Progress Learning 2nd Grade Math (TEKS)

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.

The materials include a 2nd Grade Math Scope and Sequence document that provides a chart outlining the Texas Essential Knowledge and Skills (TEKS) for each lesson. In each lesson, the “Standards” section lists the TEKS covered and the English Language Proficiency Standards (ELPS) supported in that lesson.

The 2nd Grade Math Scope and Sequence includes a “Second Grade Lesson Sequence Rationale” section that describes how each lesson connects to prior and future learning. For example, this section explains that students apply the number sense and place value understanding gained in lessons 1 through 3 to addition and subtraction with regrouping in lesson 4.

Each lesson includes “Looking Back” and “Looking Ahead” sections that list the grade 1 TEKS and the grade 3 TEKS aligned with the lesson. For example, lesson 6 “Area” states that students are building on knowledge learned in grade 1, such as illustrating that the length of an object is the number of same-size units of length that reach from one end of the object to the other (TEKS 1.7B). The same lesson states that students will use the skills developed in this lesson in grade 3 when they determine the area of rectangles with whole-number side lengths using multiplication, which is related to the number of rows times the number of squares in each row (TEKS 3.6C).

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.

The materials include an Elementary Math Implementation Guide that provides clear usage recommendations and instructional strategies for educators. The lessons offer multiple delivery options, such as using videos paired with cooperative learning strategies (e.g., think-pair-share) and assigning independent practice with follow-up discussion. These supports demonstrate flexibility in instructional approaches and guidance for use in various contexts, including whole-group instruction and independent learning.

The materials offer practical, adaptable strategies for whole-group, small-group, and individualized learning. For example, the materials provide suggested activities after each lesson for both intervention and enrichment, which allows educators to organize students into small groups based on individual learning needs. Additional lesson guidance includes flexible instructional options, such as cooperative learning strategies and independent practice, that support differentiated instruction. Intervention videos provide just-in-time supports for students struggling with grade-level content, and enrichment videos often draw from above-level resources to extend the learning for students who are ready.

Evaluation for 1.1c
Materials include a TEKS correlation guide with recommended skill entry points based on diagnostic assessment results.

The 2nd Grade Math Scope and Sequence provides a chart outlining the TEKS for each lesson, which serves as a TEKS correlation guide. The scope and sequence paired with the “Student Diagnostic Strengths and Weaknesses Report” provide educators with recommended skill entry points based on diagnostic assessment results, which enables them to make instructional decisions aligned with student readiness. For example, if diagnostic results indicate that students struggle with composing and decomposing numbers, educators can consult the TEKS chart in the 2nd Grade Math Scope and Sequence to identify suggested lessons that target those skills.

For students who demonstrate mastery, the “Student Diagnostic Strengths and Weaknesses Report” directs educators to assign enrichment opportunities. These data-informed recommendations support flexible grouping, such as small-group instruction for intervention or enrichment, and help educators connect prerequisite skills to new content.

Evaluation for 1.1d
Materials include protocols with corresponding guidance for unit and lesson internalization.

The materials include clear guidance for both unit and lesson internalization to support effective planning and implementation. The materials provide mathematical standards, a rationale for the learning progression, and key understandings to help educators plan instruction. Each lesson identifies the learning standard, questions to bring out student thinking, potential misconceptions, and appropriate instructional supports. The lesson and unit design follow the research-based 5E Instructional Model—Engage, Explore, Explain, Elaborate, and Evaluate—which promotes active learning and conceptual understanding. Understanding the underlying principles of this design enables educators to focus on the delivery of the lesson.

The Elementary Math Implementation Guide specifically includes supports for lesson internalization. The “Explore” section for each lesson includes clearly labeled subsections, such as “Objective,” “Materials,” “Supports,” and “Implementation,” which guide educators in understanding lesson expectations, planning instruction, and anticipating student needs. Additional components outlined in the lesson plan, such as standards alignment, key vocabulary, and assessment guidance, provide further structure to support educator preparation and delivery.

Evaluation for 1.1e
Materials include resources and guidance for instructional leaders to support educators with implementing the materials as designed.

The materials include resources for instructional leaders to support educators in implementing the program. The materials include implementation checklists that leaders can use to monitor and support educator use of the program. For example, instructional leaders can use these checklists to ensure that educators consistently administer diagnostic assessments, review “Student Diagnostic Strengths and Weaknesses Reports,” and group students appropriately for intervention or enrichment. The checklists can also guide leaders in observing whether educators are implementing lesson components, such as small-group instruction, TEKS-aligned tasks, and recommended program strategies.

The materials include guidance that supports leaders in planning professional development by identifying key practices, such as using diagnostic data to assign targeted skills and facilitating cooperative learning activities. This structured support allows administrators and instructional coaches to provide consistent feedback, model effective practices, and ensure fidelity of implementation.

The materials include leader-specific resources, such as training modules, webinars, and supporting documents, to guide campus and district leaders in implementing the program with fidelity. These resources provide clear guidance for onboarding new educators and supporting ongoing professional development, which ensures the consistent use of the materials across classrooms. Additionally, the resources allow administrators and instructional coaches to model effective practices and support educators in applying strategies, such as differentiated instruction and data-driven planning.

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.

The materials include detailed lesson plans that have clearly stated learning objectives at the beginning of each lesson, educator and student materials, and structured lesson components using the 5E Instructional Model. For example, in lesson “Money,” educators activate prior knowledge in the “Engage” section by asking questions from the grade 1 lesson on coin recognition. Then, students engage in structured activities using manipulatives to practice counting coins and writing the value of the coins using the cent symbol and dollar sign. Students discuss strategies during the “Explain” section and apply their learning through practice and assessment tasks. The 2nd Grade Math Scope and Sequence specifies suggested timeframes for each 5E component in each lesson.

Although Each Lesson Plan States The Teks And Elps, The Assessment Components Do Not Clearly Align With The Elps Because The Assessments Primarily Measure Content Understanding And Do Not Require Explicit Evidence Of Language Development Expectations. The Materials Include An Assessment Builder That Allows Educators To Select Questions Aligned With The Teks. However, The Assessment Builder Does Not Provide Options To Align Questions With The Elps, Which Limits Educators’ Opportunities To Intentionally Incorporate Language Development Objectives.

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.

This guidance is not applicable because the program is not designed to be adaptive.

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).

The materials include family support resources in both English and Spanish for each lesson, which ensures equitable access to instructional information. The resources provide families access to lesson slideshows and suggestions for supporting their children’s progress at home. For example, the lesson 3 “Family Support” section tells families to ask their children to show how to cut a pizza or a pan of brownies into eight equal parts. These bilingual resources promote effective communication between school and home and ensure that all families can actively support student learning.

Evaluation for 2.1a
Materials include the definition and intended purpose for the types of instructional assessments.

The “Assessment Types and Implementation Guidance” section of the Elementary Math Implementation Guide defines and explains the purpose of each instructional assessment type in the lesson sequence. This section describes pre- and post-diagnostic assessments, Learning Snapshots, and summative assessments and explains how each type supports educator decision-making during instruction.

The Elementary Math Implementation Guide describes pre- and post-diagnostic assessments and their instructional purposes. Pre-diagnostic assessments identify what students already understand before instruction begins, which allows educators to determine which students need additional support and which students are ready for more-challenging work. Post-diagnostic assessments measure what students have learned after instruction and help educators determine next instructional steps, such as reteaching a skill and advancing students to new content.

Evaluation for 2.1b
Materials include guidance to ensure consistent and accurate administration of instructional assessments.

The Elementary Math Implementation Guide provides administration guidance for each assessment type, including timing recommendations and delivery options. For example administration guidance for the Learning Snapshots says, “Administer either the print or digital assessment during the Evaluate phase of each lesson” and “Refer to the suggested assessment time listed in the Evaluate section of each lesson.”

The lesson plan for the “Fractions” lesson provides course-specific administration guidance. The “Evaluate” section identifies the assessment as the “Fractions SuperSheet” and provides an approximately 20-minute administration window. Educators can administer the assessment in two formats: a printable version or a digital version.

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.

The materials include printable versions of digital assessments. In the Elementary Math Implementation Math Guide, the “Evaluate” section explains that educators can “locate and print the Learning Snapshots from within each lesson plan file or assign a digital version from the assignment center.” The printable and digital versions share the same name, items, and answer choices.

The materials provide an online platform in which educators can customize assessments by enabling or disabling certain accommodations (such as text-to-speech and calculator use) as described in the How-To Guides article “What accommodations are available in Progress Learning?”

Evaluation for 2.1d
Materials include diagnostic assessments with TEKS-aligned tasks or questions, including interactive item types with varying complexity levels.

