Step Up to the TEKS 5th Math Full Program

Evaluation for 1.1a
Materials include a scope and sequence outlining the TEKS, ELPS, and concepts taught in the course.

The 5th Math Implementation Guide includes a scope and sequence that outlines the TEKS and concepts taught in the course. It provides a suggested timeline per unit and allows educators to ensure that lessons align with the state standards and cover all required content, promoting consistency and completeness.

The scope and sequence resource does not include the ELPS. Instead, a separate table of contents chart lists the ELPS.

Evaluation for 1.1b
Materials include suggested pacing (pacing guide/calendar) to support effective implementation for various instructional calendars (e.g., varying numbers of instructional days - 165, 180, 210).

The 5th Math Implementation Guide includes suggested pacing calendars to support effective implementation for various instructional calendars, including calendars for 165, 180, and 210 instructional days.

Materials include a suggested pacing guide for schools and districts that run for 165, 180, and 210 days. For example, the materials allot eight days for the teaching of the data analysis unit for a 165-day school calendar, nine days for a 180-day school calendar, and 12 days for a 210-day school calendar.

Evaluation for 1.1c
Materials include an explanation for the rationale of unit order as well as how concepts to be learned connect throughout the course.

The 5th Math Implementation Guide provides each unit with a “Unit Rationale,” “Big Ideas,” and “Background Knowledge.” The “Unit Rationale” includes connections with other concepts and background knowledge from prior grade levels.

Materials explain how the learning of concepts connects throughout the course. For example, in the 5th Math Implementation Guide, in the unit 3 overview, the “Unit Rationale” states, “This unit strengthens students’ fluency and conceptual understanding of whole number operations. Students use place value strategies and properties of operations to multiply and divide whole numbers, estimate to determine reasonableness, and apply operations to real-world problem situations. These concepts support efficient computation and prepare students for decimal and fraction operations later in the course. Throughout the unit, students apply the mathematical process standards by analyzing relationships, representing problems with models and equations, and communicating mathematical reasoning.”

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

The beginning of the lesson provides a conceptual learning goal regarding what students will understand. The lesson also includes explicit instructions on how an educator can best run a lesson. For example, the “Representations of Data” lesson says to “display an example of each type of bar graph, frequency table, dot plot, and stem-and-leaf plot. Have students share what they notice about the different ways of displaying data. Talk through the similarities and differences in the data displays. Bring in information about categorical and numerical data. Include which graphical display is used for each type of data. Have these available for student reference.” The unit also gives the educator misconceptions to look for such as “Students may not understand the difference between numerical data and categorical data. Numerical data are data that are numbers, and the order of the numbers matters, such as with dot plots and stem-and-leaf plots.” This allows educators to thoroughly understand and prepare to teach lessons.

Each unit includes a “Unit Rationale,” “Big Ideas,” “Background Knowledge,” “Instructional Notes,” “Key Academic Vocabulary,” “Required Materials,” and a “Unit Assessment Overview” to help educators internalize the unit. The “Unit Rationale” includes connections with other concepts and “Background Knowledge” with prior grade levels. All of these parts of a unit act as protocols with corresponding guidance for unit and lesson internalization.

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

The 5th Math Implementation Guide includes a “Leadership Lens” at the unit level that provides guidance to instructional leaders on supporting educators in implementing the materials as designed. The “Leadership Lens” includes “Implementation Priorities,” “Classroom Look-Fors,” “Common Implementation Pitfalls,” “Coaching Questions,” and “Evidence to Review” for guidance.

The materials do not include resources for instructional leaders to support educators in implementing the materials as designed. The materials do not provide a framework or tools to assist instructional leaders to monitor implementation or specific resources to help instructional leaders build their capacity to support educators such as exemplar responses to the provided coaching questions.

Evaluation for 1.2a
Materials include comprehensive unit overviews that provide the background content knowledge and academic vocabulary necessary to effectively teach the concepts in the unit.

The 5th Math Implementation Guide includes unit overviews that address background content knowledge and academic vocabulary. For example, the unit 6 overview states, “Background Knowledge for Students (Prior-Grade TEKS Alignment) students should already understand: Using number patterns to identify relationships (Grade 4 TEKS 4.5A), Writing and evaluating numerical expressions (Grade 4 TEKS 4.5B), Using the four operations to solve problems (Grade 4 TEKS 4.4A-4.4E), Using tables to represent numerical relationships (Grade 4 TEKS 4.4F).” Additionally, the materials include a vocabulary chart with the key words, definitions, and cognates.

In the 5th Math Implementation Guide, the unit overview provides educators with key academic vocabulary, which includes terms, definitions, and Spanish cognates. In unit 11, there are six key terms such as median whose definition is “the middle value of a data set” and whose Spanish cognate is mediana.

Evaluation for 1.2b
Materials contain supports for families in both Spanish and English for each unit with suggestions on supporting the progress of their student.

The materials include a parent letter, provided in both English and Spanish, that explains the concepts the students will learn based on the topic. It also provides strategies for families to reinforce TEKS-aligned content and support student progress.

The 5th Math Implementation Guide includes letters in both English and Spanish that inform families about what students are learning, why it is important, and how families can support their students. For the data analysis unit, the letter explains that students will represent categorical and numerical data, representing data in discrete pairs and solving problems with data, with explanations on what those subjects entail. The letter further elaborates that the unit is important because it will help students “gain a deeper understanding of how to present information clearly and effectively,” “develop problem-solving skills that are essential for analyzing real-world data,” and more. The letter informs families that they can help support student learning by “discuss[ing] real-world data” and “practicing graphing together.”

Evaluation for 1.3a
Materials include comprehensive, structured, detailed lesson plans that include daily objectives, questions, tasks, materials, and instructional assessments required to meet the content and language standards of the lesson (aligned with the TEKS and the ELPS).

The material includes aligned activities—“Math Talks,” “Reflections,” “Journal” writing, vocabulary activities, and formative assessments. There is a background information page; a general information page; and educator notes pages that include the ELPS, directions, materials, components, pages for educators to use, “Facilitating Questions,” blackline masters, and formative assessment answer keys. The “Lesson-at-a-Glance” is a daily lesson found in the 5th Math Implementation Guide and includes daily objectives and the relevant TEKS.

The materials include structured lesson plans aligned to TEKS 5.2A that incorporate the TEKS, ELPS, daily objectives, educator questioning, instructional tasks, and embedded assessments. Each lesson follows a clear progression from direct instruction (teaching the lesson) to “Guided Practice,” collaborative “Partner Practice,” and “Independent Practice.” This structure ensures that students develop conceptual understanding before applying skills independently while providing educators with all components necessary to deliver TEKS-aligned instruction.

The 5th Math Implementation Guide has the TEKS, lesson objectives in plain language for student understanding, and the “Lesson-at-a-Glance.” For example, the first lesson on data analysis addresses TEKS 5.9A, which is “[Students can] represent and interpret data in bar graphs and dot plots.” The student objective is “I can represent data using graphs.” There are two pathways for educators, and each has a “Lesson-at-a-Glance,” which includes the length of each component and if the educator should teach the component individually, to the whole class, in small groups, or in pairs. The suggested assessment aligned to the lesson objectives is for students to journal and “explain which graph best shows the data.”

Evaluation for 1.3b
Materials include a lesson overview listing the teacher and student materials necessary to effectively deliver the lesson, and the suggested timing for each lesson component.

