Progress Learning Kindergarten 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 Kindergarten 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 Kindergarten Math Scope and Sequence includes a “Kindergarten Lesson Sequence Rationale” section that describes how each lesson connects to prior and future learning. For example, this section explains that lesson 1 is an introductory lesson that develops the foundational understanding of quantity and number names, which is an essential prerequisite for all other mathematical operations. Lesson 2 builds on the understanding of quantity developed in lesson 1 and focuses on comparing two sets of objects.

Each lesson includes a “Looking Ahead” section that lists the grade 1 TEKS aligned with the lesson. For example, lesson 4 states that students will use the skills developed in this lesson in grade 1 when students use objects and pictorial models to solve word problems involving joining, separating, and comparing sets within 20, which aligns with TEKS 1.3B.

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 Kindergarten 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 mastery in counting objects up to 10 but show difficulty with comparing quantities (greater than and less than), educators can consult the TEKS chart in the Kindergarten Math Scope and Sequence to identify suggested lessons that target those skills.

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

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

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

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

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

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

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

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

Evaluation for 1.2a
If designed to be static, materials include detailed lesson plans with learning objectives, teacher and student materials, lesson components with suggested timeframes, and assessment resources aligned with the TEKS and ELPS.

The materials include detailed lesson plans that have clearly stated learning objectives at the beginning of each lesson, educator and student materials, and structured lesson components using the 5E Instructional Model. For example, in lesson 5 “Measurable Attributes,” educators activate prior knowledge in the “Engage” section by asking questions from the previous lesson on the concepts of more and less. Then, students identify measurable attributes, such as longer or shorter and heavier or lighter. Students discuss strategies during the “Explain” section and apply their learning through practice and assessment tasks. The Kindergarten 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 go on a shape hunt around the house to find three-dimensional objects, such as a ball (sphere) and a soup can (cylinder). These bilingual resources promote effective communication between school and home and ensure that all families can actively support student learning.

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

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

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

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

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

The lesson plan for the “More and Less” lesson provides course-specific administration guidance. The “Evaluate” section identifies the assessment as the “More and Less 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, “Call out each question number shape. Each question can be read aloud to students. Encourage students to point to each shape as they count,” 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 Math Guide, the “Evaluate” section explains that educators can “locate and print the Learning Snapshots from within each lesson plan file or assign a digital version from the assignment center.” The printable and digital versions share the same name, items, and answer choices.

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

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

The materials provide an Assessment Bank that includes questions at varying levels of complexity, which educators can select to build pre- and post-diagnostic tests aligned with the TEKS. For example, when creating a pre- or post-diagnostic test for comparing sets of objects, educators can choose from several recall questions that show students a picture of blue and yellow cars, and students must determine whether there are more blue or more yellow cars. A skill/concept-level question for this standard shows a picture of blue and red hearts, and students must select the statement that correctly compares the number of blue and red hearts. Finally, an example of a strategic-thinking question shows students four different students who have built numbers on ten frames. Students must examine the numbers represented and select the statement that is true about them.

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

Evaluation for 2.1e
Materials include a variety of formative assessments with TEKS-aligned tasks or questions, including interactive item types with varying complexity levels.

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

The lesson plans include TEKS-aligned components, such as practice questions and quick checks, that engage students in simple, developmentally appropriate tasks. For example, during a lesson, students may complete quick check questions by identifying numbers, counting objects, 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 “Comparing Numbers and Objects” lesson lists “A” as the correct answer to question 1 to confirm that students counted 20 rabbits and 18 tigers and recognized that 20 is more than 18. The answer key states that if students chose “B,” they either did not count correctly or failed to realize that 18 is not larger than 20, and that if students chose “C,” they either did not count correctly or failed to realize that 18 is not equal to 20.

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 lessons. For example, the lesson 5 plan informs educators that students need to understand the measurable attributes of length, weight, and capacity. The slide deck that accompanies the lesson asks students to practice identifying shorter and longer by using visual images. The lesson plan and slide deck emphasize the importance of students saying the inverse of each measurement to truly internalize the meaning of those words (e.g., “The purple straw is longer than the green straw” and “The green straw is shorter than the purple straw.”).

In addition, the Kindergarten Math: Educator Guide for Pre-Teaching Vocabulary and Text Supports document provides a four-step pre-instruction protocol for introducing target vocabulary. In this protocol, educators model and pronounce the target vocabulary word; provide a student-friendly definition; pair the word directly with a physical object, gesture, or visual; and provide students with a sentence stem that they can use to say the new word to a partner before the main lesson begins. The materials also include a “Unit-by-Unit Pre-Teaching and Text Reference Guidance” table that provides educators explicit pre-teaching scripts and guidance for introducing unfamiliar references found in each unit.