The materials provide an Assessment Bank that includes questions at varying levels of complexity, which educators can select to build pre- and post-diagnostic tests aligned with the TEKS. For example, when creating a pre- or post-diagnostic test for classifying and sorting shapes, educators can choose from several recall questions in which students choose the geometric shape that fits a given attribute, such as a shape with 12 edges. A skill/concept-level question for this standard presents students with a three-dimensional shape and asks them to drag and drop the number of faces, edges, and vertices for the shape. Finally, an example of a strategic-thinking question shows students a three-dimensional shape and asks students to name the shape and justify the name chosen using geometric vocabulary.

The materials also include more than two unique interactive item types. The pre-assessment item types include multiple-choice, text-entry response boxes, graphing/plotting, multiselect, matching/table-style equivalency choices, and drag-and-drop answer selections. In addition, the technology-enhanced question item types description lists additional interactive formats, including bar graph, classification, constructed response, dot plot, and drag-and-drop.

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.

The Elementary Math Implementation Guide includes a range of formative assessments aligned with the TEKS for ongoing checking of student understanding. These assessments include interactive item types, such as multiple-choice, drag-and-drop, matching, and short constructed-response. For example, students may match numbers to sets, drag counters into a ten frame, or respond to questions embedded in videos. These tasks are directly tied to specific TEKS and provide educators immediate feedback on how well students are mastering skills during instruction.

The lesson plans include TEKS-aligned components, such as practice questions and quick checks, that engage students in simple, developmentally appropriate tasks. For example, during a lesson, students may complete quick check questions by identifying the number of squares that cover a square or rectangle, comparing numbers using comparison symbols, or selecting the correct set using visuals. Practice questions may begin with basic recall, such as recognizing a number, and gradually increase in complexity by asking students to compare groups or represent quantities using drawings or manipulatives. These varied formats ensure that educators can monitor student understanding in real time and adjust instruction to support different levels of thinking.

Evaluation for 2.2a
Instructional assessments include scoring information and guidance for interpreting student performance, including rationale for each correct and incorrect response.

Each “SuperSheets” assessment includes an answer key with rationales for correct and incorrect responses to support educator interpretation of student performance. For instance, the “SuperSheets” assessment for the “Multiplication, Division, Odd, and Even” lesson lists “B” as the correct answer to question 1 to confirm that students multiplied 2 bags times 5 cars to get a total of 10 cars. The answer key states that if students chose “A,” they likely subtracted 2 from 5 to get a total of 3, and if students chose “C,” they likely added 5 to 2 to get a total of 7.

The “Teacher Progress Report” provides additional tools for interpreting student performance. In the “Teacher Progress Report,” educators can filter assessment data by subject, class, dates, assessment tags, and sources and then view class and individual student performance by standard using “Dot Rank” color categories. The report identifies performance bands, including pink for scores less than 65 percent, yellow for 65 to 79 percent, and green for 80 percent or greater, and allows educators to assign remediation to students performing below 80 percent.

Evaluation for 2.2b
Materials provide guidance for the use of included tasks and activities to respond to student trends in performance on assessments.

The Elementary Math Implementation Guide provides educators guidance on additional activities for students who might be struggling (interventions) and for those who have mastered the lesson concepts (enrichments). The guide provides suggested intervention and enrichment activities after each lesson, noting that “the teacher may organize students into small groups based on their needs.”

The “Quick-Click Remediation” guidance shows educators how to respond to assessment trends by identifying standards requiring additional support, selecting students, setting start and end dates, and assigning targeted remediation. Using the “Teacher Progress Report,” educators can select a standards-based area of need from the “Class Dot Rank” or “Student Dot Rank” views and assign remediation to students who need additional support. Together, these resources provide educators guidance on using assessment results to assign targeted tasks and activities based on student performance trends.

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.

The materials include tools for both educators and students to track progress and growth. Educators use reports to track student progress over time by reviewing performance across multiple assignments and attempts. The “Teacher Progress Report” shows each student’s scores by standard and records how those scores change after additional practice.

The “Class Dot Rank” view helps educators see progress over time by displaying how students move from pink to yellow to green on specific standards. After each assessment cycle, educators can see the report to assess growth in areas, such as adding and subtracting and classifying two-dimensional shapes. If students continue to score in the pink level across multiple assignments, educators may modify instruction by adding more guided practice or trying different approaches, such as hands-on and small-group activities.

The materials include tools to help students track their own progress and growth. Student Data Trackers allow students to monitor their progress on their individual Study Plans by recording their beginning-of-year (BOY) scores and coloring in stars as they increase in proficiency. In addition, the student “Graded Work Report” allows students to view their overall scores, review performance by domain and standard, and access additional practice suggested by the platform based on their performance. Students can also review questions from videos and practice activities, read text explanations, or watch explanation videos to learn from mistakes and receive feedback.

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.

Using the 5E Instructional Model, all lesson plans include frequent checks for understanding throughout the lessons and guidance (prompts) for educators. For example, quick write or draw activities help students recall prior knowledge and include an “Instructions for Teacher” section with administration guidance.

The “Implementation” section of each Teacher Guide provides step-by-step guidance aligned with the slides presentation sequence. The materials guide educators on when to distribute materials, which cooperative learning strategies to apply, and when to pause and check for student understanding.

Evaluation for 2.2e
If designed to be adaptive, materials provide frequent checks for understanding at key points throughout each lesson or activity.

This guidance is not applicable because the program is not designed to be adaptive.

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.

The Elementary Math Implementation Guide includes explicit educator guidance for lessons and activities that are scaffolded for students who have not yet reached proficiency in prerequisite or grade-level concepts and skills. The guide directs educators to the “Suggested Activities: Additional Activities for Intervention and Enrichment” section, which notes that each lesson includes videos with two or three questions for students to work through to reinforce key concepts and promote discussion. Educators can organize students into small groups based on their needs to complete the appropriate set of intervention activities. The intervention videos may feature instruction from below-grade-level or on-grade-level content.

The How-To Guides article “How do I assign quick-click remediation?” explains how educators can assign remediation lessons to students who scored less than 80 percent on assignments and assessments. Educators can assign up to three “weak” areas for students to practice further. In “Structured Small Groups Intervention,” educators receive explicit guidance on grouping students based on data from assignments or assessments.

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.

The Elementary Math Implementation Guide includes embedded supports for developing academic vocabulary and unfamiliar references in text. The guide provides strategies to scaffold, support, and extend academic vocabulary, including “Vocabulary Scavenger Hunts,” structured student talk routines, tiered vocabulary scaffolds, peer vocabulary exchanges, extension prompts, cognate callouts, and multilingual word walls or anchor charts.

The lesson plans include guidance for educators on developing the academic vocabulary introduced during the lesson. For example, the slide deck that accompanies the lesson “Polygons and Shapes” introduces the terms vertex and vertices by using a clearly labeled visual. Students turn and talk about the attributes of a square using the newly identified vocabulary word and then record the word on their handout.

In addition, the materials include a 2nd Grade Math: Educator Guide for Pre-Teaching Vocabulary and Text Supports document that includes a structured four-step vocabulary routine in which educators model and pronounce academic terms, provide student-friendly definitions, connect vocabulary to manipulatives and visual anchors, and engage students in turn-and-talk activities using sentence stems. For example, educators explicitly teach students key vocabulary terms (such as expanded form, thousands, hundreds, tens, ones, standard form, and word form) by using place value blocks, including thousands cubes, flats, rods, and units. Educators demonstrate that 10 hundreds equals 1,000 and provide opportunities for students to decompose three- and four-digit numbers into expanded form, such as 341 = 300 + 40 + 1. The materials also support comprehension of unfamiliar visual and textual references by pre-teaching place value representations and explaining the meaning of different models, including cubes = 1,000, flats = 100, rods = 10, and units = 1. Sentence stems, such as “The digit _____ in the hundreds place has a value of _____,” encourage students to use academic language and apply new vocabulary in context before engaging in grade-level mathematical tasks. The materials also include a “Unit-by-Unit Pre-Teaching and Text Reference Guidance” table that provides educators explicit pre-teaching scripts and guidance for introducing unfamiliar references found in each unit.

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.

The Elementary Math Implementation Guide includes explicit educator guidance on using lessons or activities for students who have demonstrated proficiency in grade-level and above-grade-level concepts and skills. The guide states that each lesson includes videos with two or three questions for students to work through to deepen their understanding of key concepts and promote discussion. For example, lesson 7 “Length” suggests that educators assign the grade 3 video “Capacity and Weight” to advanced students. Educators can organize students into small groups based on their needs to complete the appropriate set of enrichment activities.