In the 5th Math Implementation Guide, the “Lesson-at-a-Glance” sections give suggested time frames for each portion of a lesson. Unit 11, lesson 1 recommends educators spend five minutes on the warm-up, 10 minutes on the “I Do: Explicit Instruction,” seven minutes on the “We Do: Guided Practice,” eight minutes on the “Partner Practice,” 10 minutes on the “Independent Practice,” and 10 minutes on the “Exit Ticket,” which totals to a 50-minute lesson.

In the 5th Math Implementation Guide, the “Lesson-at-a-Glance” lists needed materials and suggested timing. While the “Lesson-at-a-Glance” provides a materials list, it does not clearly differentiate if it is the educator or students who need the materials. For example, unit 7, lesson 2 includes the following, “Materials & Notes: Problem of the Day SE—Spiral Review 5.5A (quadrilateral attributes), Practice SE (Eng/Span)—TEKS Lesson 5.5A (hierarchy of quadrilaterals), Practice SE (Eng/Span)—Guided Practice 5.5A, Practice SE (Eng/Span)—Partner Practice 5.5A, Practice SE (Eng/Span)—Independent Practice 5.5A, Journal: Explain why all squares are rectangles.”

Evaluation for 1.3c
Materials include guidance on the effective use of lesson materials for extended practice (e.g., homework, extension, enrichment).

The materials include a generic list of practice activities for students but do not provide guidance on how to use these materials such as determining assignments based on student performance or academic needs.

The end of each lesson features suggested extended practices that educators can provide students. In the data analysis unit, lesson 2, the suggestions include “Homework: Practice SE (Eng/Span)—Independent Practice 5.9B, Enrichment: Write two questions that can be answered using a given graph, Intervention: TEKS-tivity—Activity 5.9B with guided question stems.” However, there is no specific guidance on how to use the materials that align with a student’s performance, whether they need review and additional practice or require extensions and enrichment activities.

Evaluation for 2.1a
Materials include a variety of instructional assessments at the unit and lesson level (including diagnostic, formative, and summative) that vary in types of tasks and questions.

The materials include a variety of formative instructional assessments embedded within each book. The Practice books include “Guided Practice,” “Partner Practice,” and “Independent Practice.” The TEKS-tivity books include daily activities, “Math Talks,” “Reflection” questions, journaling, and “Exit Tickets.” The problem-of-the-day books include initialization questions, including vertically and horizontally aligned items for entry into the lesson, along with activities.

The materials include a variety of instructional assessments at the unit and lesson level, including summative assessments that vary in types of tasks/questions. In the 5th Math TEKS-tivity Student Edition, students can complete activities, such as answering, “How do you solve one-step problems using data from a dot plot?” or State of Texas Assessments of Academic Readiness (STAAR)-type questions.

Materials include diagnostic assessments that vary in the types of tasks/questions. In the TEKSnology digital platform, the beginning of each unit provides diagnostics.

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

In the 5th Math Practice Teacher Edition, the “Purpose of Instructional Assessments” section explains the “key instructional features” such as “Hands-On Activities,” “STAAR-Style Questions,” and “Collaborative Learning.” The purpose of each is to “allow students to practice and apply concepts while providing educators with opportunities to assess understanding and adjust instruction,” “solidify understanding,” and “foster discussion and collaboration . . . extensive exercises, readiness and supporting standards ensure individual mastery.”

Materials include the definitions and purpose of the included assessments. For example, the introduction to the 5th Math Practice Teacher Edition states, “Formative Assessment: Each lesson includes a short formative assessment designed to help educators monitor student understanding and identify misconceptions. These checks provide actionable information to support instructional decisions, differentiation, and targeted intervention as needed.”

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

In the 5th Math Teacher Guide, the “Teacher Guidance for Consistent and Accurate Administration of Instructional Assessments” section tells educators to “Create Uniform Instructions,” “Maintain Testing Conditions,” “Use Approved Tools,” “Provide Accommodations,” and “Give Language Support.” This ensures the administration of included assessments is consistent and standardized across examiners.

The materials provide a standardized assessment format that supports consistent administration across classrooms. The “Benchmark” includes clear directions, uniform item structure, and embedded reference materials, ensuring that all students experience consistent assessment conditions.

Evaluation for 2.1d
Diagnostic, formative, and summative assessments are aligned to the TEKS and objectives of the course, unit, or lesson.

The 5th Math TEKS-tivity Teacher Edition includes formative assessments that align with the TEKS and objectives of the unit. Each unit includes formal and informal formative assessments in the form of activities, “Math Talks,” “Reflections,” “Journal” writings, vocabulary development, and a formative unit assessment. Each piece aligns with the proper TEKS and objective of the unit. Activities also include “Facilitating Questions” that educators can use to assess students’ learning throughout the activity.

The summative assessments align with the TEKS of the course and the objectives of the unit. For example, the unit 11 assessment labels each question item with its correlating TEKS. For example, question 2 aligns with TEKS 5.9C, which is to solve one-and two-step problems using data from a frequency table, dot plot, bar graph, stem-and-leaf plot, or scatterplot. Question 2 provides students with a bar graph where they will solve a two-step problem.

Each unit includes a diagnostic aligned with the TEKS and the unit’s objectives. The TEKSnology platform includes diagnostic assessments, and the 5th Math Implementation Guide includes educator guidance for using the diagnostic assessments.

Evaluation for 2.1e
Instructional assessments include TEKS-aligned items at varying levels of complexity.

The formative and summative assessments align with the TEKS. The beginning of each unit outlines the TEKS the unit addresses. Then, each activity, “Reflection,” and/or assessment provides the associated TEKS. For example, in the data analysis and personal financial literacy unit, activity 1 corresponds with TEKS 5.9A.

Each instructional assessment includes various TEKS-aligned item types. For example, in the 5th Math Assessment Teacher Edition, “Benchmark A” includes questions involving multiple-choice, multi-select, drag-and-drop, graphing, and text-entry.

Evaluation for 2.2a
Instructional assessments and scoring information provide guidance for interpreting student performance.

Materials include an online assessment scoring through the program’s TEKSnology platform. This platform automatically grades most items and provides a gradebook view for educators to review the grading or make changes. The platform generates reports, so educators can view the results by “Course,” “Strand,” or “Reporting Category.” The platform provides a visual to procide educators with consistent information when interpreting student performance.

Materials provide educator guidance for interpreting student performance on an assessment through the TEKSnology platform. The materials provide instructional assessment reports that support educators in interpreting student performance and using assessment data to inform instruction. TEKSnology.com automatically generates multiple report types, including “Item Analysis Reports,” “TEKS Mastery Reports,” “Question Analysis Reports,” and “Class Achievement Reports,” which allow educators to analyze student performance from multiple perspectives. “Item Analysis Reports” identify student performance on specific skills; “Question Analysis Reports” reveal trends in student responses; “TEKS Mastery Reports” display progress toward standards mastery; and “Class Achievement Reports” compare individual and class performance. Educators can view “Standards Reports” by “Reporting Category” or “Strand,” which include class percentages and mastery color-coding to help educators identify strengths and areas of need. Selecting “Details” provides student-level performance data, allowing educators to interpret individual progress. Similarly, the “Course Report” displays class averages for each assessment with access to individual student reports, and the “Assignments > Gradebook” includes both “Details” and “Standards” views for reviewing assessment results. Collectively, these reports provide guidance for interpreting student performance and support data-informed instructional and curricular decisions.

