Progress Learning 1st 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 1st 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 1st Grade Math Scope and Sequence includes a “First Grade Lesson Sequence Rationale” section that explains how each lesson connects to prior and future learning. For example, this section explains that students use their place value knowledge gained in lesson 1 to compare two numbers using symbols and comparative language in lesson 2. In addition, lesson 2 prepares students for the addition and subtraction strategies presented in lesson 3 by helping students visualize where numbers sit in relation to one another on an open number line.

Each lesson includes “Looking Back” and “Looking Ahead” sections that list the grade K TEKS and grade 2 TEKS aligned with the lesson. For example, lesson 2 “Compare and Order Numbers” states that students will build on generating a number that is one more than or one less than another number (TEKS K.2F), comparing sets of objects (TEKS K.2G), and using comparative language to describe two numbers up to 20 (TEKS K.2H). The same lesson states that students will use the skills developed in this lesson in grade 2 when students use place value to compare and order numbers to 1,200 (TEKS 2.2D) and use place value understanding to determine the number that is 10 or 100 more or less than a given number (TEKS 2.7B).

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 1st 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 students demonstrate strength in number recognition but show weaknesses in addition within 10, educators can consult the TEKS chart in the 1st Grade Math Scope and Sequence document 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 3 “Adding and Subtracting Numbers,” educators activate prior knowledge in the “Engage” section by asking students to solve addition problems within 10. Then, students explore addition and subtraction concepts using manipulatives. Students discuss the strategies they used for solving problems during the “Explain” section and apply their learning through practice and assessment tasks. The 1st 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 7 “Family Support” section tells families to play I Spy using shape attributes, such as “I spy something with four equal sides and four corners.” 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, SuperSheets, 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 SuperSheets 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 “Representing Problems” lesson provides course-specific administration guidance. The “Evaluate” section identifies the assessment as the “Representing Problems SuperSheet” and provides an approximately 20-minute administration window. Educators can administer the assessment in two formats: a printable version or a digital version. For example, this SuperSheets assessment includes printable educator directions that state, “Encourage students to point to the square and identify that the square represents the missing number,” which ensures consistent administration across classrooms.

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 Guide, the “Evaluate” section explains that educators can “locate and print the SuperSheets 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 include 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 identifying two-dimensional shapes, educators can choose from several recall questions that give students a specific attribute, such as a shape with three sides, and ask students to select the shape that does not belong. A skill/concept-level question for this standard asks students to drag and drop shapes into the correct categories (rectangle, triangle, rhombus, and hexagon). Finally, an example of a strategic-thinking question shows students two shapes, and students have to name the shapes and identify how many sides each shape has.

The materials also include more than two unique interactive item types. The pre-assessment item types includes 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 numbers, 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 “Money” lesson lists “A” as the correct answer to question 1 to confirm that students correctly identified a quarter. The answer key states that if students chose “B,” they mistakenly chose the nickel instead of the quarter, and that if students chose “C,” they mistakenly chose the dime instead of the quarter.

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, in lesson 9 “Three-Dimensional Shapes,” the Teacher Guide states that students using geometric vocabulary when describing three-dimensional shapes is important. The slide deck that accompanies the lesson asks students to identify various three-dimensional shapes and then reviews the shape attributes (i.e., faces, edges, and vertices) as the slides highlight them on the images. The slide deck also reinforces academic vocabulary by pointing out real-life objects that are cylinders, spheres, etc.

In addition, the 1st Grade Math: Educator Guide for Pre-Teaching Vocabulary and Text Supports document provides a structured four-step vocabulary routine that requires educators to model and pronounce academic terms, provide student-friendly definitions, connect vocabulary to visual anchors and manipulatives, and engage students in partner discussions using sentence stems. For example, the routine introduces key mathematics vocabulary (such as digit, expanded form, hundreds, tens, ones, place value, and standard form) using base 10 blocks and place value mats so that students can build conceptual understanding before reading or engaging with mathematical text. The materials also support comprehension of unfamiliar visual and textual references by explicitly teaching students how to navigate a 120 chart, recognize subitizing patterns on ten frames, and interpret place value models, including the understanding that flats represent 100, rods represent 10, and units represent 1. Additionally, sentence stems, such as “The digit _____ in the tens place means _____,” encourage students to practice academic language and apply new vocabulary in meaningful contexts before beginning the lesson. The materials also include a “Unit-by-Unit Pre-Teaching and Text Reference Guidance” table that provides educators with 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 “Working with Shapes” suggests that educators assign the grade 2 video “Four Types of Polygons” 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” or “Challenge” 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 1: Represent Numbers includes a “Challenge” activity in which students use what they have learned about place value relationships with two-digit numbers to fill in the missing numbers on a 120 chart.

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, lesson 6 “Money and Time” shows students images of nickels and dimes and asks students to count by 5's or 10's to find the total value. The materials guide educators in providing play money to help students count by 5's or 10's to determine the total amount of the coins. Then, students use whiteboards to write the number.