Some lessons include a slideshow that provides “Lesson Extension” activities and questions. These activities and questions deepen understanding and challenge students who have demonstrated proficiency in grade-level and above-grade-level content and skills. For example, the slideshow for lesson 11 “2D and 3D Shapes” includes activities that give students a chart of presorted shapes, and students must identify the labels for the different groups of shapes. Educators facilitate discussion by encouraging justification, multiple solution pathways, and peer perspectives; help students move beyond identification to reasoning and mathematical discourse; and support deeper thinking for students who are ready for advanced exploration.

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.

The How-To Guides article “What accommodations are available in Progress Learning?” states that the materials include text-to-speech supports that educators can enable or disable to support individual students. The materials show that educators can set individual student language supports to English Default, Spanish Default, or English Only. The materials also provide Spanish translation options, Spanish video transcripts, and accessibility tools, such as color contrast, font size, zoom, highlighting, response masking, drawing tools, sticky notes, and line reader. However, the materials do not provide content and language supports for students that can be enabled or disabled.

The materials also include a section on calculator accessibility that educators can enable or disable for individual students during assessments. Educators can select one of three types of calculators (four-function, scientific, and graphing) that are powered by Desmos to include with an assessment. However, the materials do not provide the ability to turn on content and language supports for students.

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.

The Elementary Math Implementation Guide provides educator guidance on various types of exploration activities that require students to demonstrate understanding of mathematical concepts in different ways. The “Explore” section of each lesson plan includes a slideshow with educator notes that suggest different manipulatives students can use to express and represent their thinking. For example, in the “Money” lesson, the materials guide educators on providing play money so that students can replicate the coins shown on the slides to help them find the total value. Then, students write the value of coins using a cent symbol and a dollar sign with a decimal.

The materials also include graphic organizers to help students organize and represent their thinking. Graphic organizers include a Frayer model, in which students write the problem, what they need to find out, what they need to do, how they solved the problem, and how they know their answer is correct. This model allows students to demonstrate their understanding of problem situations through writing.

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.

The “Engage” section of each lesson includes explicit prompts and guidance to help educators activate prior knowledge and anchor big ideas. The Elementary Math Implementation Guide states that the “Engage” phase is when educators “activate and gain an understanding of their students’ prior knowledge.” The “Engage” section includes questions that are vertically aligned with prior grade-level standards or with grade-level content taught in previous lessons. For example, the lesson “2D and 3D Shapes” includes “Engage” questions that ask students to identify three-dimensional shapes and identify the two-dimensional shapes to make up a composite shape. The materials also include Bell Ringers that educators can project at the start of each lesson to review previously taught content.

The Teacher Guide for each lesson provides guiding questions to anchor big ideas and connect key patterns, features, and relationships throughout the lesson. For example, lesson 12 “Representing and Interpreting Data” includes questions, such as “What can we learn from a graph?” and “What predictions can you make from graphs?” and common misconceptions that help students solidify crucial learning.

Evaluation for 3.2b
If designed to be static, materials include educator guidance for effective lesson delivery and facilitation using various instructional approaches.

The Teacher Guide for each lesson provides step-by-step facilitation notes, including when to display questions, allow time for discussion, have students justify their responses, clarify misconceptions, and model problem-solving strategies.

The “Explain” section in each lesson plan provides options for different instructional approaches. For example, in lesson 9 “Time,” there are two options for structuring the lesson: showing the lesson video to the whole class and following up with a think-pair-share partner discussion or assigning the video for students to watch and answer questions independently. Lessons also include hands-on activities in which students practice using manipulatives or engage in interactive tasks while educators guide and check their progress. The materials include suggested questions, intervention ideas, and extension activities to help educators meet the needs of all students.

Evaluation for 3.2c
Materials include multi-tiered intervention methods for various types of practice and structures and educator guidance to support effective implementation.

The Elementary Math Implementation Guide provides intervention methods for multiple practice types. Students can receive support through intervention videos with accompanying questions, Study Plan practice, educator-created assignments, Learning Snapshot reflection, and reteach opportunities based on item rationales. The guide states that intervention videos may come from below-grade or on-grade-level resources and include questions for students to work through. The guide also notes that educators can gather and analyze student data as students engage with the content.

The lesson plans provide guidance for educators on implementing the intervention methods. In lesson 3 “Fractions,” educators start by reviewing halves, fourths, and eighths before moving on to comparing fractional parts of a whole using relatable pictorial models, such as pizza and brownies. The materials also provide “Show What You Know!” problems that educators can use as additional instruction for struggling students.

Educators can also use structured practice options to reinforce learning for students requiring additional practice. Some students may be assigned targeted practice problems through an online platform to reinforce addition and subtraction skills, while other students can work through related concepts in their Study Plans. Additionally, students can complete an independent activity from the “Class Activity” section to deepen their understanding. These practice structures help ensure that all students—whether they need extra support or are ready for a challenge—have meaningful opportunities to learn and apply the concept in ways that meet their needs.

Evaluation for 3.2d
Materials include enrichment and extension methods that support various forms of engagement, and guidance to support educators in effective implementation.

The Elementary Math Implementation Guide provides guidance on implementing enrichment and extension methods effectively. The Teacher Guide for each lesson provides structured and flexible strategies, such as hands-on activities, visual supports, collaborative discussions, and differentiated questioning, to ensure that all students can access and extend their understanding. Additionally, the Teacher Guides offer clear, actionable guidance to help educators effectively integrate these supports into instruction, including opportunities for student choice and independent application.

The Teacher Guide for lesson 4 “Addition and Subtraction” contains concrete and visual engagement strategies, such as number bonds, strip diagrams, and manipulatives, to help students learn to add and subtract numbers using multiple strategies. Students engage in math dialogue and discourse by explaining their thinking in response to prompts, such as “How does place value play a part when adding and subtracting larger numbers?” and “How can I use a model to represent a problem?” that promote reasoning and peer interaction. Additionally, the materials include structured problem-solving routines in which students read problems, draw representations, and write equations, which supports varied modalities of engagement.

Evaluation for 3.2e
Materials include prompts and guidance to support educators in providing timely feedback during lesson delivery.

The Elementary Math Implementation Guide explains how the online platform provides students timely feedback during lesson delivery. The guide explains that when students miss items in their Study Plans, a video appears and provides immediate feedback to help students correct misconceptions before they try again.

Lesson 7 “Length” includes intentional prompts and guidance that support educators by providing feedback as students explore distances between numbers on a number line and relate those distances to measuring length using rulers. The Teacher Guide provides questions, such as “How is a number line similar to a ruler?” and “What are some examples of the following measurements: inch, foot, yard?” These prompts help educators quickly gauge student understanding and address misconceptions right away. As students work, built-in checkpoints and modeling tips guide educators in giving specific, actionable feedback that supports both conceptual understanding and academic language.

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.

The 2nd Grade Cooperative Learning & ELPS Strategy Guide outlines all cooperative learning strategies used in the program, explains their purposes, offers grouping suggestions for different mathematics proficiency levels and emergent bilingual (EB) levels, and provides instructions and guidance for educators. The guide also includes directions for students and linguistic accommodations for the five proficiency levels as defined in the ELPS. The “Accommodations by ELPS Levels” section gives guidance and prompts for Pre-Production, Beginning, Intermediate, High Intermediate, and Advanced students. For example, in “Strategy 3: Tile & Array Builders (Area & Square Unit Models),” students at the Pre-Production level demonstrate understanding of area by placing color tiles inside a rectangle to cover the space without gaps or overlaps while using visual supports and partner guidance. At the Beginning level, students identify and use basic area vocabulary terms, such as rows, columns, square units, and area, to describe tile arrangements and complete simple sentence starters. Students at the Intermediate level use sentence frames to explain the number of rows and columns in a rectangle, calculate area using repeated addition, and use grids to count missing square units. At the High Intermediate level, students use academic language to describe how rows and columns determine area, explain solutions using repeated addition, and distinguish between perimeter boundaries and interior square units. Finally, at the Advanced level, students justify area calculations by explaining how different rectangular arrangements can have the same area; proving solutions with evidence from rows, columns, and square units; and using precise mathematical vocabulary to defend their reasoning.

Additionally, in “Strategy 4: Shape Attribute Investigators & Sculptors (2D Polygons & Decomposing Shapes),” students at the Pre-Production level demonstrate understanding of two-dimensional shapes by sorting shape cards by visible attributes, pointing to matching polygons, and using visual supports while a partner names each shape’s characteristics. At the Beginning level, students identify and name shapes and their attributes using key academic vocabulary terms, such as triangle, hexagon, sides, and vertices, with support from a visual word bank and sentence starters. Students at the Intermediate level use sentence frames to describe polygons by their number of sides and vertices, explain how shapes can be decomposed into smaller shapes, and mark vertices to support accurate counting. At the High Intermediate level, students use academic language to compare and classify shapes, explain geometric relationships, and describe how decomposing a polygon creates new geometric figures while using vocabulary terms, such as parallel lines and parallelogram. Finally, at the Advanced level, students justify geometric reasoning by explaining why a figure does or does not belong to a specific category; proving classifications using attributes, such as sides, vertices, and parallel lines; and communicating mathematical thinking with precise academic vocabulary.