Evaluation for 3.1c
Materials include explicit educator guidance for enrichment and extension activities for students who have demonstrated proficiency in grade-level and above grade-level content and skills.

The Elementary Math Implementation Guide includes explicit educator guidance on using lessons or activities for students who have demonstrated proficiency in grade-level and above-grade-level concepts and skills. The guide states that each lesson includes videos with two to three questions for students to work through to deepen their understanding of key concepts and promote discussion. For example, lesson 4 “Addition and Subtraction” suggests that educators assign the grade 1 video “Adding Three Numbers” to advanced students. Educators can organize students into small groups based on their needs to complete the appropriate set of enrichment activities.

Some lessons include a slideshow that provides “Lesson Extension” activities and questions. These activities and questions deepen understanding and challenge students who have demonstrated proficiency in grade-level and above-grade-level content and skills. For example, the slideshow for lesson 3 “Comparing Numbers and Objects” includes activities in which students use snap cubes to build a tower representing a given number. Educators facilitate discussion by encouraging justification, multiple solution pathways, and peer perspectives, which helps students move beyond identification to reasoning and mathematical discourse and supports deeper thinking for those ready for advanced exploration.

Evaluation for 3.1d
Digital materials include accommodations, including text-to-speech, content and language supports, and calculators that educators can enable or disable to support individual students.

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

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

Evaluation for 3.1e
Materials include educator guidance on offering options and supports for students to demonstrate understanding of mathematical concepts in various ways, such as perform, express, and represent.

The Elementary Math Implementation Guide provides educator guidance on various types of exploration activities that require students to demonstrate understanding of mathematical concepts in different ways. The “Explore” section of each lesson plan includes a slideshow with educator notes that suggest different manipulatives students can use to express and represent their thinking. For example, in lesson 1 “Counting,” the materials guide educators in providing counters so that students can replicate the picture on the slides by first seeing the 10 dots and then counting on for numbers greater than 10. Next, 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 4 “Addition and Subtraction” includes “Engage” questions that ask students to count sets of objects to activate prior knowledge. 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 6 “Data” includes questions such as “How can we organize the given information?” and “What does a graph show us?” 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 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 “Data,” there are two options for structuring the lesson: showing the lesson video to the whole class and following up with a think-pair-share partner discussion or assigning the video for students to watch and answer questions independently. Lessons also include hands-on activities in which students practice using manipulatives or engage in interactive tasks while educators guide and check their progress. The materials include suggested questions, intervention ideas, and extension activities to help educators meet the needs of all students.

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

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

The lesson plans provide guidance for educators on implementing the intervention methods. In lesson 4 “Addition and Subtraction,” educators start by modeling how to solve a problem, such as 3 + 2, using counters so that students can clearly see how the groups come together to make a total. During guided practice, students continue solving similar problems using hands-on tools, such as manipulatives and ten frames, while working together. 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 4 “Addition and Subtraction” 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 mathematical dialogue and discourse by explaining their thinking in response to prompts, such as “What two parts do you see?” and “Did you need to count all?” 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 “Measurable Attributes” includes intentional prompts and guidance that support educators by providing feedback as students explore and compare the length and height of various objects using cubes, linking chains, and nonstandard tools. The Teacher Guide provides questions, such as “How do you know which object is longer?” and “What could you do to check your measurement?” 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 Kindergarten 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: Show & Count Buddy (Addition & Subtraction),” the materials suggest that students at the Pre-Production level demonstrate understanding of addition and subtraction by manipulating counters, pointing to answers, and using visual supports while a partner models the language. At the Beginning level, students use single words and simple sentence starters to describe mathematical actions, such as joining and separating groups. Students at the Intermediate level use sentence frames to explain mathematical thinking and write complete number sentences while reading them aloud. At the High Intermediate level, students expand explanations by using academic vocabulary, such as plus, minus, sum, and difference, to describe how numbers are combined or separated. Finally, at the Advanced level, students justify mathematical reasoning using justification frames and peer coaching.

Additionally, in “Strategy 2: Grab, Count, & Compare (Comparing Numbers & Objects),” students at the Pre-Production level compare quantities by lining up counters one-to-one, pointing to the group with more counters, and using visual supports and partner assistance to demonstrate understanding. At the Beginning level, students identify comparisons using single words, such as more, less, and same, and complete simple sentence starters while using visual vocabulary supports. Students at the Intermediate level use sentence frames to describe and compare quantities, stating which group has more or less and recording the comparison in writing. At the High Intermediate level, students use formal comparative terms, such as greater than, fewer than, and equal to, to explain numerical relationships between groups. Finally, at the Advanced level, students justify comparisons by explaining why one quantity is greater, less, or equal to another by using evidence from the number of counters in each set.