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, lesson 8 “Partitioning Objects” includes an “Engage” question that asks students to identify squares from a set of shapes. Educators facilitate a brief whole-class discussion about two-dimensional shapes. 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 10 “Data” includes questions such as “How do you use tally marks?” and “What is data?” 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 6 “Money and 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, SuperSheets 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 “Adding and Subtracting Numbers,” educators start by modeling how to solve a problem, such as 12 + 4, using linking cubes. Students first solve this problem using the “count on” strategy and then using the “make a 10” strategy by decomposing 12 into 10 and 2. As students continue to practice the “make a 10” strategy, the materials remind educators that students can continue to use linking cubes to solve as needed. 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 concepts 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 3 “Adding and Subtracting Numbers” contains concrete and visual engagement strategies, such as five-group cards, number bonds, and manipulatives, to help students compose and decompose numbers, which allows students to move from counting all to counting on. Students engage in math dialogue and discourse by explaining their thinking in response to prompts, such as “What is the relationship between addition and subtraction?” and “How do you find the missing part of a whole?” 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 5 “Measurement” includes intentional prompts and guidance that support educators by providing feedback as students explore and compare the length of various objects using centimeter cubes, paper clips, and rulers. The Teacher Guide provides questions, such as “Why is it important for measuring tools to be connected with no gaps?” and “Where should you start measuring on a ruler?” 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 1st Grade Cooperative Learning & ELPS Strategy Guide outlines all the 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 EB 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 1: Build & Compose Buddy (Place Value & Representing Numbers 1–120),” the materials suggest that students at the Pre-Production level demonstrate understanding of place value by manipulating base 10 blocks to match a target number and using visual supports while a partner models the correct number representation. At the Beginning level, students identify place value using simple words and sentence starters, such as naming the number of hundreds, tens, and ones, with support from a word bank. Students at the Intermediate level use sentence frames to describe the value of digits, represent numbers in expanded form, write place value representations, and explain their thinking aloud. At the High Intermediate level, students use academic vocabulary, such as decompose, expanded form, and digit value, to explain how numbers can be broken apart into hundreds, tens, and ones and represented in different ways. Finally, at the Advanced level, students justify place value reasoning by explaining how base 10 blocks represent numbers, describing why decomposing and recomposing numbers do not change their value, and coaching peers through the process of converting standard form to expanded form.

Additionally, in “Strategy 2: Make-10 & Strip Diagram Storytellers (Addition & Subtraction Word Problems),” students at the Pre-Production level demonstrate an understanding of addition and subtraction word problems by using linking cubes and strip diagrams to physically model joining and separating actions after a partner’s verbal guidance. At the Beginning level, students identify key action words and quantities from a story problem, use a word bank for support, and complete simple sentence starters to determine whether to add or subtract. Students at the Intermediate level use sentence frames to explain how quantities change in a word problem, write matching equations, identify unknown numbers, and describe the mathematical process. At the High Intermediate level, students apply strategies, such as making a ten, and use academic vocabulary to explain whether a situation represents addition or subtraction and how equations remain balanced. Finally, at the Advanced level, students justify mathematical reasoning by explaining why equations are true, proving solutions with evidence from the word problem, and connecting the relationship between the whole and its parts using precise mathematical language.

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 mathematical concepts during instruction through partner activities, such as think-pair-share. For example, in lesson 10 “Data,” students discuss how tally charts, picture graphs, and bar graphs show 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 1 “Represent Numbers” includes several supports for EB students. The “Teacher Facilitation and Cross-Linguistic Notes” indicate that the lessons incorporate cross-linguistic connections through oral discourse by providing explicit cognates and structured opportunities for mathematical discussions before students complete written tasks. Students engage in oral language when they discuss place value concepts and mathematical representations with peers and educators. The Exit Ticket for lesson 4 supports the development of academic vocabulary and comprehension through written discourse when students must determine whether 12 − 8 = 11 − 5 and write about how they know when given a sentence stem. In addition, the lesson promotes cross-linguistic connections through written discourse when students apply mathematical vocabulary that may correspond to equivalent terms in their primary language and complete written responses. However, the materials do not provide opportunities for building background knowledge through written discourse.

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, in lesson 8 “Partitioning Objects,” educators guide students through hands-on practice with counters, connecting cubes, visual models, partner discussions, and independent problem-solving as students partition sets of objects into equal and unequal parts. Students represent their thinking using concrete and pictorial models and describe the relationship between parts and the whole. Students then complete the “SuperSheets” assessment “Partitioning Objects” that requires them to separate sets into parts, identify and describe those parts, and represent their thinking through drawings or equations, thereby demonstrating an understanding of partitioning aligned with the TEKS.