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.

This guidance is not applicable to the program because it is not designed to be adaptive.

Evaluation for 3.3c
Materials include implementation guidance to support educators in effectively using the materials in state-approved bilingual/ESL programs.

The materials include clear implementation guidance to help educators effectively use instructional resources within state-approved bilingual or English as a Second Language (ESL) programs. The “Standards” section of each lesson plan lists the ELPS leveraged in that lesson. The educator notes in the daily slideshows help educators implement the ELPS through visuals, vocabulary supports, and structured opportunities for speaking and writing during problem-solving.

The materials include a prerecorded webinar titled “5 Ways to Elevate Your Lessons for ELLs Learners” that describes specific ways the materials support EB students through different components of the platform. These supports include incorporating visuals, using the tools, encouraging total participation, and incorporating reading and writing. The materials explain each strategy, and a chart outlines which features help educators do each strategy. Digital tools help along the way by providing quick feedback and support tailored to each student’s needs.

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.

The materials include strategies that educators use to support academic language development during lessons. The Elementary Math Implementation Guide lists several activities and strategies, such as “Ping Pong Peer Vocabulary” and “Use-It-To-Do-It,” that provide embedded guidance to help educators scaffold, support, and extend students’ use of academic vocabulary during math instruction. The lessons provide opportunities for students to discuss math concepts during instruction through partner activities, such as think-pair-share. For example, in lesson 12 “Representing and Interpreting Data,” students discuss how graphs help them organize and analyze data.

In addition, the materials provide Exit Tickets at the end of each lesson to “evaluate student understanding at the end of each math unit, while meeting the rigorous requirements of dual-language instruction and early childhood numeracy standards.” For example, the Exit Ticket for lesson 3 “Fractions” includes several supports for EB students. The “Teacher Facilitation and Cross-Linguistic Notes” promote making cross-linguistic connections through oral discourse by explicitly highlighting cognates, such as fraction/fracción, fractional parts/partes fraccionarias, and equal parts/partes iguales. These intentional language connections help students discuss mathematical concepts using both languages during instruction. The Exit Ticket supports the development of academic vocabulary through written discourse because students must use content-specific vocabulary terms, such as larger, smaller, fraction, and equal parts, when completing sentence stems and writing their responses. The materials also support increasing comprehension through written discourse as students demonstrate their understanding of fractions by explaining how the sizes of pizza pieces change when pizzas are divided into more or fewer parts and by applying their learning to a real-world scenario. Additionally, the lesson provides opportunities to make cross-linguistic connections through written discourse as students can transfer knowledge of the cognate vocabulary introduced during instruction when completing the written tasks. However, the materials do not explicitly build background knowledge through written discourse. Although the “Math in My World” prompt connects fractions to a familiar context involving a pizza, the materials ask students to apply their understanding rather than develop new background knowledge through writing about their experiences or prior knowledge.

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.

This guidance is not applicable because the program is not designed for dual language immersion (DLI) programs.

Evaluation for 4.1a
Practice opportunities throughout learning pathways (including instructional assessments) require students to demonstrate depth of understanding aligned to the TEKS.

The materials include “SuperSheets,” which are formative assessments intended to mirror the rigor, verbiage, and cognitive complexity of the depth of understanding aligned with the TEKS. For example, during a lesson on partitioning objects (in lesson 4 “Addition and Subtraction”), educators lead students through hands-on activities using counters, connecting cubes, and drawings to break apart groups into equal or unequal parts. Students talk with partners about how they separated a set—such as dividing 10 objects into 6 and 4—and explain how the parts make the whole. Students then work independently to represent their ideas with pictures or number sentences. When students complete the “SuperSheets” assessment, they solve similar problems that ask students to separate groups, describe each part, and show their thinking using drawings or equations. These activities encourage students to think deeply, explain their reasoning, and apply their understanding in clear and meaningful ways.

In lesson 10 “Polygons and Shapes,” students actively build their understanding of geometry as they identify, classify, and describe polygons by examining their attributes. Students sort shapes (such as triangles, quadrilaterals, and pentagons) by the number of sides, vertices, and angles; compare figures; and explain why each shape belongs in its category. For example, students may group shapes with four sides and explain that they are quadrilaterals, or students may compare a triangle and a pentagon by discussing the number of sides and corners. Students also draw and build shapes to reinforce what they learn. Students then use “SuperSheets” assessments to practice what they have learned by identifying and sorting shapes based on attributes.

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.

The Elementary Math Implementation Guide explains how each lesson is structured using the 5E Instructional Model, which scaffolds the tasks as they increase in complexity. For example, in lesson 7 “Length,” the “Engage” section helps students activate prior knowledge of measuring length with nonstandard units. The section helps students frame the lesson. In the next section, “Explore,” educators help students connect their prior learning to the current grade-level learning standard. Students move beyond measuring objects using nonstandard units, such as cubes and paper clips, to measuring length using a ruler, which leads to grade-level proficiency. The materials include an Assessment Bank with questions of varying levels of complexity that educators can assign.

In addition, the materials include meaningful extensions for students ready for more-advanced work. Advanced students work with grade 3 TEKS-aligned content in ways that push their thinking further. The materials give students opportunities to deepen their understanding and use their skills in more-complex and more-meaningful ways. The materials design extensions to add rigor and challenge so that students who are ready to go beyond grade-level expectations receive the support they need to continue growing and reach higher levels of proficiency. For example, in lesson 9 “Time,” students tell time to the nearest minute and distinguish between a.m. and p.m. The extension materials for this lesson challenge students at an above-grade level by having them calculate elapsed time across multiple hours (e.g., from 1:45 to 4:20) and represent their thinking using equations, open number lines, or written explanations. These structured progressions ensure that students not only reach grade-level proficiency but also engage in above-grade-level thinking.

Evaluation for 4.2a
Materials demonstrate coherence across concepts horizontally within the grade level by connecting patterns, big ideas, and relationships.

In the 2nd Grade Math Scope and Sequence document, the materials clearly show how lessons build on one another and connect key concepts across the grade level using active, student-centered instruction. The document explains that in lesson 1 “Read and Write Numbers,” students develop a strong foundation in number sense by representing numbers using models, expanded form, standard form, and word form. This understanding of how numbers are structured becomes essential for future learning. In lesson 2 “Locate and Compare Numbers,” students build directly on this foundation by using their knowledge of place value to compare numbers; use symbols, such as > and <; and locate numbers on an open number line. The connection between these lessons helps students recognize patterns in the number system and strengthens their ability to reason about quantity. This understanding then extends into lesson 4 “Addition and Subtraction,” in which students apply their knowledge of number relationships and place value to solve problems using a variety of strategies. Because students already understand how numbers are composed and compared, they can more easily explain their thinking when adding and subtracting, making connections between operations and number sense. Later in lesson 10, students classify two-dimensional shapes based on attributes. This lesson “focuses on the ‘flat’ world before adding the ‘solid’ world in the next.” The 2nd Grade Math Scope and Sequence document highlights how each lesson connects to the next, which helps students develop a strong, integrated understanding of numbers, operations, and shapes in the grade level.

Each lesson begins by activating prior knowledge of concepts taught earlier in the course that support the new content. In the “Engage” section of lesson 12 “Representing and Interpreting Data,” educators begin by reviewing students’ understanding of tally charts and basic pictographs. During the lesson, students create a tally chart, a pictograph, and a bar graph; discuss how all three representations show the same information; and make predictions using the data.

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.

Each lesson plan helps educators build strong foundations by clearly connecting skills across grade levels and concept areas. The “Looking Ahead” section in lesson 4 “Addition and Subtraction” shows how learning to add and subtract three-digit numbers connects to what students will do in later grades. The section demonstrates that adding and subtracting within 1,000 using place value, models, and strategies, such as breaking numbers apart and making tens, will become important when students must add and subtract numbers fluently in grade 3.

Additionally, the “For Advanced Learners” section in the “Additional Activities for Intervention and Enrichment” section extends this coherence across the K–6 grade band. In lesson 3 “Fractions,” advanced students connect what they learned about halves, fourths, and eighths in grade 2 as they explore related grade 3 concepts, such as thirds and sixths, and formalize their understanding of numerator and denominator. These connections reinforce coherence across grade bands and help students recognize patterns and relationships over time.