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 6 “Data,” students discuss what the graph shows and which category has more or less.

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, lesson 1’s exit ticket includes several supports for EB students. The “Teacher Facilitation and Cross-Linguistic Notes” provide cross-linguistic connections through oral discourse by prompting educators to contrast the English terms backward with the Spanish term hacia atrás and forward with the Spanish term hacia adelante. Students also engage in discussions about counting backward in real-life situations, such as a rocket launch countdown. The Exit Ticket supports the development of academic vocabulary through written discourse because students must write the sentence stem “I count _____ to find my number” using the target vocabulary word backward. The written task also supports increasing comprehension through written discourse as students demonstrate understanding of counting backward by identifying the missing number in the sequence and explaining their thinking in writing. However, although some educator notes suggest discussing real-world examples of the content being taught, the materials do not explicitly require students to build or expand their 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 2 “More or Less,” educators guide students through hands-on practice using counters, Unifix® cubes, partner discussions, and independent problem-solving, and students generate numbers that are more than, less than, equal to, one more than, and one less than a given number using concrete and pictorial models. Students then complete the “SuperSheets” assessment “More and Less,“ which has questions that require students to identify sets of objects and numbers that are more or less than the given number, thereby demonstrating an understanding of comparing numbers aligned with the TEKS.

In lesson 7 “Shapes,” students consistently demonstrate a depth of understanding aligned with the TEKS through hands-on practice and embedded instructional assessments. Students sort, identify, and describe both two- and three-dimensional shapes by focusing on their attributes, such as their sides, vertices, and faces, rather than simply naming the shapes. The lesson includes visual models and hands-on manipulatives that encourage students to explain how they know a shape is a triangle or rectangle, which supports their thinking with mathematical language. Educators guide class discussions by asking questions, such as “How do you know these shapes are the same?” and “What makes this shape different?” to help students think more deeply rather than just recognize shapes. Students then use “SuperSheets” assessments to practice what they have learned by sorting shapes, making connections to real-world objects, and comparing their attributes.

Evaluation for 4.1b
Questions and tasks, including enrichment and extension materials, increase in rigor and complexity, leading to grade-level and above grade-level proficiency in the mathematics TEKS.

The Elementary Math Implementation Guide explains how each lesson is structured using the 5E Instructional Model, which scaffolds the tasks as they increase in complexity. For example, in lesson 4 “Addition and Subtraction,” the “Engage” section helps students activate prior knowledge of counting objects. The section helps frame the lesson for students. In the next section, “Explore,” educators help students connect their prior learning to the current grade-level learning standard. Students use counters to model addition and subtraction situations and write the corresponding equations for each, 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 5 “Measurable Attributes,” students compare objects using measurable attributes and academic vocabulary, such as shorter or taller and heavier or lighter. In the extension activity for this lesson, students apply what they have learned about measurable attributes and begin exploring how to measure length with nonstandard objects. 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 Kindergarten Math Scope and Sequence document, the materials clearly show how lessons build on one another and connect key concepts across the grade level using active, student-centered instruction. The document explains that lesson 2 moves students from identifying quantities to comparing two sets of objects, such as counting groups and deciding which has more or fewer, and then lesson 3 builds on that understanding by having students compare written numerals and larger sets using the same “more and less” concept. This sequence demonstrates coherence by reinforcing the big idea of comparison across different representations—objects, sets, and numbers—so that students deepen their understanding through consistent patterns and relationships.

Each lesson begins by activating prior knowledge of concepts taught earlier in the course that support the new content. In the “Engage” section of lesson 6 “Data,” educators begin by reviewing students’ understanding of the comparison words previously taught in lessons 2 and 3, then move on to activities involving data and graphs. Students use terms, such as more than, less than, and equal to, as they sort information and make sense of picture graphs. For instance, students might look at categories, such as favorite fruits; compare the groups; and explain which has more or fewer and why. As they study the graph, students discuss what they notice and how the groups relate to one another. By linking comparison skills to data work, the lesson helps students see how earlier ideas support new learning and prepares students for more advanced concepts later on.

Evaluation for 4.2b
Materials demonstrate coherence vertically across concepts and grade bands, including connections from grade K–6, by connecting patterns, big ideas, and relationships.