In lesson 7 “Working with Shapes,” students consistently demonstrate a deep understanding of TEKS through hands-on practice and embedded instructional assessments. Students identify, describe, and compare two-dimensional shapes using attributes, such as sides and corners, and extend their understanding by composing new shapes and classifying figures as regular or irregular. The lesson includes manipulatives, such as tangrams and pattern blocks, that encourage students to explain how shapes are alike and different and to support their reasoning with mathematical language. Educators guide discussions by asking questions, such as “How are these shapes the same?” and “What makes this shape different?” to promote deeper thinking. Students then complete independent and “SuperSheets” tasks in which they sort shapes, create composite figures, and explain their reasoning, which reinforces their understanding of geometric attributes aligned with the TEKS.

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 their complexity increases. For example, in lesson 5 “Measurement,” the “Engage” section helps students activate prior knowledge by comparing objects using measurement vocabulary, such as longer and shorter. The “Explore” section allows students to connect their prior understanding to grade-level expectations by measuring objects with nonstandard units, such as cubes and paper clips. Students describe their findings and determine object lengths, 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 1 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 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 6 “Money and Time,” students begin by identifying coins and reading time to the hour, then move to hands-on experiences using play coins and analog clocks to count collections and represent time. In the extension activity for this lesson, students count mixed coins beyond one dollar, represent the same value in multiple ways, and describe simple elapsed time. 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 1st 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. For example, students progress from understanding the structure of numbers up to 120 in lesson 1 to comparing numbers in lesson 2 and applying relationships, such as greater than and less than. This understanding is extended in lesson 3 as students develop strategies for basic facts within 20 and further applied in lesson 4 when solving word problems. This sequence demonstrates coherence by reinforcing the big idea of number relationships across different contexts—counting, comparing, and operations—so that students deepen their understanding through consistent patterns and relationships.

Each lesson activates prior knowledge taught earlier in the course or in grade K and connects it to new learning. In the “Engage” section of lesson 9 “Three-Dimensional Shapes,” educators begin by reviewing the attributes of two-dimensional shapes and extend this understanding to three-dimensional figures. Students apply their prior knowledge of sides and vertices to new concepts, such as faces and edges, while working with real-world objects, such as boxes and cans. Through discussion and hands-on activities, students identify patterns and relationships among shapes, which reinforces key concepts, such as classification and comparison. This consistent connection across lessons supports a strong, integrated understanding of mathematical ideas at the grade level.

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. In lesson 2 “Comparing and Ordering Numbers,” the “Looking Ahead” section shows how understanding comparisons, such as more, less, and equal, connects to what students will do in later grades. The section demonstrates that ideas, such as more, less, and equal, will become important when students begin comparing larger numbers and locating numbers on an open number line in grade 2. These early comparisons help students recognize relationships between numbers and build a foundation for combining and separating quantities in later grades. This vertical alignment helps students see how current learning fits into a larger mathematical progression.

Additionally, the “For Advanced Learners” section in the “Additional Activities for Intervention and Enrichment” section extends this coherence across the K–6 grade bands. In lesson 8 “Partitioning Objects,” advanced students extend their understanding of halves and fourths in grade 1 to eighths. 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 students’ prior knowledge by reviewing skills, such as counting, recognizing numbers, and grouping objects. These foundational skills support new learning in grade 1, including addition, subtraction, place value, and problem-solving. Students apply what they already know to combine groups, separate quantities, and represent their thinking using manipulatives, drawings, and equations, which strengthens their understanding and makes meaningful connections across lessons.

For example, in lesson 4, students build on their prior understanding of joining and separating objects by using manipulatives to model addition and subtraction situations. Students transition from hands-on models to drawings and eventually to number sentences, which demonstrates a progression from concrete to abstract thinking. Students solve word problems within 20, explain their reasoning, and connect their strategies to prior experiences. The lesson also prepares students for future learning by introducing concepts, such as grouping tens and ones and using multiple strategies, which supports readiness for more-advanced problem-solving and place value concepts in grade 2.

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 practice and to 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 1 mathematics by giving students short, focused opportunities to revisit key skills, such as counting, comparing numbers, and recognizing shapes. For example, students may begin a lesson by ordering numbers, identifying which group has more, or partitioning sets of objects. These activities activate prior knowledge and provide spaced retrieval, which helps students strengthen foundational concepts and build long-term retention.

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

The Assessment Bank supports interleaved practice by intentionally combining a variety of math skills in a single assessment so that students regularly shift between concepts and apply appropriate strategies. For example, students may solve an addition problem, count forward in a sequence, compare groups, and identify shapes, which requires students to apply multiple skills in one task. This approach reinforces connections between concepts and promotes flexible thinking.

In lesson 8 “Partitioning Objects,” students engage in interleaved practice when they divide shapes and objects into equal parts and apply previously learned skills, such as counting, addition, and shape recognition. Students count the number of equal parts, relate those parts to whole numbers, and combine parts to form a whole, which integrates operations and number sense. By connecting partitioning to earlier lessons on numbers, operations, and geometry, the materials provide meaningful opportunities for students to practice across learning pathways, which strengthens understanding and promotes deeper connections across mathematical concepts.