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 5th Math Teacher Guide provides educators with a flow of a lesson. The guide instructs educators to make a “Data Informed Decision” after students take an “Exit Ticket” (formative assessment) and then to teach an “Extend/Enrich” or “Reteach / Power Review” activity based on the data. The 5th Math Implementation Guide provides the “Extend/Enrich” and “Reteach / Power Review” activities.

When students complete their “Exit Tickets,” the materials instruct educators to make a decision on whether students receive an “Extend/Enrich” or “Reteach / Power Review” lesson based on “Exit Ticket” data. For unit 11, lesson 2, students who need enrichment should “write two questions that can be answered when given a graph.” Students who need intervention should complete “TEKS-tivity—Activity 5.9B with guided question stems.” The specified activity provides directions, materials, and “Facilitating Questions” to guide the educator.

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.

Materials include tools for students to track their own progress and growth. For example, at the end of each “Benchmark” assessment, students have a “My STAAR Chart” that they use to “chart [their] progress by coloring in each star that [they] got correct on the Benchmark.” The “My STAAR Chart” allows students to visualize and monitor their own progress.

Materials include tools for educators to track student progress and growth. For example, the TEKSnology platform has reports that educators can use to track student progress and growth with assessments and assignments. By clicking “Details,” the educator can see the data regarding each student, in particular if a student is at “Does not meet,” “Approaching,” “Meets,” or “Masters” levels on assessments and assignments.

Evaluation for 3.1a
Materials include teacher guidance for differentiated instruction, activities, and paired (scaffolded) lessons for students who have not yet reached proficiency on grade-level content and skills.

The 5th Math Practice Teacher Edition includes embedded educator guidance for differentiation for students who have not yet reached proficiency. For example, in “TEKS Lesson 5.3K,” the “Misconceptions” section states, “Students may not understand how the model represents a multiplication problem. Have the students create the model of the fraction of one whole, then have them repeat the model as many times as it takes to represent the whole number.”

The 5th Math Implementation Guide directs educators to activities in the TEKS-tivity book, should students need intervention. For example, in unit 11, lesson 1, students who require intervention can complete “TEKS-tivity—Activity 5.9A” with structured templates. Concerning this activity, the 5th Math TEKS-tivity Teacher Edition provides educators with “Facilitating Questions” such as “How do you represent data on a dot plot?” with sample answers.

Evaluation for 3.1b
Materials include pre-teaching or embedded supports for unfamiliar vocabulary and references in text (e.g., figurative language, idioms, academic language).

Materials provide educator guidance that highlights key academic terms in each lesson and addresses common language misunderstandings, utilizing visuals to reinforce learning. For example, in the “TEKS-tivity Pathway,” every lesson begins with a “Math Talk,” which can serve as a pre-teach for students who are unfamiliar with the vocabulary. These questions facilitate discussions that encourage further understanding of new terms and the lesson’s content.

In the “Practice Book Pathway,” lessons offer vocabulary previews to help students with unfamiliar vocabulary and references in text. For example, in the personal financial literacy unit, the lessons define key vocabulary terms such as income tax, payroll tax, sales tax, and property tax. Students work through a problem with educator guidance and then the lessons ask them, “Why is income tax necessary?”

Evaluation for 3.1c
Materials include teacher guidance for differentiated instruction, enrichment, and extension activities for students who have demonstrated proficiency in grade-level content and skill.

The 5th Math Practice Teacher Edition includes embedded educator guidance for differentiation for students who have demonstrated proficiency. For example, in “TEKS Lesson 5.3K,” the “Extension Learning Opportunity” section states, “Design a Real Life Math Menu,” in which students choose meals with prices (decimals) or quantities (fractions) and then calculate total cost or remaining change, showing fluent reasoning in both addition and subtraction.

In the 5th Math Implementation Guide, the “Lesson-at-a-Glance” sections include enrichment activities. For example, the unit 4, lesson 4 guidance states, “Enrichment: Create a division problem where the quotient is less than 1.”

Evaluation for 3.2a
Materials include explicit (direct) prompts and guidance to support the teacher in modeling and explaining the concept(s) to be learned.

The “TEKS Lesson” component provides explicit instruction through direct teaching of grade-level concepts prior to student practice. This structure ensures that educators model new learning aligned to the TEKS before students engage in guided and independent work. For example, the 5th Math Practice Teacher Edition provides explicit prompts such as “Display the problem and read it aloud to students. Give the students 30 seconds to think on their own how they would use the graph to solve the problems.” Lessons also include an “Important Concepts” section that outlines what students need to understand.

In the 5th Math Practice Teacher Edition, the “Guided Practice” regularly includes “Facilitating Questions” to support the educator. This section offers questions and sample student responses to support the educator in explaining concepts. For example, “TEKS Lesson 5.4B” includes “Facilitating Questions: Ask the students these questions as they are working the problems (Answers will vary, sample answers are provided.) What does a multi-step problem mean? (Multi-step problems involve more than one operation to solve the problem) Why are parentheses important when solving multi-step problems? (Parentheses are important when solving multi-step problems because they indicate what part of the problem needs to be done first.) What is the order of operations? (What is inside the parentheses needs to be done first. Next, multiplication/division, working from left to right should be done, then addition/subtraction from left to right.)”

Evaluation for 3.2b
Materials include teacher guidance and recommendations for effective lesson delivery and facilitation using a variety of instructional approaches.

Materials include a variety of instructional approaches with educator guidance and recommendations. In the 5th Math TEKS-tivity Teacher Edition, the introduction explains, “TEKS-tivity resources are designed to help students deepen conceptual understanding, strengthen reasoning, and build confidence with grade-level TEKS through structured learning routines that promote engagement and meaningful thinking. Rather than focusing primarily on repetitive practice, the lessons in this book emphasize: Hands-on and discussion-based learning, Productive struggle and sense-making, Multiple representations and strategies, Student reflection and metacognition, [and] Ongoing formative assessment.”

The materials support differentiation through multiple instructional pathways, including direct instruction and hands-on “TEKS-tivity” activities. These options allow educators to adjust instruction based on student readiness and learning preferences, ensuring that all students can access TEKS-aligned content. The 5th Math Teacher Guide includes a description of the two-pathway instructional model, stating, “The Two-Pathway Model reflects research demonstrating that no single instructional approach sufficiently addresses the range of student needs in elementary mathematics. Instead, effective instruction blends explicit modeling, guided practice, conceptual exploration, and structured discourse.”

Evaluation for 3.2c
Materials support multiple types of practice (e.g., guided, independent, collaborative) and include guidance for teachers and recommended structures (e.g., whole group, small group, individual) to support effective implementation.

The “Practice Book Pathway” explains that lessons facilitate a gradual release model. The “Lesson-at-a-Glance” provides time stamps on the length and purpose of each component and activity. For example, in unit 8, lesson 1, the suggested time stamps for the following components and activities include “5 min, Warm-Up/Spiral; 10 min, I Do: Explicit Instruction; 7 min, We Do: Guided Practice; 8 Min, Partner Practice; 10 min, Independent Practice; 10 min, Exit Reflection.” The “Lesson-at-a-Glance” sections support educators to effectively deliver lessons with diverse practice opportunities for active student engagement.