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.

The “Engage” section of each lesson activates prior knowledge by reviewing skills, such as counting within 100 or 1,000; skip counting by 2s, 5s, and 10s; identifying place value (tens and ones); and recalling basic addition and subtraction facts within 20. Educators then introduce current grade 2 concepts, such as adding and subtracting within 100 or 1,000, by linking the concepts to familiar strategies, such as counting on, making ten, using number lines, and breaking apart numbers into tens and ones with base 10 blocks or drawings. Throughout the lesson, educators sequence activities so that students move from concrete models (such as base 10 blocks and place value charts) to more-abstract representations, such as writing equations and solving multistep word problems. Educators also connect current learning to future concepts by modeling how place value supports regrouping, encouraging students to explain their thinking, and showing how strategies, such as breaking apart numbers, will support multiplication and division in later grades. By linking what students have learned before, what they are learning now, and what they will learn next, educators help students build a strong and connected understanding of mathematics.

In lesson 10, the materials build on students’ prior knowledge of basic shapes from earlier grades, such as recognizing triangles and rectangles, to help students identify and describe polygons based on specific attributes, such as the number of sides and vertices. Students classify shapes, including triangles, quadrilaterals, pentagons, and hexagons, by counting sides and corners and explaining their reasoning. For example, students identify a hexagon by recognizing that the shape has six sides and compare the shape to a pentagon with five sides. Students also sort and group shapes based on shared attributes, which reinforces connections to earlier experiences with categorizing objects. In addition, students draw shapes based on given attributes, such as “draw a shape with 4 sides and 4 vertices,” which deepens their understanding of defining features. The lesson extends learning by having students explore how shapes can be combined or partitioned into equal parts, which connects geometry to fractions and area concepts introduced in grade 2. For example, students may divide a rectangle into equal parts and describe those parts as halves, thirds, or fourths. These experiences prepare students for future grades, in which they will analyze composite figures, understand more complex properties of shapes, and work with area and fractions in greater depth.

Evaluation for 4.3a
Materials provide spaced retrieval opportunities with previously learned skills and concepts across learning pathways.

The Study Plan feature of the online platform and the strategic use of Bell Ringers intentionally revisit previously learned skills and concepts across multiple learning pathways, which ensures that students strengthen retention over time. The Study Plans allow students to self-select previously taught skills to work on and monitor their progress toward mastery. This feature provides spaced retrieval opportunities and gives students who struggle additional practice and attempts at mastery. In addition to questions, each student’s Study Plan comes with instructional videos to review previously taught content as needed. The Skills Practice feature helps to build fluency by revisiting important concepts in new ways and situations, which helps students strengthen their understanding and use what they have learned more effectively.

Bell Ringers reinforce learning in grade 2 mathematics by giving students short, engaging opportunities to revisit and practice key skills. For example, educators might begin the day with a quick activity in which students identify a number shown by a dot on a number line and identify the number that is 100 less or use base 10 block models to represent a given number. The tasks activate prior knowledge and provide spaced retrieval, which helps young students strengthen their foundational knowledge in mathematical concepts over time.

Evaluation for 4.3b
Materials provide interleaved practice opportunities with previously learned skills and concepts across learning pathways.

The Assessment Bank supports interleaved practice opportunities that connect previously learned skills and concepts across learning pathways. Students actively count objects, compare numbers, and recognize patterns as they revisit earlier lessons during new activities. Educators guide students to apply general math concepts, such as identifying shapes and understanding quantities, while blending new ideas with familiar tasks. The materials encourage students to practice addition, sorting, and number recognition in meaningful ways, which helps students strengthen understanding and confidence.

In lesson 3 “Fractions,” the materials build interleaved practice across learning pathways by bringing forward number sense and comparison skills from earlier lessons while students connect, create, define, and explain fractional ideas during slideshow activities and “SuperSheets.” Educators display fraction circles and partitioned shapes on the slideshow and ask, “How many equal parts do you see?” and “Which piece is one-half?” Students connect these concepts to prior work with whole numbers by counting equal parts and relating them to division into equal groups, which aligns with TEKS 2.1(A), 2.2(A), and 2.3(A). Students create their own models by folding paper strips into equal sections and shading parts on the “SuperSheets” assessments, and students define fractions using words, such as halves, fourths, and equal parts. During partner discussions, students explain how two-fourths relates to one-half, which links previously learned comparison language, such as greater than and less than, to fraction reasoning. This interleaving requires students to move between concrete folding, pictorial shading, and writing symbolic fractions while revisiting earlier counting and comparing skills in a new context.

Evaluation for 5.1a
Questions and tasks provide opportunities for students to interpret, analyze, and evaluate models and representations for mathematical concepts and situations.

In lesson 2 “Locate and Compare Numbers,” students interpret and analyze models using base 10 blocks, place value charts, hundreds charts, and number lines. Students build, locate, and compare numbers using place value understanding and mathematical language. For example, each student builds a three-digit number and compares the number with a partner’s number by using terms such as greater than, less than, and equal to. Students answer questions, such as “Which number is greater?” and “How do you know?”. During think-pair-share discussions, students compare models and determine whether each representation matches the number shown. Students support their evaluations with evidence from the model and explain any errors they identify.

In lesson 4 “Addition and Subtraction,” students interpret, analyze, and evaluate mathematical models as they solve addition and subtraction problems within 1,000. Students use base 10 blocks, place value charts, drawings, open number lines, and equations to represent mathematical situations. For example, students may model 248 + 125 with base 10 blocks and explain how the quantities are combined. Students describe what each block represents and explain how the total changes as hundreds, tens, and ones are added. Students also model subtraction by removing quantities and explaining how the model represents taking away. During partner and whole-class discussions, students compare models, identify errors, and justify their evaluations with evidence from the representations.

Evaluation for 5.1b
Questions and tasks provide opportunities for students to create concrete models and pictorial representations to represent mathematical situations.

In lesson 1 “Read and Write Numbers,” students represent numbers by building and drawing. Educators model how to use base 10 blocks, place value disks, or connecting cubes to represent numbers and then ask students to create their own representations. For example, when educators say, “Show me 324,” students build the number using 3 hundreds, 2 tens, and 4 ones. Next, students draw a picture of the same number and make a direct connection between the objects and the drawing. Students describe their thinking by explaining how their pictures match their models (e.g., “I drew three hundreds, two tens, and four ones because I used those pieces in my model.”).

In lesson 10 “Polygons and Shapes,” students use pattern blocks, craft sticks, straws, geoboards, or other manipulatives to construct triangles, quadrilaterals, pentagons, hexagons, and other polygons and focus on each shape’s attributes, such as sides and vertices. After building, students combine shapes to form larger figures and explain how the smaller shapes make a composite figure. Educators ask guiding questions, such as “How many sides does your polygon have?” and “Which shapes did you use to build it?” Students also complete a matching task in which they identify and classify shapes on a handout.

Evaluation for 5.1c
Questions and tasks provide opportunities for students to apply conceptual understanding to new problem situations and contexts.

In lesson 4 “Addition and Subtraction,” students apply their conceptual understanding to new problem situations through guided practice and real-life contexts. In this lesson, educators present a slideshow image showing groups of objects and ask, “How many are there altogether?” Students use base 10 blocks, place value disks, drawings, or equations to model each group shown in the picture, then combine them to find the total. Some students draw pictures to show their thinking. For example, students might model 126 books and 43 more books using base 10 blocks to determine that there are 169 books altogether. Students explain how they used addition and place value to solve the problem. These tasks help students transfer their understanding of joining quantities to everyday situations and build confidence in solving problems.

In the “SuperSheets” assignment for lesson 4, students apply addition and subtraction strategies to solve a variety of multistep and single-step problems. Students read word problems, determine which operations to use, and select the correct answer from multiple-choice options. Several problems require students to complete equations with missing numbers, use place value charts to add and subtract, and analyze strip diagrams to represent relationships between quantities. For example, students solve problems involving candy, rocks, stickers, toy cars, bookmarks, sandwiches, and fair sales, and students use representations, such as strip diagrams and place value models, to support their reasoning. Educators guide students in identifying key information, choosing an efficient strategy, and explaining how their work connects to the problem. Students justify their answers using equations, models, and mathematical reasoning.

Evaluation for 5.2a
Materials provide tasks that are designed to build student automaticity and fluency necessary to complete grade-level mathematical tasks.

In a “Think or Swim” activity, educators display a rapid sequence of standards-based questions, and students respond aloud in a whole-class game format, which builds automaticity through quick recall and fluency through repeated practice. Students practice previously taught skills, such as reading numbers, comparing values, identifying place value, skip counting, and solving addition and subtraction facts, multiple times. For example, educators may display a three-digit number and ask students to identify the value of a digit or determine 10 more or 10 less. Students respond aloud, check answers as a class, and correct errors immediately.