Each lesson plan helps educators build strong foundations by clearly connecting skills across grade levels and concept areas. The “Looking Ahead” section in lesson 3 shows how learning to compare numbers and groups of objects 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 learning addition and subtraction in grade 1. For example, when students notice that one group has more objects than another, they begin to see how numbers relate to one another. These early comparisons help build the foundation for future mathematical skills. As students become more comfortable recognizing differences between quantities, they are better prepared to understand how numbers can be combined or separated. 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 band. In lesson 4 “Addition and Subtraction,” advanced students connect what they learned about addition and subtraction in grade K as they explore related grade 1 concepts, such as the properties of addition, adding three numbers, and identifying true equations. 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.

This guidance statement is not applicable to the program because kindergarten does not have a preceding course with prior knowledge to connect to the current grade level and future grade levels.

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

The Study Plan feature of the online platform and the strategic use of Bell Ringers intentionally revisit previously learned skills and concepts across multiple learning pathways, which ensures that students strengthen retention over time. The Study Plans allow students to self-select previously taught skills to work on and 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 K mathematics by giving students short, engaging opportunities to revisit and practice key skills. For example, educators might begin the day with a quick activity in which students count objects to 10, identify which number is greater, or recognize basic shapes, such as circles and squares. The tasks activate prior knowledge and provide spaced retrieval, which helps young students strengthen their foundational knowledge in mathematical concepts over time.

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

The Assessment Bank supports interleaved practice by intentionally mixing a variety of mathematical skills in a single assessment so that students regularly shift between concepts and apply the appropriate strategy for each task. For example, students may count a group of objects, identify a numeral, compare two groups to determine which has more, and then recognize a shape such as a triangle or circle. In another sequence, students might solve a simple addition problem using manipulatives, then count forward in a number sequence, and identify a growing pattern. Assessments can also combine measurement and comparison by asking students to determine which object is longer, then count items in a group, and decide which group has fewer. By connecting skills students have already learned—such as counting to 10—to newer ideas—such as number composition and patterning—the Assessment Bank helps reinforce prior understanding and introduce new concepts. This approach supports stronger connections, better retention, and more-flexible problem-solving.

In lesson 6 “Data,” students actively collect, organize, and represent information using concrete and visual models to build foundational data concepts. Students use real objects, such as colored cubes and classroom items, to create simple graphs, such as sorting favorite fruits and colors, which helps students connect hands-on experiences to mathematical ideas. Students then create pictographs or tally charts to represent the same data, transitioning from concrete objects to representational models. This lesson provides interleaved practice by incorporating previously learned skills, such as counting objects, comparing quantities (more and less), and identifying numbers, as students analyze the data. For example, students count how many classmates chose each color, compare which category has more or fewer, and describe the results using numbers, which are all skills learned in earlier lessons.

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 3 “Comparing Numbers and Objects,” students use counters, ten frames, and picture sets to compare quantities within 20. Students count two groups and use comparison language, such as more, less, and equal to, to explain their thinking. For example, students analyze and compare their models with a partner’s model and answer questions, such as “Which group has more?” Students also use counters and ten frames to present quantities within 20. In a think-pair-share activity, students first solve the problem independently and then compare their models with a partner’s model. As students discuss their work, they evaluate whether each model accurately represents the quantity shown and correctly supports comparisons of more, less, or equal. For example, a student may explain that a ten frame does not show 15 because only 14 spaces are filled. During class discussions, students identify errors, defend their reasoning, and use evidence from models to support their conclusions.

In lesson 4 “Addition and Subtraction,” students use counters, connecting cubes, drawings, and ten frames to model and solve joining and separating situations within 10. For example, students use four counters, add two more to represent an addition story problem, and explain how the model matches the situation. Students interpret the model by identifying what each counter represents and explaining how the groups were combined or how one group was separated from the other group. Students analyze the representation by counting the total number of counters and describing how the quantity changed when objects were added or taken away. Guiding questions, such as “What happened to the group when more objects were joined?” and “How does your model show the addition story?” encourage students to connect the model to the mathematical situation. In think-pair-share discussions, students compare models and evaluate whether they match a story problem and equation. For example, a student may identify an error when only one counter is removed, even though the problem states that two objects were taken away. During class discussions, students explain their reasoning, identify mistakes, and support their conclusions with evidence from their models.

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

In lessons 3 and 4, students represent numbers by building and drawing. Educators model how to use counters or cubes to show small quantities, then ask students to create their own sets. For example, when educators say, “Show me four,” students count out four cubes and place them in a group. Next, students draw a picture of the same group and make a direct connection between the objects and the drawing. Students describe their thinking by explaining how their pictures match their models (e.g., “I drew four circles because I used four blocks.”).