The 5th Math Teacher Guide offers detailed lesson plans with step-by-step instructions, suggested pacing, and differentiation strategies for each lesson. For example, unit 6 includes “Math Talks,” “Exit Tickets,” “Journal” and vocabulary activities, and formative assessments. Each component has guidance for implementation as an independent or collaborative activity. “Math Talks” include instructions to “place students in pairs. Have the students spend 3–5 minutes discussing each of the prompts provided in their student books.” In activity 1, part 1 of the directions says, “Students should work independently on this activity.” In contrast, in activities 2–4, part 1 of the steps says, “Students should work in pairs on this activity.” Each activity includes “Facilitating Questions” to help educators guide students during the lesson component and to monitor understanding. The “Exit Ticket,” “Journal,” “Reflection,” vocabulary, and formative assessment are independent activities.

Evaluation for 3.3a
Materials include teacher guidance on providing linguistic accommodations for various 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.

In the 5th Math Implementation Guide, each lesson includes educator guidance on providing linguistic accommodations for various levels of language proficiency. Each lesson provides an “Emergent Bilingual Oral and Written Discourse Support” resource and includes “Embedded Oral Discourse Guidance,” “Embedded Written Discourse Guidance,” and “ELPS Sentence Stem” guidance sections.

Additionally, the “ELPS Sentence Stem” section includes the five levels of language proficiency, with sentence stems that increase in academic language as students progress through the levels.

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

The 5th Math Teacher Guide includes “Guiding Principles to Support Emergent Bilinguals in Mathematics” to support educators in better using Step Up to the TEKS products within bilingual/ESL programs. Implementation guidance includes 10 different ways educators can effectively differentiate the material to fit the needs of emergent bilingual (EB) students.

An example of the support for EB students that the 5th Math Teacher Guide provides educators includes, “Create Opportunities for Meaningful Interaction. Collaborative Learning: Use pair and group activities where students engage in mathematical discussions. Encourage Talk: Provide opportunities for emergent bilinguals to verbalize their thinking, both in English and their home languages. Use Turn-and-Talk: Structure peer interactions to allow processing and verbal rehearsal of mathematical ideas.”

Evaluation for 3.3c
Materials include embedded guidance for teachers to support emergent bilingual students in developing academic vocabulary, increasing comprehension, building background knowledge, and making cross-linguistic connections through oral and written discourse.

Materials include embedded guidance for educators to develop vocabulary and increase comprehension through oral discourse using “Math Talks” and working in pairs to complete activities. The “Reflection,” “Exit Ticket,” and “Journal” sections allow students to utilize vocabulary and improve comprehension through written discourse of math concepts using prompts like “What method do you use to represent multi-step problems with an equation that includes a letter to represent the unknown quantity?”

The 5th Math Implementation Guide includes “Emergent Bilingual Oral and Written Discourse Support” at the lesson level. The chart provides examples of connections, guidance on embedded oral discourse, guidance on embedded written discourse, and ELPS sentence stems. The embedded oral and written discourse guidance includes sections that address vocabulary, comprehension, background knowledge, and cross-linguistic connections for each lesson.

Evaluation for 3.3d
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 over the course of a lesson and/or unit (including instructional assessments) require students to demonstrate depth of understanding aligned to the TEKS.

Materials include practice opportunities throughout lessons that require students to demonstrate depth of understanding aligned with the TEKS. For example, in the the 5th Math Practice Student Edition, “TEKS Lesson 5.4H” requires students to use a variety of strategies to solve problems involving area, perimeter, and volume. Practice includes using a ruler to measure a figure to determine its area and/or perimeter, as well as single- and multi-step problems in which students must apply their knowledge of area, perimeter, and volume to determine which one applies to the given real-world situation before solving the problem.

Instructional assessments throughout the course include practice opportunities that require students to demonstrate depth of understanding aligned to the TEKS. In the 5th Math TEKS-tivity Student Edition, the unit 8 assessment requires students to apply their understanding of area, perimeter, and volume to real-world situations. For example, item 3 states, “Ms. Smith is painting her house. She uses tape to outline the rectangular window so she does not get paint on the glass. If the glass has a length of 3.25 feet and a width of 4.5 feet, what is the total length of the tape she uses? (5.4H. RS, AC3)” Educators can use the assessments to collect data on the TEKS taught and make informed decisions based on student needs.

Evaluation for 4.1b
Questions and tasks progressively increase in rigor and complexity, leading to grade-level proficiency in the mathematics TEKS.

The 5th Math Practice Teacher Edition includes questions and tasks that progressively increase in rigor and complexity throughout lesson cycles. Lessons move from educator modeling during the mini-lesson to “Guided Practice,” “Partner Practice,” and “Independent Practice,” gradually requiring students to demonstrate greater independence and deeper understanding aligned to the TEKS.

“TEKS Lesson 5.6B” lesson begins with an educator-modeled activity that focuses on building rectangular prisms using cubes to determine their volume. Students then work in pairs/groups to use the 2D representation of a rectangular prism to find the figure’s volume. Students then complete the “Engaging Activity” in the appendix, which provides a 2D representation of a rectangular prism and instructs them to build the figure and determine the area of the base, the number of layers, and finally the volume. Students then work through guided and partner questions that guide them through finding the area of the base and the number of layers to determine the volume. The “Independent Practice” questions continue to increase in rigor and complexity, with multiple-choice items; the final question is open-ended and no longer provides the 2D model of the rectangular prism. This lesson exemplifies how the course offers questions and tasks that progressively increase in rigor and complexity, leading to grade-level proficiency in the mathematics TEKS.

Evaluation for 4.2a
Materials demonstrate coherence across units by explicitly connecting patterns, big ideas, and relationships between mathematical concepts.

The 5th Math Implementation Guide connects mathematical concepts across units through a coherent instructional progression that builds from foundational number relationships to algebraic reasoning, geometry, measurement, and real-world application. The “Unit Sequence Rationale” states, “The sequence ensures a logical progression, moving from foundational skills to more complex applications, while connections between units reinforce learning and support long-term retention. Each unit builds on prior knowledge, deepens conceptual understanding, and prepares students for the next stage of learning. This coherent progression fosters mathematical fluency, problem-solving ability, and confidence in mathematics.”

In the 5th Math Implementation Guide, the “Unit Sequence Rationale” explains that unit 6 occurs at this point in the sequence because “by this stage, students are ready to apply their operational skills in more complex contexts, such as solving equations and identifying numerical patterns.” This follows units 3 through 5, which address whole-number, decimal, and fraction operations. The placement of unit 6 demonstrates the program’s coherence across units because “algebraic reasoning bridges arithmetic and higher-level problem-solving,” showing a clear relationship between the mathematical concepts.

In the 5th Math Practice Book Teacher Edition, educator guidance explicitly connects patterns and relationships among math concepts at the lesson level. For example, when introducing students to volume, the 5th Math Practice Book Teacher Edition states, “Give students centimeter cubes. Have them build a 2 x 3 x 4 rectangular prism. Ask students how many cubes it took to build their rectangular prism. Ask them what strategy they used to find the total number of cubes. Look for the strategy of finding the area of the base and then multiplying by the number of layers. If that strategy does not come up, introduce the strategy to the students.” This guidance ensures that the educator makes the connection between the previously taught skill of area and the new learning of volume, helping students make meaningful math connections between concepts.

Evaluation for 4.2b
Materials demonstrate coherence across units by connecting the content and language learned in previous courses/grade levels and what will be learned in future courses/grade levels to the content to be learned in the current course/grade level.