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 “Compare and Order Numbers,” students use place value blocks, counters, and hundreds charts to represent and compare numbers within 120. Students build numbers with tens and ones and compare them using terms, such as greater than, less than, and equal to. Students explain their thinking by answering questions, such as “Which number is greater?” and “How do you know?” During partner and class discussions, students compare models and determine whether they accurately represent numbers. Students identify errors and use evidence from models to justify their conclusions.

In lesson 3 “Adding and Subtracting Numbers,” students use images of base 10 blocks and linking cubes to model the “make ten” strategy. Then, students use linking cubes to model and story problems and explain how quantities change when objects are joined or separated. During think-pair-share discussions, students compare models and determine whether each representation matches the story problem and equation. Students identify errors in representations and explain their reasoning using evidence from the model. During class discussions, students justify their thinking and explain why one representation is more accurate than another.

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, students represent numbers by building and drawing. Educators model how to use place value blocks, counters, or connecting cubes to represent numbers, then ask students to create their own representations. For example, when educators say, “Show me 24,” students build the number using two tens and four ones. Next, students draw a picture of the same number to make a direct connection between the objects and the drawing. Students describe their thinking by explaining how their picture matches their model (e.g., “I drew two tens and four ones because I used two tens rods and four cubes.”).

In lesson 7 “Working with Shapes,” students use pattern blocks, craft sticks, straws, or other manipulatives to construct triangles, rectangles, squares, hexagons, and other two-dimensional shapes, focusing on each shape’s attributes, such as its sides and vertices. After building, students arrange pattern blocks or tangram pieces to form new figures, then explain how the smaller shapes combine to make a larger shape. Educators ask guiding questions, such as “How many sides does your shape have?” and “Which shapes did you use to build it?” Students also complete a matching task in which they locate shapes on a handout and color them according to the directions.

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

In lesson 4 “Representing Problems,” 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 counters, cubes, or place value models to build each group shown in the picture, then combine them to find the total. Some students draw pictures to show their thinking, such as by sketching the objects and counting them as they add. For example, students might model 12 flowers and seven more flowers with cubes, push the groups together, and say the total is 19. Students also explain how they used counting and addition to solve the problem.

In lesson 5 “Measurement,” students learn to measure the length of objects using centimeter cubes and paper clips. Students progress from measuring physical objects with centimeter cubes and paper clips, discussing why measurements of the same object can differ, to measuring pictures of objects in their handouts. Students complete a culminating activity in which they find objects around the room to measure. This activity allows students the opportunity to apply what they have learned about measuring length during the lesson to a new situation.

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 counting, comparing numbers, place value, and basic addition and subtraction, multiple times. For example, educators may display a number card and ask students to identify one more or one less, or educators may show two numbers and ask which is greater. 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 “Represent Numbers,” educators help students develop automaticity and fluency by engaging students in repeated, hands-on activities that connect quantities to numerals and place value. Educators present groups of base 10 blocks, counters, or pictures, and students count and organize the representations into tens and ones. For example, students build the number 27 using two tens and seven ones and then match the model to the numeral “27.” Educators also use visual tools, such as hundreds charts, number lines, and ten frames, to encourage quick recognition and efficient counting strategies. Students practice counting forward, identifying numbers, and representing numbers in both whole-group and small-group settings.

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 strategies, counting-on strategies, and number relationships rather than counting all objects from the beginning, which helps them solve problems more quickly. The materials promote flexible procedures by encouraging students to solve problems in different ways, such as using base 10 blocks, drawings, number lines, hundreds charts, or equations to check their thinking. For example, students may represent 34 using base 10 blocks and then verify the value using a place value chart or by counting by tens and ones. 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 their strategies, verify their solutions, and explain how they know their answers are correct.

In lesson 7 “Working with Shapes,” students practice applying efficient, flexible, and accurate mathematical procedures by creating and analyzing shapes in various ways. Students use pattern blocks, straws, craft sticks, or tangram pieces to build triangles, rectangles, squares, hexagons, and other two-dimensional shapes and describe the shapes’ sides and vertices as they work. Students then combine smaller shapes to create composite figures and explain how the shapes fit together and what attributes they observe. Students also identify, sort, and color specific shapes on a handout, which reinforces recognition and classification skills.

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 3 “Adding and Subtracting Numbers,” students use counters, number lines, drawings, and mental math strategies to solve addition and subtraction problems. Students compare different strategies and determine which methods are most efficient. For example, students may recognize that counting on from 8 is faster than counting all 13 objects. Students solve the same problem using different tools and representations. Students also evaluate accuracy by checking whether each strategy produces the correct answer and explain their reasoning.

In lesson 10 “Data,” students view a collection of responses about favorite fruit and favorite lunch choice, count the responses, and organize the data using tally charts, picture graphs, and simple bar graphs. Students evaluate efficiency when deciding whether comparing categories by reading the graph is faster than recounting every object. Students evaluate flexibility by answering questions using different approaches, such as counting pictures, comparing graph columns, and using number comparisons. During the “Show What You Know!” portion of the lesson, students assess accuracy by determining which tally chart matches a given data set.