In lesson 7 “Shapes,” students actively build their understanding by creating and describing models. They use straws, cotton swabs, or popsicle sticks to construct circles, triangles, rectangles, and squares and focus on each shape’s attributes, such as sides and corners. After building, students arrange 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 “Addition and Subtraction,” students apply their conceptual understanding to new problem situations through guided practice and real-life contexts. In this lesson, educators present a slideshow image of a picnic with different food items and ask, “How many snacks are there altogether?” Students use counters to build each group they see in the picture, then combine them to find the total. Some students draw pictures to show their thinking, such as sketching the snacks and counting them as they add. For example, students might model two sandwiches and 3 cookies with cubes, push the groups together, and say the total is five. Students explain how they used counting and addition to solve the problem.


In the “SuperSheets” assignment, students continue to apply their understanding of addition in new contexts using visual supports. Each problem includes pictures and number sentences, and some parts of the equation are placed inside boxes to help students see how the numbers relate. For example, students might look at a picture showing two apples and three apples and match those groups to complete 2 + 3 = 5. Educators can also connect this work to a real-life example, such as the picnic slideshow, by asking students to think about combining groups of snacks. Students use counters or drawings to solve the problem, then explain how they found their answers. Students describe how their counting and addition strategies helped them combine the groups correctly.

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, and completing basic addition, multiple times. For example, educators may display a number card and ask students to say the next number, or educators may show two groups of objects and ask which group has more. 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 “Counting,” educators help students develop automaticity and fluency by engaging students in repeated, hands-on counting activities that connect quantities to numerals. Educators present groups of objects, such as cubes, counters, and pictures, and students count each item aloud while touching it to ensure one-to-one correspondence. For example, students count a set of seven apples and then match the group to the numeral 7. Educators also use visual tools, such as dot cards and ten frames, to encourage quick recognition and ask students to identify the number without recounting to build automaticity. Students practice counting forward, recognizing numbers, and matching numerals 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 counting strategies, such as counting on from a known number rather than starting at one each time, which helps them solve problems more quickly. The materials promote flexible procedures by encouraging students to solve problems in different ways, such as counting objects, using pictures, comparing groups, and using a number line to check their thinking. For example, students may count a set of bears one time and verify the total by grouping the bears or counting on from a smaller group. Students build accurate procedures as they match numbers to quantities, 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 “Shapes,” students practice applying efficient, flexible, and accurate mathematical procedures by creating and analyzing shapes in various ways. Students use straws, cotton swabs, or popsicle sticks to build circles, triangles, rectangles, and squares and describe the sides and corners as they work. They then use tangrams to combine smaller shapes into new figures and explain how the shapes fit together and what attributes they see. Students also identify and color specific shapes on a handout, which reinforces recognition and classification.

Evaluation for 5.2c
Materials provide opportunities for students to evaluate mathematical representations, models, strategies, and solutions for efficiency, flexibility, and accuracy throughout learning pathways.

In lesson 4 “Addition and Subtraction,” students use counters, number lines, drawings, and their fingers to solve problems, such as 5 + 3, and compare their strategies. Students evaluate efficiency by determining which method helps them find an answer more quickly. For example, students recognize that counting on from five is more efficient than counting all eight objects from the beginning. Students evaluate flexibility by solving the same problem with different tools and representations, including counters, drawings, and mental strategies. Students evaluate accuracy by checking whether each strategy produces the same correct answer and explaining how they know their solution is correct. As students share and compare approaches, they justify which strategies they find most efficient in different situations using mathematical evidence.

In lesson 6 “Data,” students evaluate accuracy by checking that the graph matches the class data. For example, students count objects in each category and compare the totals to the graph. 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 class discussions, students explain their strategies, listen to classmates’ approaches, and determine which methods are most effective.

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 counting objects one by one and recognizing a group without recounting. In another approach, students first work independently using tools, such as drawings and manipulatives, then explain their process 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.

In lesson 2, students progress from counting concrete objects to using mental number strategies as they build fluency with one-more or one-less relationships. Students begin by using counters and Unifix® cubes to build and count sets when finding one more or one less. As students gain confidence, they transition to using number charts and mental strategies, such as identifying the next number without recounting every object. For example, students who first count five cubes one at a time may later say “one more is six” by thinking about the number sequence. Students explain how they know their answers using objects, numbers, and words, which helps them recognize faster and more-reliable strategies.

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

The Kindergarten Math Scope and Sequence document clearly develops both conceptual understanding and procedural fluency as students move from counting and recognizing quantities to comparing sets, performing basic operations, and exploring measurement, data, and geometry. Educators guide students to explain how numbers represent quantities and relationships, and students also practice skills, such as counting objects, composing and decomposing numbers, and comparing groups using appropriate strategies. As instruction continues, students connect ideas across strands. For example, students classify objects, describe measurable attributes, and interpret simple data while applying procedures, such as sorting, counting, and recording information, which aligns with the TEKS K.6 and K.7.