The 5th Math Implementation Guide connects prior-grade knowledge to current grade-level learning by explicitly identifying prerequisite skills and foundational understandings necessary for new mathematical concepts. The “Unit Sequence Rationale” demonstrates how students extend their prior learning and connect it to the next unit’s concept. The “Background Knowledge for Students” lists the TEKS and concepts that students should already understand prior to the unit. The “Key Academic Vocabulary” sections pull vocabulary words directly from the unit’s TEKS, allowing the TEKS to provide a natural coherence of language.

The 5th Math TEKS Checklist includes a vertical alignment component that connects current grade-level standards to both prior and future learning. For example, grade 5 TEKS 5.9A, “represent categorical data with bar graphs or frequency tables and numerical data,” aligns with grade 3 TEKS 3.8A, grade 4 TEKS 4.9A, and grade 6 TEKS 6.12A, which progressively extend students’ data representation skills using more complex numerical data. The vertical alignment component demonstrates coherence across grade levels and supports the progression of mathematical concepts and academic vocabulary.

Evaluation for 4.2c
Materials demonstrate coherence at the lesson level by connecting students' prior knowledge of concepts and procedures from the current and prior grade level(s) to new mathematical knowledge and skills..

The 5th Math Practice Teacher Edition provides the following guidance to aid educators in making connections between previous and current grade levels: “TEKS 5.3H Supporting Standard: Students represent and solve addition and subtraction problems involving fractions. The representations specified include objects, pictorial models, and properties of operations. In 4th grade, students focused on equal denominators by using number lines and properties of operations. In the 5th grade standard, the focus shifts to unequal denominators referring to the same whole.”

The “Problem of the Day" Journal activities provide this coherence by systematically spiraling prior and current grade-level concepts and procedures, using diverse methods to support vertical alignment and ensure that students consistently build on foundational knowledge for future success.

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

Through the “Problem of the Day" Journal” activities, the materials provide spaced retrieval opportunities with previously learned skills and concepts across lessons and units. The materials explain that “the Problem of the Day Journal incorporates research-based instructional practices shown to strengthen retention and transfer of learning: Spaced Retrieval to reinforce long-term retention of essential concepts.” Additionally, the framework for the design of the questions used the “Instructional Structure: Monday–Thursday. Students complete five problems per day: Problems 1–2: Spiral Review. Prior grade-level standards that support readiness and previously taught grade 5 concepts. Problems 3–5: New Learning Current grade 5 TEKS focus. This intentional balance promotes retention of prerequisite skills while building depth in grade-level standards.”

In the data analysis unit, “Problem of the Day” questions range from multiplication, measurement, and representation of numbers, all concepts introduced in previous units. These activities bridge learning across lessons and units to ensure that students maintain proficiency and achieve long-term mastery.

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

The “Problem of the Day" Journal provides interleaved practice opportunities with previously learned skills and concepts across lessons. Daily problem sets include five problems designed for “interleaved practice to develop flexible thinking across mathematical domains.” In the representing data unit, students solve a variety of mathematical problems and represent data in multiple ways throughout the week. For example, the students view a pictograph of favorite sandwiches in which each sandwich picture represents four students, and then students must organize the same data into a frequency table. This activity requires students to apply previously learned multiplication skills while connecting multiple data representations. These activities provide interleaved practice opportunities that connect previously learned concepts across units.

The 5th Math Practice Book Teacher Edition instructs educators to have students solve multiple problems using different methods, a practice that strengthens mathematical proficiency and aligns with interleaved practice opportunities for previously learned skills and concepts across lessons and units. This approach encourages students to shift between varied strategies, fostering the cognitive flexibility necessary to integrate new knowledge with past learning. For example, “TEKS Lesson 5.3D” provides students with a graphic organizer to represent the multiplication of decimals using area models. The “Guided,” “Partner,” and “Independent Practice” activities present a mixture of opportunities to use a variety of strategies. Later lessons such as “TEKS Lesson 5.3F” ask students to use area models to represent the division of decimals, which acts as another demonstration of skills and concepts used across lessons and units. By consistently applying these interleaved techniques, the curriculum ensures that students not only solve individual problems but also develop a deeper, more cohesive understanding of mathematical concepts over time.

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

Materials include opportunities for students to interpret, analyze, and evaluate mathematical reasoning and representations. The 5th Math TEKS-tivity Student Edition provides students with four different graphs. For each graph, students must determine if the provided answer is correct or incorrect upon solving the problem. This task requires students to interpret and analyze the data and evaluate its accuracy.

In the 5th Math TEKS-tivity Student Edition, unit 5, the “Engaging Activity 1: 5.3H” provides a task in which students interpret and analyze models and scenarios to determine the represented expression and solution. The “Engaging Activity 2: 5.3I” directs students to “match the expression in the table at the bottom of the page to the representation and then solve. Each representation shares a box with a fraction word problem. The “Engaging Activity 3: 5.3J” instructs students to “write an expression for each representation shown.” The last activity gives students the opportunity to draw their own model to represent a given expression. All three of these The “Engaging Activity” tasks engage students in interpreting, analyzing, and evaluating models representing computational and algebraic relationship situations.

Evaluation for 5.1b
Questions and tasks require students to create models to represent mathematical situations.

In the 5th Math TEKS-tivity Student Edition, “Reflection Activity 3: 5.3F” has students “represent 3.24 divided by 6 using a model.” Students further their thinking by answering the next prompt, “Explain your model in question #1.” This activity exemplifies how the program includes questions and tasks that require students to create models to represent math situations.

The 5th Math Practice Student Edition directs students to draw a model to determine the amount remaining when subtracting fractions with unlike denominators. The prompt states, “Micah had 3 7/9 gallons of punch. He drank 2 1/3 gallons. Draw a model and determine the amount of punch Micah has left.” This task provides an opportunity for students to create their own model after analyzing the given models to support their understanding of the concept. Students have the opportunity to create a model during the “Independent Practice” to represent adding fractions with unlike denominators. This activity exemplifies how the program includes questions and tasks that require students to create models to represent math situations.

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

In the 5th Math Practice Teacher Edition, “TEKS Lesson 5.2B” begins with students using a place value chart to compare two numbers based on place value. The educator then guides students in ordering three numbers, using the place value chart to determine their positions. During the “Guided Practice,” students receive new comparison problems and new real-world situations to apply what they have learned about ordering decimal numbers. Students then apply what they have learned to a variety of new real-world situations involving comparing and ordering numbers. For example, in the “Independent Practice,” question 3 states, “Erin and her friends play softball. Erin lives 0.8 of a mile west of the softball field. Laurel lives 0.7 of a mile north of the softball field, Nicole lives 0.67 of a mile north of the softball field, and Tara lives 0.71 of a mile east of the softball field. List the friends in order from greatest distance to least distance from the softball field.” This task provides an example in which students apply conceptual understanding to a new problem situation and context.

In the 5th Math Practice Student Edition, students first answer questions such as “Which of the following could be the volume of a cube?” Later, students build shapes with a given volume and determine whether each figure is a cube or a rectangular prism. This progression supports students in applying their conceptual understanding of volume to new mathematical situations and contexts.

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

The course’s “Problem of the Day" Journal activities support automaticity and fluency through repeated opportunities for cumulative practice, retrieval, and ongoing application of previously learned mathematical concepts and procedures. Monday to Thursday, students complete five problems per day, each designed to take only five to seven minutes as a structured warm-up or instructional launch. The first two questions are a spiral review, and the last three questions focus on new learning. For example, in the “Week 19 Problem of the Day,” the Wednesday practice set includes a spiral practice of solving expressions using the order of operations, as well as fraction operations with models from the current unit. This daily routine builds the automaticity and fluency needed to complete grade-level tasks by reinforcing concepts during the first five to seven minutes of class each day.

