less than 10 in order to strengthen their understanding of making 10.