In lesson 7 “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, which strengthens recognition and classification, then construct shapes using straws, cotton swabs, or popsicle sticks to model attributes and compare size by directly applying geometric reasoning and comparison skills. Students extend this thinking by composing new figures with tangrams, showing how smaller shapes combine to form larger ones, and practicing procedures for building and describing shapes, which aligns with the TEKS K.6(D).

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 2 “More or Less,” students count a set of objects to determine the quantity, then use counters to show a number that is more or less than the given quantity. As the lesson progresses, students use Unifix® cubes to build a tower to represent a given number, then add or take away one cube to determine which number is one more or one less than the given number. Students progress to determining one more and one less using a portion of a hundreds chart. Finally, students are asked to “think about” what number is one more or one less than a given number and verify using Unifix® cubes or the hundreds chart.

In lesson 6 “Data,” students gather real-world data, such as favorite colors, pets, and foods, and organize the information using concrete objects, counters, or linking cubes. The slides then display picture graphs and simple bar-type representations that help students visualize and compare quantities. Students count and compare the data shown in the graphs by identifying categories with the most, least, or the same number of responses. Educator questions, such as “Which category has the most?” and “How many more students chose blue than red?” encourage students to analyze and discuss the information using mathematical vocabulary. As students progress, they move from using physical objects to interpreting pictorial graphs and recording data through numbers and symbols. Learning tasks require students to answer questions, compare quantities, and explain their reasoning using evidence from the data displays.

Evaluation for 5.3c
Materials include supports for students in connecting, creating, defining, and explaining concrete and representational models to abstract (symbolic/numeric/algorithmic) concepts, as required by the TEKS.

The Elementary Math Implementation Guide shows educators how to use slideshow prompts, instructional videos, and “SuperSheets” assignments to move students from hands-on experiences to written mathematics while students connect, create, define, and explain their thinking during daily lessons. During whole-group instruction, educators pause on slides to ask guiding questions, such as “What do you notice?” and “How can you show that another way?” so that students connect concrete models, such as counters and cubes, to pictorial drawings displayed on the screen and to numbers or symbols they record on their papers. Students create their own representations in “SuperSheets” assignments by drawing objects or using marks 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 they write, which builds a clear bridge from what they see and touch to abstract understanding.

In lesson 3 “Comparing Numbers and Objects,” the slideshow and student work mats guide students through collaborative tasks in which students connect, create, define, and explain comparisons using multiple representations. Students grab handfuls of counters and place them on their side of the mat to create a concrete model of quantity, then count and organize their counters to prepare for comparison. Working with a partner, students line up or group objects to visually represent more or less, which strengthens the connection between physical objects and pictorial arrangements on the mat. Sentence stems on the slide, such as “I have more than . . .” or “I have 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 numbers and selecting comparison statements, which shows that students can move from hands-on models and shared dialogue to clear symbolic representations of their reasoning.

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 counting, number relationships, and operations; and explaining how visuals or representations support their thinking. These language-rich interactions help students build confidence in using academic mathematical language and engaging in meaningful mathematical discourse.

In lesson 1 “Counting,” the materials provide opportunities for students to develop academic mathematical language through visuals and hands-on manipulatives, such as counters, ten frames, and number cards. Students count objects, represent numbers up to 20, and explain how many items they see using structured prompts and sentence stems. The lesson introduces important vocabulary terms, including count, more, less, equal, number, and group, which are reinforced through colorful visuals and interactive activities. Educators model counting aloud while pointing to each object, demonstrating one-to-one correspondence, and using academic language to compare quantities. Students manipulate counters on ten frames, identify groups with more or fewer objects, and explain their thinking using complete sentences, such as “I have more because I counted 8 counters and this group has 5.”

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 “More or Less,” embedded educator guidance 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 more, less, and same, when comparing groups of objects. For example, educators think aloud while examining two sets of counters and demonstrate how to describe the comparison using complete mathematical statements. The materials provide guiding questions such as “Which group has more? How do you know?” and sentence frames such as “This group has more because . . .,” to help students communicate their ideas. Students use counters and visuals to compare quantities 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 provide additional details, justify their answers, 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 to help students 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 compare, greater than, less than, equal, attribute, and pattern, 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 compared the groups 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, and connecting new vocabulary to previous learning. Additionally, Cognate Callouts highlight connections between English and Spanish mathematical terms, such as attribute to atributo and equal to igual, which helps multilingual students strengthen vocabulary comprehension.