In the 5th Math TEKS-tivity Student Edition, students develop procedural fluency by graphing ordered pairs from tables, identifying coordinates, locating points relative to other points, and representing data on coordinate planes. “Reflection,” “Journal,” and “Math Talk” prompts require students to explain how to graph fractions and decimals, describe their graphing process, and explain the relationship between ordered pairs, input-output tables, and coordinate planes. These activities help build student fluency necessary to complete grade-level tasks.

Evaluation for 5.2b
Materials provide opportunities for students to practice the application of efficient, flexible, and accurate mathematical procedures within the lesson and/or throughout a unit.

In the 5th Math Practice Teacher Edition, “TEKS Lesson 5.3C,” the educator guidance provides flexibility as students learn the standard algorithm for division. For example, the “Important Concepts” section states, “Students may solve using strategies such as partial quotients, area/box models, or compatible numbers before connecting these strategies to the traditional long division algorithm.” While the materials do state that “using the standard argument allows you to move to more efficient methods when dividing larger numbers,” there is flexibility in getting all students there. Students then practice accuracy through a variety of problems included in the “Independent Practice.”

In the 5th Math TEKS-tivity Student Edition, students develop accurate, efficient, and flexible mathematical procedures by graphing ordered pairs from tables, identifying coordinates, locating points relative to other points, and representing data on coordinate planes. “Reflection,” “Journal,” and “Math Talk” activities require students to explain how to graph fractions and decimals, describe the process for graphing ordered pairs, and explain the relationship between input-output tables and coordinate planes. These activities support accurate graphing procedures, the efficient application of graphing conventions, and the flexible use of multiple mathematical representations.

Evaluation for 5.2c
Materials provide opportunities for students to evaluate procedures, processes, and solutions for efficiency, flexibility, and accuracy within the lesson and throughout a unit.

The materials provide opportunities for students to evaluate the efficiency of mathematical procedures by comparing multiple solution strategies. In the 5th Math Practice Teacher Edition, “TEKS Lesson 5.3B” directs the educator to model a comparison between the area model and the standard multiplication algorithm through a think-aloud. The educator then prompts students to compare the two representations by identifying what they notice when they view the array and the standard algorithm for “380 x 62” side by side. Additionally, the “Why Do I Need to Know This?” section explains that students have learned multiple multiplication strategies, and the section identifies the standard algorithm as “the most efficient way to multiply numbers.” These embedded opportunities support students in evaluating procedural efficiency by analyzing multiple strategies and considering the advantages of standard algorithms.

Materials provide tasks that provide opportunities for students to evaluate procedures, processes, and solutions for accuracy. For example, in the 5th Math TEKS-tivity Student Edition, activity 3 directs students to “read the problem and the answer given. Decide if you agree or disagree with the answer. Describe how you know the answer is right or wrong. Find a partner and discuss each problem when you are finished.” This task requires students to determine the accuracy of a given solution, justify their reasoning with mathematical evidence, and discuss their conclusions with a partner.

Across the materials, students engage in tasks that require them to refine accurate and flexible mathematical procedures throughout units. For example, in the 5th Math Practice Student Edition, students progress from the “TEKS Lesson” to “Guided Practice,” “Partner Practice,” and “Independent Practice,” as they graph ordered pairs, create scatterplots, represent categorical and numerical data, and interpret multiple graphical representations. Students repeatedly apply mathematical procedures across a variety of representations and problem types, strengthening procedural accuracy while demonstrating flexibility in selecting and using appropriate representations to solve mathematical problems.

Evaluation for 5.2d
Materials contain embedded supports for teachers to guide students toward increasingly efficient approaches.

In the 5th Math Practice Book Teacher Edition, “TEKS Lesson 5.4F” embeds educator guidance that helps students develop increasingly efficient procedural approaches by facilitating discussion about why they must consistently apply the order of operations. Students compare different solution orders, determine whether changing the order affects the result, and conclude why mathematicians follow a consistent procedure when simplifying expressions.

In the 5th Math TEKS-tivity Teacher Edition, unit 3, activity 2, the “Facilitating Questions” section provides three questions for educators to ask. One of these questions asks, “What are some strategies you can use to multiply a three-digit number by a two-digit number?” Another question in the section instructs educators to ask, “Why use the standard algorithm rather than other strategies?” These questions guide students toward using the standard algorithm as the most efficient approach.

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

In the 5th Math Practice Teacher Edition, the beginning of each new “TEKS Lesson” explicitly states how the lesson addresses conceptual and procedural emphasis of the TEKS. For example, in “TEKS Lesson 5.4G,” the “Conceptual Learning Goal” states, “Students understand how volume formulas are derived and what each part of the formula represents through hands-on and visual models.”

In the 5th Math TEKS-tivity Teacher Edition, the unit 4 overview states, “The focus of this unit is on the concepts of decimal operations. Students will represent the products of decimals to the hundredths place using a variety of models, including the area model.” Additionally, the overview mentions that students will use a variety of strategies, including the standard algorithm, to solve multiplication and division problems with decimals and that they will add and subtract decimals. It ends by saying, “Throughout this unit, students need to explain their thinking of how they represent and solve problems involving decimals.” This relates to the conceptual understanding of operations with the ability to utilize procedural strategies such as algorithms to solve problems, which is knowledge and skills the TEKS emphasizes.

Evaluation for 5.3b
Questions and tasks include the use of concrete models and manipulatives, pictorial representations (figures/drawings), and abstract representations, as required by the TEKS.

The 5th Math Practice Teacher Edition includes questions and tasks requiring students to use concrete models and manipulatives, pictorial representations, and abstract representations. For example, “TEKS Lesson 5.3I” states, “Model the second problem for the students. Start with 16 shapes. Think aloud that you are looking for 3/4. First, I need to create fourths. 16 divided by 4 is 4, so there are four shapes in each group. Make the groups. Next, you are finding 3/4 of 16, so shade the shapes for 3/4.” Students then draw the model as a pictorial representation before moving to abstract real-world situations.

In the 5th Math TEKS-tivity Teacher Edition, unit 5 includes activities and tasks related to computations and algebraic relationships. Activities 1, 2, and 3 have students match or write the correct expression relating to various visual representations. Activity 4 presents real-world situations such as “Monica ate 2 3/4 cups of chocolate pudding on Monday and Tuesday. On Wednesday and Thursday, she ate 1 1/2 cups. How many total cups of pudding did she eat on these days?” The activities require students to match corresponding expressions and answers to each scenario, thereby emphasizing practice with abstract representations.

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.

In the 5th Grade Math Practice Book, students create concrete models of rectangular prisms using centimeter cubes to determine volume. Educators guide students in explaining the strategy of finding the area of the base and multiplying it by the number of layers before introducing the formula V = Bh. “Facilitating Questions” ask students to explain how the concrete model demonstrates the relationship between the area of the base, the number of layers, and volume. This progression supports students in creating, connecting, defining, and explaining concrete models to develop abstract concepts of volume.