The lessons also provide opportunities for students to build automaticity and fluency. In lesson 1 “Read and Write Numbers,” educators help students develop automaticity and fluency by engaging them in repeated, hands-on activities that connect quantities, number words, and numerals. Students represent numbers using base 10 blocks; identify hundreds, tens, and ones; and match models to written numerals. Educators also use place value charts, hundreds charts, and number lines to encourage quick recognition and efficient counting strategies. Students practice reading, writing, and representing numbers in multiple formats.

Evaluation for 5.2b
Materials provide opportunities for students to practice the application of efficient, flexible, and accurate mathematical procedures throughout learning pathways.

The Study Plan feature provides students opportunities to apply efficient, flexible, and accurate mathematical procedures throughout each activity. Students develop efficient procedures when they use place value reasoning, mental-math strategies, skip counting patterns, and number relationships rather than counting individual objects. The materials promote flexible procedures by encouraging students to solve problems in different ways, such as using base 10 blocks, place value charts, open number lines, drawings, and equations. For example, students may represent 347 with base 10 blocks and verify the number’s value with a place value chart or expanded form. Students build accurate procedures as they represent numbers, complete practice items, receive immediate feedback, and revise their answers when needed. Short instructional lessons and repeated practice opportunities allow students to refine strategies, verify solutions, and explain how they know their answers are correct.

In lesson 10 “Polygons and Shapes,” students practice applying efficient, flexible, and accurate mathematical procedures by creating, identifying, and analyzing polygons in multiple ways. Students use pattern blocks, geoboards, craft sticks, and drawings to build and classify polygons based on attributes, such as sides and vertices. They compare shapes, sort shapes into categories, and explain why a shape belongs in a particular group.

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.

In lesson 4 “Addition and Subtraction,” students use base 10 blocks, open number lines, equations, drawings, and mental-math strategies to solve problems and compare their approaches. Students evaluate efficiency by determining which strategy helps them solve a problem more quickly. For example, students recognize that using place value strategies is often more efficient than counting individual units. Students evaluate flexibility by solving the same problem using different tools and representations. Students evaluate accuracy by checking whether each strategy produces the same correct answer and by explaining how they know the solution is correct. As students share and compare approaches, they discuss which strategies work best in different situations and justify their thinking using mathematical evidence.

In lesson 12 “Representing and Interpreting Data,” students look at a collection of pictures of fruit representing their favorite fruits, organize the responses into a tally chart, create a pictograph and a horizontal bar graph from the data, and verify that the graphs reflect accurate totals. Students answer questions about the data, compare categories, and explain how students found their answers using different approaches and strategies.

Evaluation for 5.2d
Materials contain guidance to support students in selecting increasingly efficient approaches to solve mathematics problems.

The Elementary Math Implementation Guide supports students in selecting increasingly efficient approaches to solving mathematical problems by providing educators clear options for structuring lessons and guiding student thinking. Students compare strategies during thinkpair-share discussions; work independently with tools, such as drawings, number lines, and base 10 blocks; and explain their approaches during whole-class conversations. In the “Elaborate” section, students revisit skills and refine strategies, such as moving from modeling every quantity with blocks to using place value reasoning and mental strategies.

In lesson 2 “Locate and Compare Numbers,” students progress from using concrete models to using mental number relationships as they build fluency with place value. Students begin by using base 10 blocks to build and compare numbers. As students’ confidence grows, they transition to using place value charts, number lines, and mental strategies to determine which numbers are greater than, less than, or equal to without physically building every number. For example, students who initially build 462 and 487 with blocks may later explain that 487 is greater because both numbers have 4 hundreds and 8 tens, which is greater than 6 tens.

Evaluation for 5.3a
Materials explicitly state how the conceptual and procedural emphasis of the TEKS are addressed.

The 2nd Grade Math Scope and Sequence document develops both conceptual understanding and procedural fluency as students move from reading, writing, locating, and comparing numbers to solving addition and subtraction problems and exploring fractions, multiplication, division, measurement, money, time, geometry, data, and personal financial literacy. Educators guide students to explain how numbers represent quantities and relationships while students practice skills, such as composing and decomposing numbers, comparing values, solving equations, representing mathematical situations, and applying place value reasoning. As instruction continues, students connect ideas across strands. For example, students partition objects into fractional parts, solve addition and subtraction problems, determine area and length, count money, tell time, identify attributes of polygons and three-dimensional figures, and interpret data while applying procedures, such as counting, comparing, recording, measuring, and solving problems.

In lesson 10 “Polygons and Shapes,” students build conceptual understanding by identifying the attributes of three-dimensional shapes and using precise vocabulary, such as faces, edges, and vertices, and “Show What You Know!” questions reinforce procedural skills. Students build conceptual understanding when they identify three-dimensional shapes and count the number of faces, edges, and vertices each figure has. The materials encourage educators to provide three-dimensional models for students so that they can physically touch the faces, edges, and vertices as they count. Then, students apply their learning in a “Guess My Shape” activity in which they are given a set of attributes and must identify the correct three-dimensional shape. Finally, students demonstrate procedural fluency in the “Show What You Know!” questions and the “SuperSheets” assessment questions by identifying three-dimensional shapes and their attributes.

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.

In lesson 1 “Read and Write Numbers,” educators use slides and “SuperSheets” assignments to guide students in building their number sense using models that shift from visual to symbolic forms. The slideshow displays base 10 blocks so that students can see groups of ones organized into tens and hundreds, and students count the blocks aloud to connect quantities to number names. Place value charts and hundreds charts on the slides help students recognize number patterns as they identify digits, count forward and backward, and describe how numbers increase or decrease, while the “SuperSheets” assignment asks students to read, write, identify, or represent numbers. Students then use a place value chart to match base 10 blocks to numerals and record numbers in the correct place value positions, which strengthens students’ ability to represent quantities without physical manipulatives. Educator questions on the slides, such as “How many hundreds do you see?” and “What number does this represent?” require students to explain their reasoning, which helps them connect the models, drawings, and written numbers in a consistent understanding.

In lesson 7 “Length,” students begin by reviewing how to measure length using concrete objects, such as paper clips. Then, students locate numbers on a number line and discuss increasingly efficient methods for determining the distance between two numbers. Students transition from concrete to pictorial models as they apply their learning from the number line activity to measuring length using a ruler. Finally, students record their results by writing numbers and measurement statements and answering slide questions, such as “How many units long is the object?” and “How do you know your measurement is accurate?”

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.

The Elementary Math Implementation Guide shows educators how to use slideshow prompts, instructional videos, and “SuperSheets” assignments to move students from hands-on experiences to written mathematics while students connect, create, define, and explain their thinking during daily lessons. During whole-group instruction, educators pause on slides to ask guiding questions, such as “What do you notice?” and “How can you show that another way?” so that students connect concrete models, such as base 10 blocks, counters, place value disks, and measuring tools, to pictorial drawings displayed on the screen and to numbers, symbols, equations, or written responses they record on their papers. Students create their own representations in “SuperSheets” assignments by drawing objects, modeling quantities, writing equations, or recording measurements to match what they built, and students define their ideas using mathematical vocabulary during peer discussions. Turn-and-talk moments and partner-sharing encourage students to explain how their drawings match the models and how both connect to the numbers and equations they write, which builds a clear bridge from concrete experiences to abstract understanding.

In lesson 2 “Locate and Compare Numbers,” the slideshow and student work mats guide students through collaborative tasks in which students connect, create, define, and explain number comparisons using multiple representations. Students build numbers using base 10 blocks and place the models on their work mats, which creates concrete representations of quantity, then count and organize hundreds, tens, and ones in preparation for comparison. Working with a partner, students align models, compare place value representations, and use hundreds charts or number lines to visually represent greater-than, less-than, and equal relationships. Sentence stems on the slide, such as “My number is greater than . . .” and “My number is less than . . .,” help students articulate their thinking aloud as they engage in repeated rounds of discussion and comparison. As they complete the “SuperSheets” problems independently, students transition to abstract recording by writing numerals and comparison statements using symbols, such as >, <, and =.

Evaluation for 5.4a
Materials provide opportunities for students to develop academic mathematical language using visuals, manipulatives, or other language development strategies.