In lesson 5 “Measurable Attributes,” 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, weight, longer, shorter, taller, heavier, and lighter. Students first think independently about comparison questions, such as “Which object is longer?” or “Which item is heavier?” and use the vocabulary to formulate responses. Next, students pair with a classmate to discuss observations using complete sentences, such as “The pencil is longer than the crayon” and “The backpack is heavier than the notebook because it has more items inside.” As partners exchange ideas, they compare observations, 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 determined an object’s measurable attribute, and support their responses by referring to the objects they compared. 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, heavier, and lighter. These repeated opportunities to think, discuss, explain, and justify ideas help students build confidence in academic vocabulary when engaging in meaningful mathematical conversations about measurable attributes.

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

The “Math Sentence Stems” resource provides educators with structured prompts that encourage students to explain 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 “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 slide 3, the materials direct educators to “Allow students to give their descriptions of the circle” and “Allow students to give examples of real-life objects that are circles.” During a think-pair-share routine, students discuss shape attributes with partners using formal geometric vocabulary, such as vertex, vertices, 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 for additional two-dimensional and three-dimensional shapes. For example, when introducing a cone, educators say, “This is a cone. Talk to your partner. How would you describe this cone?” Students use academic vocabulary to describe attributes, such as one vertex and no edges, and compare their ideas with classmates.

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 6 “Data,” the materials include embedded guidance that anticipates a variety of student answers as students interpret graphs and compare categories. 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, or the same number of items. When students misread the graph or make inaccurate comparisons, educators use targeted questions to redirect students’ attention to the data and guide them toward a correct interpretation.

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. The materials 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. This embedded support enables educators to address a variety of student needs and ensures that inaccurate responses become opportunities for clarification and deeper learning.

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

The Kindergarten Math Scope and Sequence document embeds the TEKS process standards throughout the development of mathematical concepts. Students engage in problem-solving tasks as they explore number sense, operations, measurement, data, and geometry through hands-on activities, interactive practice, and visual models. Educators 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 “Measurable Attributes,” the lesson slides and instructional activities directly integrate the process standards. Educators model how to compare objects based on measurable attributes, such as length and weight, and students use pictures, diagrams, classroom objects, and mathematical vocabulary to communicate their observations and reasoning. Students represent and compare various objects to determine which are longer, shorter, heavier, or lighter and explain their conclusions using multiple representations, including drawings, symbols, and spoken language. Through guided questioning and collaborative discussions, the materials support students in sharing mathematical ideas and reasoning and developing a deeper understanding of measurement concepts, which is aligned with the TEKS K.1(D).

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

The Kindergarten Scope and Sequence document 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 while learning number sense, operations, measurement, data, and geometry. Students participate in activities, such as counting and comparing sets of objects, representing numbers with pictures and manipulatives, sorting attributes, identifying shapes, and collecting and interpreting simple data. The materials intentionally build these skills from one lesson to the next and guide educators on facilitating mathematical discussions and providing opportunities for students to make connections across concepts and apply reasoning in different contexts. As students progress through the sequence, they consistently communicate their thinking, explain solution strategies, and use multiple representations to demonstrate understanding, which reinforces 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 solution methods with peers, using drawings and manipulatives to model mathematical situations, exploring patterns, justifying answers during class discussions, and applying concepts during guided and independent practice.

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

The Kindergarten Scope and Sequence document provides an overview of each lesson, including the content focus, aligned TEKS, and instructional expectations. Lesson descriptions show that students solve problems, explain 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 counting objects, sorting items into categories, drawing pictures to represent quantities, using manipulatives to solve problems, 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 6 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-collection investigation in which students survey classmates about a question, such as “What is your favorite fruit?” record responses, and organize the results in charts and picture graphs. For example, students apply problem-solving and reasoning skills as they collect and sort data, use mathematical tools and representations to create tally marks and picture graphs, and communicate mathematical ideas when explaining which category has more, less, most, or least. The lesson also prompts students to justify their conclusions by answering questions, such as “How many more students chose apples than bananas?” 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 individualized Study Plans, students engage with skills, such as counting objects, comparing numbers, identifying shapes, recognizing patterns, and solving simple addition and subtraction problems. When students answer a question incorrectly, the Study Plans immediately provide targeted support through a video explanation that models the correct strategy and walks students through the steps needed to solve the problem. For example, if students miscount a group of objects, the video may demonstrate how to count each object one-by-one. If students struggle to identify a triangle, the video may highlight the shape’s attributes and explain how a triangle differs from other shapes. This immediate feedback encourages students to revisit the problem, learn from their mistakes, and try again rather than give up.