Students transition from representational models to abstract volume concepts by analyzing drawings of rectangular prisms to identify the area of the base, determine the number of layers, and calculate volume. Students use these visual representations to solve increasingly complex volume problems, connecting the diagrams to the symbolic formula V = Bh. Educator questioning, important concepts, and guidance on misconceptions require students to explain how the representations demonstrate the relationship among the area of the base, height, and volume, supporting students in creating, connecting, defining, and explaining representational models of abstract mathematical concepts.

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

In the 5th Math Practice Teacher Edition, “TEKS Lesson 5.4G” directs the educator to use visual examples of cubes and rectangular prisms to help students identify the attributes of three-dimensional figures and make connections between dimensions and volume. Students’ challenge is to determine the possible dimensions of a rectangular prism with a volume of 48 cubic units. Students have time to independently consider solutions before participating in a think-pair-share routine to discuss and explain their reasoning with a partner. During the “Engaging Activity,” students use centimeter cubes to build a rectangular prism or cube, draw a visual model of the figure, and record its dimensions and volume. These instructional routines integrate visual representations, concrete manipulatives, collaborative mathematical discourse, and educator-facilitated discussion, providing students with opportunities to develop and apply precise academic mathematical language related to three-dimensional figures, dimensions, and volume.


In the 5th Math TEKS-tivity Student Edition, students respond to prompts such as “What is the difference between a dot plot and a scatterplot?” and “What strategy would you use to determine if a stem-and-leaf plot and a dot plot represent the same data?” These questions require students to explain mathematical concepts using academic language. Additionally, each unit includes a vocabulary section where students interact with key mathematical terms. For example, in unit 1, students work with the terms graph, scale, dot plot, scatterplot, and more and respond to prompts such as “Pick 3 words and describe the relationship between them” and “Pick 3 new words and describe the relationship between them.” These activities provide opportunities for students to develop and use academic mathematical vocabulary through oral and written language.

Evaluation for 5.4b
Materials include embedded teacher guidance to scaffold and support students' development and use of academic mathematical vocabulary in context.

In the 5th Math Practice Teacher Edition, the “TEKS Lesson 5.4A” educator guidance states, “Begin this lesson by having students create displays for several prime and composite numbers that include rectangle arrays on cm graph paper to represent the multiplication facts for those numbers. Using those representations, sort the displays into two groups, one rectangle and more than one rectangle, and introduce the vocabulary of prime and composite numbers. Have students turn and talk about what they notice about prime and composite numbers. Having students share out helps build student knowledge.” This guidance exemplifies how the materials include embedded educator guidance to scaffold and support students’ development and use of academic mathematical vocabulary in context.

In the 5th Math Practice Teachers Addition, “TEKS Lesson 5.2B,” the “Important Concepts” section provides educators with the guidance that “students need to understand the symbols < (less than), > (greater than), and = (equal to). Just a reminder, numbers do not eat other numbers. Always try to use correct mathematical vocabulary.” Since the “Independent Practice” provides this guidance as well, embedded educator guidance to scaffold and support students’ development and use of academic mathematical vocabulary in context is present in both the “TEKS-tivity Pathway” and the “Practice Book Pathway.”

Evaluation for 5.4c
Materials include embedded teacher guidance to support the application of appropriate mathematical language to include vocabulary, syntax, and discourse to include guidance to support mathematical conversations that provide opportunities for students to hear, refine, and use math language with peers and develop their math language toolkit over time as well as guide teachers to support student responses using exemplar responses to questions and tasks.

The “Math Talks” provide educator guidance that supports the use of appropriate mathematical language through academic vocabulary and structured mathematical discussions. Educator guidance encourages students to share their thinking during “Math Talks” and other collaborative learning experiences, providing opportunities to hear and refine the mathematical language their peers use and to engage in mathematical discourse.

Additionally, the 5th Math Implementation Guide provides “Emergent Bilingual Oral and Written Discourse Support” for each lesson. This chart provides guidance for vocabulary support, exemplar responses to tasks, and sentence stems for syntax support.

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

Materials integrate the TEKS process standards appropriately throughout. For example, in the 5th Math Practice Student Edition, “TEKS Lesson 5.8C,” students organize data from tables, graph ordered pairs, interpret graphical representations, and explain the relationships between tables and coordinate graphs. Students create and use multiple representations to communicate mathematical ideas and analyze relationships, all of which demonstrates how the lesson integrates TEKS process standards throughout.

In the 5th Math TEKS-tivity Student Edition, unit 11, students create and interpret scatterplots, bar graphs, frequency tables, dot plots, and stem-and-leaf plots while solving mathematical problems and explaining their reasoning. Students analyze mathematical relationships, communicate ideas using multiple representations, and justify their solutions, all of which demonstrates how the lesson integrates TEKS process standards throughout.

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

The 5th Math Teacher Guide explicitly describes how the course includes TEKS mathematical process standards. The guide explains that “Practice Lessons,” “TEKS-tivities,” “Problem of the Day,” and “Power Review” intentionally embed problem-solving, reasoning, communication, representation, and strategic use of tools. The guide further states that the 5th Math Practice Teacher Edition and 5th Math TEKS-tivity Teacher Edition provide supports that guide educators in incorporating these process standards throughout daily instruction.

The 5th Math Practice Teacher Edition includes a “Process Standards” alignment matrix that crosswalks each grade-level content TEKS with the applicable mathematical process standards (5.1A–5.1G). The matrix demonstrates that the curriculum intentionally incorporates process standards throughout the course rather than addressing them in isolated lessons.

Evaluation for 5.5c
Materials include a description for each unit of how TEKS process standards are incorporated and connected throughout the unit.

Materials include a description within each unit of how the unit regularly incorporates and connects TEKS process standards. Each lesson includes the section “Incorporation and Connection Through the Learning Pathway” that outlines the process standards and connects them to the learning objectives throughout the unit.

The unit 1 overview states, “Throughout the unit, students apply the mathematical process standards by analyzing relationships, representing problems with models and equations, and communicating mathematical reasoning.” The overview then provides further elaboration on the lesson’s incorporation and connection with the particular TEKS process standards.

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

In the 5th Math Implementation Guide, each lesson includes an “Incorporating and Connection Through the Learning Pathway” section that specifies how and where the lesson incorporates TEKS process standards.

Unit 1, lesson 1 states, “The learning pathway begins in the TEKS Lesson as students represent the value of digits in decimals through the thousandths and translate between standard and expanded notation. Through place-value charts, decimal grids, standard notation, expanded notation, money, measurements, and tables, students build a shared conceptual model, communicate ideas in multiple forms, and analyze the relationships that define the content (5.1D, 5.1C, 5.1E, 5.1F, 5.1G). Guided Practice maintains the same conceptual anchors while increasing student responsibility. Students analyze parallel examples, select relevant information or techniques, and use feedback to connect procedures to meaning (5.18, 5.1C, 5.1D, 5.1E, 5.1F). Partner Practice extends the pathway through mathematical discourse as students compare methods, explain evidence, and refine reasoning with precise vocabulary (5.1A, 5.1C, 5.1D, 5.1E, 5.1F, 5.1G). Independent Practice completes the pathway by requiring students to transfer the same ideas to varied formats and applications, determine a solution without immediate support, and evaluate or justify the result (5.1A, 5.1C, 5.18, 5.1D, 5.1E, 5.1F, 51G).” This excerpt from unit 1 exemplifies how the lesson specifies how and where it incorporates TEKS process standards.