The Elementary Math Implementation Guide provides opportunities for students to develop academic mathematical language through instructional videos, educator-led questioning, visual representations, and mathematical discussions. Educators use models, diagrams, number representations, and interactive activities presented throughout the lessons to introduce mathematical concepts and encourage students to describe their observations using precise mathematical vocabulary. During classroom discussions, educators ask open-ended questions that prompt students to explain their reasoning, compare strategies, and justify solutions. Students actively participate by discussing mathematical ideas with peers; using vocabulary related to place value, fractions, operations, measurement, geometry, data analysis, and financial literacy; and explaining how visual models support their thinking.

In lesson 1 “Read and Write Numbers,” the materials provide opportunities for students to develop academic mathematical language through visuals and hands-on manipulatives, such as base 10 blocks, place value charts, number lines, and pictorial models. Students read, write, represent, and compare numbers using standard form, expanded form, word form, and visual models. The lesson introduces important vocabulary terms, including digit, place value, hundreds, tens, ones, standard form, expanded form, compare, and represent, which are reinforced through lesson videos, visual representations, and guided practice activities. Educators model how to describe numbers using precise mathematical language and multiple representations. Students use manipulatives to build numbers, identify place value relationships, explain the value of each digit, and justify their thinking using complete sentences, such as “The digit 6 represents 60 because it is in the tens place.”

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.

The Elementary Math Implementation Guide includes embedded educator guidance that scaffolds, supports, and extends students’ use of academic mathematical vocabulary during discussions with peers and educators. Structured discourse routines, such as “Use-It-To-Do-It,” think-pair-share, and “Ping Pong Peer Vocabulary,” provide educators opportunities to explicitly introduce mathematical terminology, model appropriate usage, and support students as they incorporate new vocabulary into mathematical conversations. Educators encourage students to use mathematical language when explaining strategies, asking questions, defending solutions, and responding to classmates’ ideas.

In lesson 2 “Locate and Compare Numbers,” the materials include embedded educator guidance that scaffolds students’ use of academic vocabulary through educator modeling, visual representations, and structured questioning. Educators explicitly model terms, such as greater than, less than, equal to, compare, order, ascending, and descending, while examining numbers on number lines and place value charts. The materials provide guiding questions, such as “Which number is greater? How do you know?” and sentence stems, such as “I know _____ is greater than _____ because _____.” Students use place value understanding and visual models to compare and order numbers, then communicate their reasoning with partners and educators. As students become more proficient, educators extend students’ language by prompting them to justify comparisons using place value reasoning and explain multiple solution methods.

Evaluation for 5.4c
Materials include embedded guidance to support student application of appropriate mathematical language and academic vocabulary in discourse.

The Elementary Math Implementation Guide provides embedded guidance to help students use mathematical language and academic vocabulary during discussions, partner work, and problem-solving activities. Structured academic discourse routines help students use mathematical vocabulary in meaningful contexts. Students engage in activities, such as “Vocabulary Scavenger Hunts,” “Use-It-To-Do-It” discussions, and collaborative problem-solving tasks, that require students to explain strategies and communicate mathematical ideas using precise terminology.

In lesson 7 “Length,” the materials provide explicit guidance to support students’ application of mathematical language during a structured think-pair-share routine. The “Explain” section introduces students to key vocabulary terms, including length, measure, unit, centimeter, inch, estimate, longer than, and shorter than, through instructional videos and educator demonstrations. Students independently analyze measurement scenarios and discuss their observations with a partner using complete mathematical statements, such as “The pencil is longer than the eraser because it measures 12 centimeters.” During whole-group sharing, students explain their measurement strategies, compare results, and justify conclusions using measurement vocabulary. Educators facilitate discussions by asking students to clarify reasoning, restate a peer’s explanation, and compare different approaches using precise mathematical language.

Evaluation for 5.4d
Materials include embedded guidance to facilitate mathematical conversations allowing students to hear, refine, and use math language with peers.

The “Math Sentence Stems” resource provides educators with structured prompts that encourage students to explain reasoning and respond to classmates using mathematical vocabulary. Educators incorporate prompts, such as “I agree with _____ because _____,” “My strategy was _____,” and “I solved the problem by _____,” during partner discussions, collaborative problem-solving, and class discussions. These opportunities allow students to hear mathematical language in context and refine their own understanding through meaningful conversations.

In lesson 10 “Polygons and Shapes,” the materials provide embedded guidance that facilitates mathematical conversations and encourages students to hear, refine, and use mathematical language with peers. Educator notes direct educators to engage students in discussions about attributes of polygons and other two-dimensional figures. Students participate in think-pair-share activities and use vocabulary terms, such as polygon, side, vertex, angle, quadrilateral, pentagon, hexagon, triangle, and rectangle. For example, educators ask questions, such as “How would you describe this polygon?” and “What attributes make this figure a quadrilateral?” As students share descriptions and listen to their peers’ ideas, students hear mathematical language in context and refine their understanding of shape attributes through discussion.

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.

In lesson 12 “Representing and Interpreting Data,” the materials include embedded guidance that anticipates a variety of student responses as students organize, analyze, and interpret data. The Teacher Guide provides questions that encourage students to examine graphs and explain conclusions using evidence from the data. Educators facilitate discussions using follow-up questions that prompt students to justify their reasoning and clarify their responses. The materials include expected responses and exemplar explanations to support accurate interpretation of bar graphs, picture graphs, and frequency tables. When students misinterpret graph information, the materials provide targeted questions and redirection strategies to help students focus on the relevant data and correct misconceptions.

The Elementary Math Implementation Guide further supports educators in anticipating student responses through the “Elaborate” section of the 5E Instructional Model. Students complete standards-aligned practice activities that include immediate feedback and video supports when students select incorrect responses. These explanations model accurate problem-solving strategies, provide exemplar responses, and address common misconceptions. Rather than simply identifying errors, the materials guide students through the reasoning process necessary to arrive at the correct solution. As students review feedback, they refine their understanding and apply corrected strategies during subsequent practice opportunities.

Evaluation for 5.5a
TEKS process standards are integrated appropriately into the materials.

The 2nd Grade Math Scope and Sequence document embeds the TEKS mathematical process standards throughout the development of mathematical concepts. Students engage in problem-solving tasks as they explore place value, fractions, addition and subtraction, multiplication foundations, measurement, geometry, money, time, data analysis, and personal financial literacy through hands-on activities, visual models, and interactive lessons. Educators facilitate discussions that require students to explain their thinking, compare strategies, justify solutions, and represent ideas using mathematical tools, diagrams, symbols, and academic language. Throughout the course, students connect mathematical ideas and apply previously learned concepts in new situations, which strengthens mathematical reasoning and conceptual understanding.

In lesson 6 “Area,” the activities and instructional discussions directly integrate the process standards. Students use tiles, arrays, drawings, and models to determine area and compare surfaces. Educators model problem-solving strategies and encourage students to explain their reasoning using mathematical vocabulary. Through guided questioning, collaborative discussions, and hands-on investigations, students represent mathematical ideas using multiple tools and communicate conclusions about area using pictures, symbols, models, and verbal explanations, which is aligned with the TEKS.

Evaluation for 5.5b
Materials include a description of how process standards are incorporated and connected throughout the learning pathways.

The 2nd Grade Math Scope and Sequence demonstrates how the learning pathway embeds the process standards as students solve problems, communicate mathematical reasoning, use models and tools, and justify solutions while learning about number concepts, fractions, operations, measurement, money, time, geometry, area, data, and financial literacy. Students participate in activities, such as reading and writing numbers, comparing quantities, representing fractions, solving addition and subtraction problems, exploring foundations of multiplication and division, measuring length, determining area, identifying geometric attributes, collecting and analyzing data, and applying financial literacy concepts.

The Elementary Math Implementation Guide explains how the instruction integrates the process standards through structured learning experiences that require students to reason mathematically, solve problems, communicate thinking, and model mathematical situations. Students use number lines, place value charts, base 10 blocks, arrays, graphs, rulers, clocks, and geometric models to investigate mathematical concepts. Educators facilitate exploration, questioning, discourse, and reflection while students justify their reasoning, evaluate different strategies, and make connections among concepts. These recurring instructional structures connect process standards across lessons and provide a coherent progression of mathematical learning throughout the curriculum.

Evaluation for 5.5c
Materials include an overview of the TEKS process standards incorporated into each lesson.

The 2nd Grade Math Scope and Sequence document provides an overview of each lesson, including the content focus, aligned TEKS, and instructional expectations. Lesson descriptions show that students solve problems, explain thinking, use mathematical vocabulary, and represent concepts through models, diagrams, manipulatives, symbols, and written explanations. Educators facilitate discussions and ask guiding questions that encourage students to justify solutions, compare strategies, and communicate reasoning. Students actively participate by representing numbers, solving problems, measuring, classifying shapes, analyzing data, and explaining mathematical conclusions. These learning experiences demonstrate how daily instruction integrates reasoning, communication, representation, and problem-solving.