In lesson 4 “Addition and Subtraction,” students think mathematically as they use manipulatives, such as counters, connecting cubes, ten frames, and number mats, to model addition and subtraction situations. For example, students may combine two groups of cubes to find a total or remove counters from a set to determine how many remain, and students explain their thinking to classmates. Students persevere by solving problems, including story problems that require students to count, represent, and check their work using multiple strategies. The lesson encourages students to try different approaches, revisit their models, and correct mistakes when needed. Students make sense of mathematics by connecting addition and subtraction concepts to real-life situations, such as combining groups of toys, sharing snacks, or finding how many objects are left after some are taken away.

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 combining two groups of objects with counters, while another student uses a drawing or a ten frame to represent the same problem. Similarly, subtraction videos may model removing objects, crossing out pictures, or counting backward to find 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 represented the problem, and justify why their solution works. The videos encourage students to recognize that mathematical problems can be represented in multiple ways using manipulatives, pictures, numbers, spoken explanations, and concrete objects.

In lesson 7 “Shapes,” the materials support students in understanding that there are multiple ways to represent problems by providing a variety of hands-on materials, including straws, cotton swabs, and popsicle sticks, for creating shapes. Students learn that the same shape can be represented using different materials, sizes, and arrangements while still maintaining its defining attributes. For example, one student may use short cotton swabs to create a square, while another student uses longer popsicle sticks to create a larger square. Students need to explain and justify that there are multiple ways to represent and complete shape-building tasks. As students share their creations with partners, students describe the attributes of their shapes using both informal and geometric language, such as sides, corners, straight, larger, and smaller. For example, one student may explain that a triangle was created using three straws, while another student may represent the same triangle using three popsicle sticks. During partner discussions, students compare the sizes and attributes of their shapes and explain how their representations match the shape prompt. Students then justify their thinking by identifying the defining attributes that make their shape correct, regardless of the material used or the shape’s size.

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 “Counting,” students actively engage in counting objects, identifying quantities, matching numbers to sets, and representing numbers using manipulatives, such as counters, linking cubes, and ten frames. Students work collaboratively with classmates to solve counting tasks, compare strategies, and explain how they determined the number of objects in a set. Educators facilitate mathematical thinking by asking questions, such as “How did you count the objects?” and “Can you show your answer another way?” Students also record their mathematical thinking through drawings, numerals, and number representations, which provides opportunities to write about mathematics.

In lesson 6 “Data,” students draw pictures, use tally marks, create object graphs, or complete picture graphs to record information gathered from class surveys about favorite colors, fruits, or classroom activities. As students analyze the data, they can write numbers, labels, and responses to questions, such as “Which category has the most?” and “How many students chose each option?” Drawing and recording their observations helps students communicate their mathematical thinking and compare quantities. Educators encourage students to explain their observations, compare quantities, and justify their conclusions using evidence from the graph or chart in 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 presents situations in which students must determine which mathematical claim is correct, such as deciding whether a graph shows more apples or bananas and whether 7 or 9 represents the greater quantity. The materials direct educators to “Give students time to talk to a partner to determine who is correct,” which creates a structured opportunity for students to explain their observations, compare quantities, and justify their conclusions using evidence from the graph, chart, or model. For example, when comparing 7 and 9, students explain that 9 is greater because it comes later in the counting sequence and represents more objects in a set. As partners discuss their reasoning, they construct mathematical arguments supported by evidence, 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 6 “Data,” students explain that they used counters to represent a quantity and counted the objects to determine the answer. During whole-group discussions, students compare their strategies with classmates, construct arguments explaining why their methods work, and justify their answers using mathematical evidence. Educators facilitate peer-to-peer conversations by asking questions, such as “How did you figure that out?” and “Can you explain why your answer is correct?” After students share their strategies, the materials prompt students to reflect on their own approach by considering their peers’ methods. For instance, students who counted objects one at a time may reconsider their strategy after hearing classmates describe grouping objects by twos and reflect on whether their own method was the most efficient. 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 selected 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 count objects and select the wrong quantity, the video may demonstrate one-to-one correspondence by counting each object aloud and matching each count to a single item. If students struggle to identify a number because they confuse numerals, such as 6 and 9, the explanation provides visual cues and step-by-step guidance to correct the misunderstanding. 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, 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 write and represent number bonds when solving subtraction problems. This guidance helps students understand the relationship between the whole and its parts, which builds a foundation for future subtraction concepts. If students incorrectly identify the missing part of a number bond, the material guides educators on modeling how the whole can be separated into two parts and asking students to use manipulatives or drawings to verify the relationship. Additionally, the lesson anticipates that some students may view subtraction as only taking away objects rather than understanding part-whole relationships. The educator notes address this misconception by encouraging students to explain their thinking and represent the problem in multiple ways.