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. In one approach, students think, pair, and share their strategies, which allows students to hear how classmates solved the same problem in different ways, such as by building numbers with manipulatives and using place value reasoning. In another approach, students first work independently using tools, such as drawings, number lines, and base 20 blocks, then explain their processes during a whole-class discussion. In the “Elaborate” section, educators direct students to tasks that connect to their Study Plans, in which they revisit skills and try improved strategies, such as moving from counting all to counting on and using place value patterns.

In lesson 2 “Compare and Order Numbers,” students progress from using concrete objects to using mental number strategies as they build fluency with number relationships and place value. Students begin by using base 10 blocks and connecting cubes to build and compare numbers. As students gain confidence, they transition to using hundreds charts, place value charts, and mental strategies to determine which numbers are greater than, less than, or equal to without physically building each number. For example, students who initially build 42 and 47 with blocks may later explain that 47 is greater because both numbers have four tens, but 47 has more ones.

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

The 1st Grade Math Scope and Sequence clearly develops both conceptual understanding and procedural fluency as students move from representing and comparing numbers to solving addition and subtraction problems and exploring measurement, geometry, fractions, money, time, and data. Educators guide students to explain how numbers represent quantities and relationships, and students also practice skills, such as composing and decomposing numbers, comparing values, solving equations, and representing mathematical situations using models and symbols. As instruction continues, students connect ideas across strands. For example, students measure objects, identify geometric attributes, partition shapes, tell time, and interpret data while applying procedures, such as counting, comparing, recording, and solving problems.

In lesson 7 “Working with Shapes,” students build conceptual understanding by identifying the attributes of two-dimensional shapes and using precise vocabulary, such as sides and vertices, and hands-on tasks reinforce procedural skills. Students first locate and color shapes on a handout to strengthen recognition and classification, then construct shapes using craft sticks, pattern blocks, or other manipulatives to model attributes and compare shapes. Students extend this thinking by composing larger figures from smaller shapes, showing how two-dimensional shapes can be combined to create new designs, and practicing procedures for building, sorting, and describing shapes.

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 “Represent Numbers,” educators use slides and Student Explore Worksheet 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 students count the blocks aloud to connect quantities to number names. The hundreds chart on the slide helps students recognize number patterns as students point to numbers, count forward, and describe how numbers increase, and the Student Explore Worksheet assignment asks students to circle, 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, which strengthens students’ ability to represent quantities without physical manipulatives. Educator questions on the slides, such as “How many tens 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 lesson 5 “Measurement,” students begin by measuring classroom objects with nonstandard units, such as cubes and paper clips, physically placing each unit end to end, and counting how many units are needed. Then, students turn to the Student Explore Worksheet assignment to sketch what they measured by drawing the object and recording the units of measurement to connect the hands-on activity to a pictorial representation. 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 as 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, and cubes, to pictorial drawings displayed on the screen and then to numbers, symbols, or equations they record on their papers. Students create their own representations in “SuperSheets” assignments by drawing objects, modeling quantities, or writing equations 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 “Compare and Order 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 work mats to create concrete representations of quantity, then count and organize tens and ones in preparation for comparison. Working with a partner, students align models, compare place value representations, and use hundreds charts 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 students 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, visuals, and mathematical discussions. Educators use visual models and representations shown in the videos to introduce mathematical concepts and guide students in describing what they notice using precise mathematical vocabulary. During class discussions, educators ask open-ended questions that encourage students to explain their reasoning, compare strategies, and justify their answers. Students actively participate by discussing mathematical ideas with peers; using terms related to numbers, operations, measurement, geometry, and data; and explaining how visual models support their thinking.

In Lesson 1 “Represent Numbers,” the materials provide opportunities for students to develop academic mathematical language through visuals and hands-on manipulatives, such as connecting cubes, counters, number lines, base 10 models, and ten frames. Students represent and identify numbers up to 120 and explain the value of digits using structured prompts and sentence stems. The lesson introduces important vocabulary terms, including digit, number, represent, tens, ones, greater than, and less than, which are reinforced through colorful visuals and interactive activities. Educators model how to represent numbers using multiple representations and explain mathematical thinking using precise language. Students build numbers with manipulatives, identify tens and ones, compare quantities, and explain their reasoning using complete sentences, such as, “The number 47 has 4 tens and 7 ones.”

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 conversations with peers and educators. The guide provides structured discourse routines, such as “Use-It-To-Do-It” and “Ping Pong Peer Vocabulary,” which help educators introduce new mathematical terms, model their correct use, and gradually release responsibility to students. Educators explicitly define and demonstrate vocabulary in mathematical tasks, then prompt students to use those terms when explaining their thinking and responding to classmates. Students practice using academic language in meaningful contexts as they discuss solutions, ask questions, and justify answers during partner and whole-group discussions. These routines encourage students to move beyond single-word responses and communicate mathematical ideas using complete sentences and precise vocabulary, which strengthens both mathematical understanding and oral language development.