In lesson 12, students collect information, organize data into tables and graphs, interpret graphical representations, and communicate findings using mathematical language. Students apply problem-solving and reasoning skills as they analyze data, use mathematical tools and representations when creating graphs, and justify conclusions based on the information presented. Questions, such as “How many more students selected one category than another?” and “What patterns do you notice in the graph?” require students to explain reasoning and support conclusions with evidence.

Evaluation for 6.1a
Materials provide opportunities for students to think mathematically, persevere through solving problems, and to make sense of mathematics.

As students work through activities in their individualized Study Plans, students engage with skills, such as representing numbers to 1,200, comparing and ordering numbers, solving addition and subtraction problems within 1,000, measuring length, working with money, telling and writing time, identifying geometric shapes, and interpreting data. When students answer a question incorrectly, the Study Plans immediately provide targeted support through a video explanation that models the correct strategy and walks students through the steps needed to solve the problem. For example, if students incorrectly compare two three-digit numbers, the video may demonstrate how to use place value to compare the hundreds, tens, and ones digits. If students struggle to solve a multistep addition problem, the video may model how to use base 10 blocks, expanded form, or drawings to find the answer. This immediate feedback encourages students to revisit the problem, learn from their mistakes, and try again rather than give up.

In lesson 4 “Addition and Subtraction,” students think mathematically and make sense of addition and subtraction by using place value blocks, disks, strip diagrams, equations, and drawings to represent problems, guided by questions, such as “How does place value play a part when adding and subtracting larger numbers?” and “When is regrouping necessary?” For example, when solving 72 − 38, students use place value blocks to reason through the problem, discovering that there are not enough ones to subtract 8 from 2 and determining they must regroup a ten into ten ones. During the “Explore” and “Elaborate” sections of the lesson, students persevere through increasingly challenging multistep word problems, and educators support students’ struggle through probing questions and tools rather than direct answers. Students revisit problems, test different strategies, and revise their thinking, such as by solving a word problem about a student with 65 stickers who gives away 28, drawing models, and writing equations until they arrive at a justified solution.

Evaluation for 6.1b
Materials support students in understanding, explaining, and justifying that there can be multiple ways to solve problems and complete tasks.

In lesson 1 “Read and Write Numbers,” students use place value blocks and place value disks to explore and represent numbers in multiple ways. The lesson supports students in understanding that there can be more than one way to represent a problem by modeling numbers using concrete manipulatives, expanded form, standard form, and word form. For example, in the student activity, students examine base 10 block models showing hundreds, tens, and ones, then identify the same number in expanded form (e.g., 500 + 70 + 5), standard form (e.g., 575), and word form (e.g., five hundred seventy-five). As students use different representations, students develop flexibility in their mathematical thinking and learn that numbers can be expanded and decomposed in various ways. The lesson also supports students in solving problems and completing tasks using different strategies as students determine which tools and representations best communicate their thinking. Through class discussions, guiding questions, such as “How can you represent a number in different ways?” and independent practice activities, students justify their reasoning by explaining why their representation is accurate and how different representations can describe the same quantity.

In lesson 5 “Area,” students use color tiles and rectangular arrays to model area using rows and columns, which helps students visualize that area can be found in different ways. For example, in the student activity showing a rectangle with two rows and five columns, students can determine the area by counting each of the 10 square units individually or by using repeated addition (5 + 5 = 10) and multiplication. Likewise, students analyze larger arrays by identifying the number of rows and columns and explaining how these dimensions relate to the total area. Through hands-on modeling, classroom discussions, and guiding questions, such as “How can repeated addition help when finding the area of a rectangle?” students learn that different strategies can lead to the same correct answer. The lesson encourages students to justify their thinking by explaining why counting squares, using repeated addition, or applying multiplication accurately represents and solves the area problem, which builds flexibility in mathematical reasoning and problem-solving.

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.

In lesson 2 “Locate and Compare Numbers,” students locate, compare, and represent numbers using number lines, comparison symbols, and place value charts. Students work with partners and small groups to determine missing numbers on a number line, identify values between benchmark numbers, and explain their reasoning. Students compare numbers using the symbols for greater than (>), less than (<), and equal to (=) and record numbers in a place value chart showing thousands, hundreds, tens, and ones. For example, students determine that 35 belongs on the middle hatch mark between 30 and 40 and compare 78 with 87 by explaining that 78 is less than 87 because 78 has fewer tens. Educators facilitate mathematical discourse by asking questions, such as “What symbol represents greater than, less than, or equal to?” and “How can a place value chart help you when comparing whole numbers?” Students write about mathematics in the “Comparing Numbers Through Hundreds” class activity. In this activity, students analyze 549 and 594, determine which number is larger, and write to explain how they know.

In lesson 12 “Representing and Interpreting Data,” students collect, organize, and represent data using picture graphs, bar graphs, tally charts, and frequency tables. For example, students may survey classmates about favorite books, sports, or school subjects and record the results using graphs and tables. As students analyze the data, they write numbers, labels, and responses to questions, such as “Which category has the greatest number?” and “How many more students chose reading than science?” Recording and analyzing information helps students communicate their mathematical thinking and compare quantities. Educators encourage students to explain their observations, compare results, and justify conclusions using evidence from the graph or chart during think-pair-share discussions.

Evaluation for 6.2a
Materials support educators in guiding students to share and reflect on their problem-solving approaches, including explanations, arguments, and justifications.

Lesson 2 “Locate and Compare Numbers” presents situations in which students share their problem-solving approach when they determine which mathematical claim is correct, such as deciding whether 458 or 485 is greater and ordering a set of numbers from least to greatest. The materials direct educators to provide opportunities for students to discuss their reasoning with a partner before sharing with the class. For example, when comparing 458 with 485, students explain that 485 is greater because both numbers have 4 hundreds, but 485 has 8 tens while 458 has 5 tens. As partners discuss their reasoning, they construct mathematical arguments supported by place value understanding, listen to and evaluate different perspectives, ask questions, and defend their thinking.

In lesson 5 “Multiplication, Division, Odd, and Even,” students use counters, color tiles, arrays, instructional videos, and handouts to investigate odd and even numbers and explore multiplication and division concepts. Students learn different methods for determining whether a number is even or odd, such as by sorting counters, using skip counting, and thinking of their doubles facts. Then, students use one of the strategies to determine if a number is even or odd. As students share their strategy with the class, they are encouraged to reflect on their strategy. Mathematical arguments occur when students examine classmates’ claims, such as whether a number is odd or even, and use mathematical reasoning to support or challenge those claims. Students justify their answers by using arrays, counters, drawings, and mathematical vocabulary. In the second part of the lesson, through think-pair-share activities, partner discussions, and whole-class conversations, students continue reflecting on their problem-solving approaches by creating different arrays and discussing how various arrangements can represent the same quantity. For example, students may compare a 3 × 4 array and a 2 × 6 array and reflect on what they notice about both models. Students provide explanations by describing how equal groups and arrays represent multiplication and division concepts.

Evaluation for 6.2b
Materials include prompts and guidance to support educators in providing explanatory feedback based on student responses and anticipated misconceptions.

In the Study Plans, each student practices the standards taught during the lesson using randomized items aligned with the TEKS. As students respond to questions, the program evaluates their answers and provides immediate feedback. When students answer incorrectly, a video tutorial appears to explain the error, model problem-solving strategies, and guide students toward the correct solution. For example, if students incorrectly compare two three-digit numbers, the video may demonstrate how to use place value blocks or a place value chart to identify the greater number. If students struggle to solve an addition or subtraction problem, the explanation models strategies, such as using base 10 blocks to represent the problem. Educators can also assign standards-based activities through the Assignments feature, which allows all students to receive the same questions while still benefiting from individualized explanatory feedback. In addition, educators may use “SuperSheets” to analyze student work, identify misconceptions, and provide targeted feedback that reinforces mathematical concepts and promotes mastery.

In lesson 4 “Addition and Subtraction,” the educator notes provide specific guidance that helps educators deliver explanatory feedback based on student responses and anticipated misconceptions. For example, the notes instruct educators to ask students to represent one-step and multistep word problems using equations and strip diagrams. This guidance helps students connect mathematical symbols to real-world situations. If students incorrectly identify the operation needed to solve a problem, the materials guide educators to model the situation with manipulatives and encourage students to explain each step of the solution process. Additionally, the lesson anticipates that some students may struggle to distinguish between situations requiring addition and those requiring subtraction. The educator notes address this misconception by encouraging students to analyze key information, model the situation with concrete materials, and explain how the quantities in the problem relate to the operation selected. These supports help educators provide meaningful explanatory feedback and deepen students’ understanding of mathematical problem-solving.