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

In the 5th Math TEKS-tivity Student Edition, unit 11, students engage in “Math Talks” by discussing prompts such as “How do you solve a one-step problem from a frequency table?” and “How do you solve a two-step problem from a dot plot?” Students also respond to questions such as “How do you solve a one-step problem from a dot plot?” These prompts require students to analyze mathematical concepts, explain the purpose of mathematical representations, and connect the use of graphs to problem-solving. These prompts provide opportunities for students to think mathematically and develop conceptual understanding of mathematics.

The materials support perseverance and sustained mathematical effort by requiring students to analyze solution strategies, determine whether they agree or disagree with the mathematical reasoning, and justify their conclusions through written explanations and discussion. For example, question 2 states, “Lyla is putting her photos into a photo album. She has 256 photos to place in the album. Each page will hold 4 photos. How many pages will she need to fit all the photos? Lyla will need 61 pages to put all of her photos in.” This activity provides students with opportunities to write their explanation and, after they finish each problem, verbalize their thinking to a partner.

In the “Practice Book Pathway,” the “Problem of the Day" Journal activity allows students to engage with open-ended questions, multipart tasks focused on the problem-solving process, and diverse visual models to connect math concepts. Built-in tools help students persevere through challenges by gradually increasing task difficulty and facilitating educator-led questioning.

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

The materials support students in understanding and explaining multiple ways to represent mathematical information. In the 5th Math TEKS-tivity Student Edition, unit 11, students work with multiple representations of data, including frequency tables, dot plots, and bar graphs. “Reflection” activities and “Math Talk” prompts require students to explain their thinking using these representations through questions such as “How do you solve a one-step problem from a frequency table?” These opportunities support students in understanding that they can represent data using different mathematical models and in explaining how to use those representations to solve problems.

The materials support students in understanding and explaining that there can be multiple ways to solve mathematical problems. For example, in the 5th Math Practice Teacher Edition, “TEKS Lesson: Dividing Using the Standard Algorithm” states that “examples of strategies can include drawing a picture and partial quotients.” Educator guidance directs educators to begin by modeling the problem with drawings, asking students questions such as “How many pencils do we know for sure can go into each box?” and “How many pencils can go into each box from the ___?” before connecting the strategy to the standard algorithm. The lesson further explains that “you could do partial quotients with the drawings side by side to show mathematically what is happening” and instructs educators to “model solving the first problem using the standard algorithm” after students have explored the strategy. These supports demonstrate that the lesson expects students to make connections between multiple solution strategies and understand how they relate to the standard algorithm.

Although the materials frequently ask students to explain their mathematical thinking, the materials do not support students in justifying that multiple representations or solution methods are valid. In the 5th Math TEKS-tivity Student Edition, unit 11, the “Reflection” activities ask students to respond to prompts such as “How do you solve one-step problems using data from a dot plot?” Similarly, “Math Talk” prompts ask students questions such as “How do you solve a one-step problem from a frequency table?” These prompts require students to explain how they solved problems or describe the strategies they used. However, the materials do not require students to defend why they should select one data representation over another, justify why one representation is more appropriate than another for a given data set, or compare and justify multiple solution strategies for solving the same problem.

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 teachers.

In the 5th Math Practice Student Edition, students engage in an educator-guided lesson followed by “Guided Practice” and “Partner Practice,” in which they solve mathematical tasks and record their work. Educator guidance incorporates turn-and-talk prompts throughout the “TEKS Lesson,” providing opportunities for students to discuss their mathematical thinking with peers and educators. For example, in the 5th Math Practice Teacher Edition, “TEKS Lesson 5.3A” instructs educators to “have students turn and talk with a partner about the second question for two minutes.” The lesson expects students to “share out their thinking in order to solve the problem.” The “Partner Practice” section provides three additional questions for students. The 5th Math Practice Teacher Edition directs educators to call on volunteers to share answers and notes that “it is important that the students are able to explain how to estimate to solve the problems.” This guidance emphasizes allowing students to make sense of mathematics through opportunities to do math and discuss it with peers. During the “Guided Practice,” the “Facilitating Questions” provide opportunities for students to discuss math with the educator.

In the 5th Math TEKS-tivity Student Edition, students engage in collaborative mathematical activities with peers, participate in “Math Talks” to discuss mathematical ideas, and complete written “Reflection” and “Journal” prompts to explain and record their mathematical thinking. For example, in unit 11, the “Reflection” asks students to explain mathematical ideas with prompts such as “Explain how to represent categorical data on a bar graph,” “How do you solve one-step problems using data from a dot plot?” and “Explain how data is represented on a scatterplot.” Journal activities require students to compare representations by responding to prompts such as “What is the difference between a dot plot and a scatterplot?” The 5th Math TEKS-tivity Teacher Edition directs the educator to have students discuss “Math Talk” prompts in pairs before sharing responses with the class. Together, these routines provide recurring opportunities for students to communicate mathematical reasoning through both writing and discussion with peers and educators.

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

In the 5th Math Teacher Guide, the “The Importance of Productive Struggle in Mathematics” section supports educators in guiding students to share and reflect on their problem-solving approaches by providing explicit guidance for facilitating reflection after solving mathematical problems. The guide directs educators to ask reflective questions such as “What strategies worked well?” and “What would you do differently next time?” to encourage students to explain and evaluate their problem-solving approaches. The materials also encourage educators to have students use math journals to document challenges, strategies, and breakthroughs, providing opportunities for students to reflect on and justify their mathematical thinking.

In the 5th Math Teacher Guide, the “Using Facilitating Questions to Extend and Enrich Student Learning” section supports educators in guiding students to share and reflect on their problem-solving approaches by providing guidance for using “Facilitating Questions” to promote mathematical discourse. The educator guidance recommends using “Reflection” questions to help students think about their learning processes and outcomes, questions that require explanation and justification to help students articulate their reasoning, and “Facilitating Questions” that drive group discussions in which students share ideas and learn from one another. These supports encourage educators to facilitate discussions that deepen students’ mathematical understanding through explanations, reflection, and justification.

In the 5th Math Practice Teacher Edition, “TEKS Lesson 5.2A” directs educators to have students talk with partners about expanded notation representations and to call on volunteers to share out. The lesson provides the educator with several questions that engage students in partner discussions and share-outs. As a student shares, the lesson directs educators to “ask the [other] students to give a thumbs up if they agree, or a thumbs down if they disagree with the expanded notation.” The student conversations should continue until “students determine the correct answer.” Partner discussions and share-outs prompt students to share their thinking, justify the reasoning behind a solution, or argue an alternative solution during a mathematical discussion about expanded notation.

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

Although the materials include a “Misconceptions” box in each lesson, the materials do not provide prompts or educator guidance for delivering explanatory feedback based on those anticipated misconceptions. For example, in the Teacher Edition, unit 11, “TEKS Lesson: Representations of Data” states, “Students may not understand the difference between numerical data and categorical data. Numerical data are data that are numbers, and the order of the numbers matters, such as with dot plots and stem-and-leaf plots.” While the “Misconceptions” box identifies misconceptions and explains the mathematical concept, the materials do not include educator prompts or instructional guidance describing how to respond to the misconception or provide principle-based explanatory feedback when students demonstrate this misunderstanding.

The materials do not provide prompts or guidance to support educators in providing explanatory feedback based on student responses. Unit 11 tasks students with creating dot plots, frequency tables, and stem-and-leaf plots based on given data. The Teacher Edition only includes the answer key, with no educator prompts or guidance on how to respond to students’ explanations or to provide principle-based feedback when a student’s response is correct or incorrect.