In lesson 2 “Compare and Order Numbers,” the materials include embedded educator guidance that scaffolds students’ use of academic mathematical vocabulary through structured prompts, visual representations, hands-on manipulatives, and educator modeling. Educators use support notes that guide them to explicitly model terms, such as greater than, less than, equal to, compare, and order, when examining sets and numerals. For example, educators think aloud while comparing two numbers represented with base 10 blocks and demonstrate how to describe the comparison using complete mathematical statements. The materials provide guiding questions, such as “Which number is greater? How do you know?” and sentence frames, such as “_____ is greater than _____ because . . .,” to help students communicate their ideas. Students use place value models and number lines to compare and order numbers and explain their reasoning to partners and educators using academic vocabulary in context. As students gain confidence, educators extend students’ language by prompting students to justify their answers, explain multiple strategies, and respond to classmates’ explanations.

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 that helps students consistently use mathematical language and academic vocabulary during instruction and discussion through structured discourse and vocabulary routines. During the “Vocabulary Scavenger Hunt” routine, students search lesson materials, visuals, manipulatives, and word walls to locate terms, such as number, compare, greater than, less than, equal, addition, subtraction, measurement, and data, then explain the meaning of each term to a partner and identify examples in the lesson. In the “Use-It-To-Do-It” routine, educators model academic language and provide sentence stems, such as “I know _____ is greater than _____ because _____” and “I solved the problem by _____,” and students use precise vocabulary to explain strategies and defend solutions. The Tiered Vocabulary Scaffolds support students by introducing picture cues, gestures, and simplified explanations before progressing to grade-level mathematical terminology. Through the “Ping Pong Peer Vocabulary” routine, students take turns discussing problems with a partner and intentionally incorporating target vocabulary into their responses. Extension Prompts challenge students to elaborate by explaining why a strategy works, comparing multiple solutions, or connecting new vocabulary to previous learning. Additionally, Cognate Callouts highlight connections between English and Spanish mathematical terms, such as compare to comparar and equal to igual, which helps multilingual students strengthen vocabulary comprehension.

In lesson 5 “Measurement,” the materials provide explicit guidance to help students apply mathematical language through a structured think-pair-share discourse routine. During the “Explain” section of the lesson, educators present a lesson video and introduce key vocabulary, including length, height, measure, unit, longer, shorter, and estimate. Students first think independently about comparison and measurement questions, such as “Which object is longer?” and “How many units long is the pencil?” and use the vocabulary to formulate responses. Next, students pair with a classmate to discuss observations using complete sentences, such as “The book is longer than the marker because it measures 8 units.” As partners exchange ideas, they compare measurements, ask follow-up questions, and clarify their reasoning using the academic vocabulary introduced in the lesson. During the share phase, students present their conclusions to the class, explain how they measured an object, and support their responses by referring to measurement tools and representations. Educators facilitate the discussion by prompting students to defend their reasoning, restate a partner’s explanation using mathematical language, and make comparisons using the terms longer, shorter, and measure.

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 structured prompts that encourage students to explain their thinking and respond to classmates using mathematical vocabulary. Educators can incorporate sentence stems, such as “I know _____ because _____,” “I agree with _____ because _____,” and “My answer is _____ because _____,” during partner discussions and think-pair-share activities. As students listen to their peers’ explanations, students hear mathematical language in context and refine their own responses by building on ideas shared in conversation. The materials encourage educators to use slideshows and discussion prompts to guide discourse and provide opportunities for students to communicate their reasoning using complete sentences.

In lesson 7 “Working with Shapes,” the materials provide embedded guidance that facilitates mathematical conversations and encourages students to hear, refine, and use mathematical language with peers. In the educator notes for the lesson slides, the materials direct educators to allow students to describe and compare two-dimensional shapes and explain the attributes they observe. During a think-pair-share routine, students discuss shape attributes with partners using geometric vocabulary, such as side, vertex, vertices, shape, rectangle, square, triangle, circle, straight sides, and curved sides. 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. The slideshow continues to prompt partner conversations as students analyze and compare various two-dimensional shapes. For example, when introducing a rectangle, educators stay, “Talk to your partner. How would you describe this rectangle?” Students use academic vocabulary to describe attributes, such as four sides and four vertices, and compare their ideas with classmates. Students may also discuss how a square and a rectangle are alike and different by referring to the number of sides and vertices. Through educator-facilitated discussions, students explain their observations, respond to classmates’ reasoning, and refine the use of precise mathematical language.

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 10 “Data,” the materials include embedded guidance that anticipates a variety of student answers as students interpret graphs and organize data. The Teacher Guide provides discussion questions that encourage students to analyze graph results and explain their reasoning using evidence from the displayed data. As students respond, educators facilitate discussion by asking follow-up questions that help students clarify their thinking and justify their conclusions. The materials support educators by providing expected responses and prompts that encourage students to accurately describe which categories have more, fewer, most, or least data points. When students misread a graph or make inaccurate comparisons, educators use targeted questions to redirect students’ attention to the data and guide them toward a correct interpretation. These supports help educators anticipate different student responses, reinforce accurate mathematical reasoning, and address misconceptions during classroom discussions.

The Elementary Math Implementation Guide further supports educators in anticipating a range of student responses through the “Elaborate” section of the 5E Instructional Model. In this section, students apply newly learned concepts by completing practice activities in their Study Plans, which include randomly selected items aligned with the lesson standards. The materials provide exemplars and immediate instructional support by giving students access to video explanations when they answer an item incorrectly. These explanations model correct problem-solving processes, demonstrate accurate mathematical reasoning, and provide exemplar responses that help students understand how to approach similar tasks. When students make errors, the materials do more than identify an incorrect answer. They actively guide students through each step of the solution and redirect misconceptions through targeted explanations. 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 1st Grade Math Scope & Sequence Guide document intentionally embeds the TEKS process standards throughout the development of mathematical concepts. Students engage in problem-solving tasks as they explore number sense, operations, measurement, money, time, geometry, fractions, and data through hands-on activities, interactive practice, and visual models. The materials guide educators to facilitate discussions in which students explain their thinking, compare strategies, and justify solutions using manipulatives, pictures, symbols, and mathematical language. As students progress through lessons, students make connections among mathematical ideas by representing concepts in multiple ways and applying previously learned skills to new situations, which strengthens both conceptual understanding and mathematical reasoning.

In lesson 5 “Measurement,” the lesson slides and instructional activities directly integrate the process standards. Educators model how to measure and compare objects using nonstandard and standard measurement tools, and students use pictures, diagrams, classroom objects, and mathematical vocabulary to communicate their observations and reasoning. Students represent and compare measurements using different nonstandard units, such as paperclips and centimeter cubes; discuss why measuring an object’s length requires fewer paperclips than centimeter cubes; and justify their conclusions using multiple representations, including drawings, measurement models, symbols, and spoken language.

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

The 1st Grade Math Scope & Sequence Guide demonstrates how the learning pathway embeds the process standards as students actively solve problems, explain their mathematical thinking, use models and representations, and justify their solutions when learning number concepts, operations, measurement, money, time, geometry, and data. Students participate in activities, such as representing numbers with concrete and pictorial models, comparing and ordering numbers, solving addition and subtraction problems, measuring and comparing the lengths of objects, identifying and describing two- and three-dimensional shapes, partitioning shapes into equal parts, telling time to the hour and half-hour, recognizing coins and their values, and collecting and interpreting simple data. The materials intentionally build these skills from one lesson to the next lesson and guide educators in facilitating mathematical discussions and providing opportunities for students to connect concepts and apply reasoning in a variety of situations. As students progress through the sequence, they consistently communicate their thinking, explain solution strategies, and use multiple representations to demonstrate understanding, reinforcing mathematical reasoning throughout the program.

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 their thinking, and use representations to develop understanding. Students engage in activities, such as discussing addition and subtraction strategies with peers; using drawings, ten frames, number lines, and manipulatives to model mathematical situations; exploring the attributes of shapes; measuring objects; interpreting class-generated graphs; justifying answers during class discussions; and applying concepts during guided and independent practice. The materials support educators in facilitating exploration, questioning, and mathematical discourse and encouraging students to explain their reasoning and evaluate different approaches.

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

The 1st Grade Math Scope & Sequence Guide provides an overview of each lesson by identifying the content focus, aligned TEKS, and instructional expectations. Lesson descriptions show that students solve problems, explain their thinking, use mathematical vocabulary, and represent ideas with models, drawings, and manipulatives. Educators facilitate discussions, model strategies, and ask guiding questions that encourage students to share and compare their thinking. Students participate by representing numbers, comparing quantities, solving addition and subtraction problems, measuring objects, collecting data, and explaining how they arrived at an answer. During partner and whole-group discussions, students justify their solutions, listen to classmates’ strategies, and make connections between different approaches. These opportunities for active engagement demonstrate how the lessons incorporate and the daily instruction embeds reasoning, communication, representation, and problem-solving.

Lesson 10 “Data” provides an overview of the TEKS process standards in the lesson’s “Standards” section that identifies the mathematical process standards and content standards addressed in the lesson. The materials connect these standards to the lesson’s data investigation in which students collect information about topics, such as favorite school activities or favorite fruits; record responses; and organize the results using tally charts, picture graphs, and bar-type representations. For example, students apply problem-solving and reasoning skills by collecting and sorting data, use mathematical tools and representations by creating charts and graphs, and communicate mathematical ideas by explaining which category has more, fewer, most, or least responses. The lesson also prompts students to justify their conclusions by answering questions, such as “How many more students chose recess than art?” and discussing patterns students observe in the graph with partners and the class.

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 Study Plans, students engage with skills, such as representing numbers up to 120, comparing and ordering numbers, solving addition and subtraction problems within 20, measuring objects, telling time to the hour and half-hour, identifying two-dimensional and three-dimensional shapes, and interpreting data. When students answer a question incorrectly, the Study Plan immediately provides 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 numbers, the video may demonstrate how to use a number line or a set model to determine which number is greater. If students struggle to solve an addition problem, the video may model how to use counters, ten frames, or number relationships 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 3 “Adding and Subtracting Numbers,” students think mathematically as they use manipulatives, such as counters, connecting cubes, ten frames, number lines, and drawings, to model addition and subtraction situations. For example, students may combine two groups of cubes to find a sum or separate a group to find the difference, and students explain their strategies to classmates. Students persevere by solving story problems that require students to represent, solve, and justify solutions using different methods. The lesson encourages students to try multiple strategies, revisit their representations, and correct mistakes when needed. Students make sense of mathematics by connecting addition and subtraction concepts to real-life situations, such as adding collections of classroom supplies, determining how many students are present, and finding how many items remain after some are removed.

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

The instructional videos included in the online platform provide visual models and real-world scenarios that demonstrate different approaches to the same mathematical task. For example, when learning addition, students may watch a video showing one student solving a problem with connecting cubes, while another student uses a number line or ten frame. Similarly, subtraction videos may model removing objects, counting back, or using related addition facts to determine a solution. During and after viewing the videos, students engage in educator-led discussions and think-pair-share activities to compare strategies, explain how they solved the problem, and justify why their solution works. The videos encourage students to recognize that mathematical problems can be represented and solved in multiple ways using manipulatives, drawings, equations, spoken explanations, and concrete models.

In lesson 7 “Working with Shapes,” the materials support students in understanding that there are multiple ways to represent and construct shapes by providing a variety of hands-on tools, including tangrams, craft sticks, straws, and geoboards. Students learn that the same shape can be represented using different materials, sizes, and orientations while still maintaining its defining attributes. For example, one student may build a rectangle with craft sticks, while another student builds the same rectangle with straws. Students explain and justify that there are multiple ways to complete shape-building tasks. As students share their work with partners, students describe attributes, such as sides, vertices, straight edges, and equal lengths. During partner discussions, students compare their representations and explain how each model meets the shape’s requirements. Students then justify their thinking by identifying the defining attributes that make their representations correct, regardless of the material, size, or orientation used.

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 1 “Represent Numbers,” students actively represent numbers up to 120 using manipulatives, such as counters, linking cubes, ten frames, place value mats, and drawings. Students work collaboratively with classmates to build numbers, compare representations, and explain how they determined the value of a number. Educators facilitate mathematical thinking by asking questions, such as “How do you know this number is 78?” and “Can you show this number differently?” Students also record their mathematical thinking through drawings, numerals, equations, and place value representations, which provides opportunities to write about mathematics.

In lesson 10 “Data,” students collect, organize, and represent data using picture graphs, tally charts, and bar-type representations. For example, students may survey classmates about favorite fruits, pets, or activities and record the results using tally marks or pictures. As students analyze the data, they write numbers, labels, and responses to questions, such as “Which category has the most?” and “How many more students chose apples than bananas?” 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 “Compare and Order Numbers” presents situations in which students must determine which mathematical claim is correct, such as deciding whether 56 or 65 is greater and determining which set contains more objects. 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 56 with 65, students explain that 65 is greater because it has six tens and 56 has five 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. These discussions encourage students to reflect on their own problem-solving strategies, consider alternative explanations, and revise their thinking when necessary.

In lesson 10 “Data,” students explain how they collected, organized, and interpreted information from a graph or chart to answer questions. During whole-group discussions, students compare strategies, construct arguments explaining why their conclusions are correct, and justify their responses using evidence from the displayed data. Educators facilitate peer-to-peer conversations by asking questions, such as “What data helped you answer the question?” and “How do you know your answer is correct?” After sharing their strategies, students are prompted to reflect on their own approach by considering their classmates’ methods. For example, students who counted every picture individually may reconsider their strategy after hearing classmates explain how they used skip counting or grouping. These opportunities allow students to articulate their reasoning, listen to alternative approaches, and recognize that different strategies can lead to the same solution.

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 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 counting on, using doubles, and representing the problem with manipulatives. 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 “Representing Problems,” 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 word problems using drawings, equations, counters, ten frames, and number sentences. This guidance helps students connect mathematical symbols to real-world situations. If students incorrectly represent the action in a story problem, the materials guide educators to model the situation with manipulatives and encourage students to explain each step. Additionally, the lesson anticipates that some students may struggle to determine whether a situation involves joining, separating, or comparing quantities. The educator notes address this misconception by encouraging students to act out the problem, use concrete models, and explain how the numbers in the story relate to the operation used. These supports help educators provide meaningful explanatory feedback while deepening students’ understanding of mathematical problem-solving.