Math Journeys Texas, Grade 2

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 in Math Journeys, Grade 2, include a TEKS Correlation Guide that outlines the TEKS that correspond to each lesson, including the content and process standards for educators. Additionally, the TEKS and ELPS are included in the scope and sequence document, which is organized into different sections called “Journeys.” The Journey Instructional Guide provides a detailed rationale for each journey. For example, section 2 of the guide provides a vertical rationale for how each journey builds upon the previous journey to prepare students for the next concept. The A2 Journey Instructional Guide focuses on identifying numbers and counting from 1–100. This extends the concepts of counting, comparison, ordering, and estimation from the previous journey, which focused on numbers 1–20. The horizontal rationale is provided in section 3, which explains how the learning moves from concrete to representational to abstract models of number sense.

The materials in Math Journeys include an Alignment Guide that outlines the TEKS, ELPS, and concepts covered in the A1 Journey Instructional Guide. The materials state, “the guide shows the alignment among the TEKS, ELPS, lesson concepts, and the learning progression across A1.” Additionally, the materials include a rationale for learning paths across grade levels and within the same grade level. For example, lessons 1–4 build the oral counting sequence, numerical quantity matching, and early classification and comparison of numbers.

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 in Math Journeys include a Program Guide that provides comprehensive guidance for educator implementation, including a three-step framework of build, consolidate, and practice. Each lesson starts with an educator-led small group lesson, followed by logsheets for students to complete independently with educator feedback. The adaptive digital practice, Atlas Math, contains optional additional practice. Additionally, the “Lesson Internalization and Planning” section provides guidance on planning for learner variability, including explanations for multiple entry points, just-in-time supports, extensions, and multiple representations and modes of expression.

The materials in group 1 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. For example, materials in the program overview note 10 practices that educators can use for effective math intervention. Educators can “identify each student’s starting point, set realistic and meaningful goals, create a safe environment where students dare to think, foster conceptual understanding, and guide reasoning through modeling, questioning, and feedback.”

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

The Math Journeys materials include a TEKS Correlation Guide with the recommended skill entry points based on students’ diagnostic assessment results. The journeys and lessons are aligned to the TEKS content and process standards. Additionally, the TEKS Correlation Guide shows educators how to implement instruction by connecting lessons and activities to specific standards within each journey. The guide alone does not provide a recommended skill entry point.

The placement test report sample presents data on the TEKS assessed in the diagnostic assessment, and proposes grouping structures for students. The “Proposed Group Distribution” section of the report recommends how to group students and identifies an entry point for each group. The report also offers a snapshot of each student to show educators their current understanding and suggest an entry point for instruction.

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

The materials in the Math Journeys Program Guide, “Lesson Internalization and Planning” section, include protocols with corresponding guidance for both unit and lesson internalization. The “Preparing for a Journey” section provides unit internalization guidance by directing educators to understand how the journey builds on prior learning. Educators review lesson objectives and mastery criteria, identify scaffolds and enrichment opportunities, gather materials, and analyze learning progressions before instruction. Additionally, the materials include lesson internalization protocols through the sections “Preparing for a Building Session,” “Preparing for a Consolidating Session,” and “Preparing for an Additional Practice Session.” These sections guide educators to clarify objectives, anticipate student thinking and misconceptions, prepare materials, identify formative assessment opportunities, analyze student responses, and use progress-monitoring data to inform future instruction.

In the unit, Journeys A, “Counting and Numbers,” educators can preview the key standards and objectives for upcoming lessons in the learning brief. The learning brief states, “In this journey, students practice rote counting and identify numbers in the 1–10 range.”

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

The materials in Math Journeys include resources to help instructional leaders with the implementation of the program. In the Program Guide, the “Hands on Partnership” section provides examples of how a math success manager can partner with and provide guidance for instructional leaders. Examples include “facilitation of [professional learning community] sessions, student work and progress monitoring analysis, aligning instructional practices, and developing a long-term tier two math model.”

Additionally, the on-demand video resources in the training materials provide guidance on specific strategies, such as “Let’s Add by Breaking Down.” The videos can help educators and leaders who may need more guidance on a specific strategy.

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 in the Math Journeys Program Guide include detailed guidance for lesson implementation and a breakdown of the instructional components within each journey lesson, along with suggested time frames for each part of the lesson. The materials outline components that educators can use to support consistent implementation of the program as designed. These components include educator-led instruction, student exploration, discussion, and practice activities. Additionally, multiple assessment resources are outlined in the Program Guide, including diagnostic and progress-monitoring tools. The digital practice progress reports specifically provide TEKS-aligned assessment data by identifying student performance for each TEKS to support instructional decision-making and monitor student growth.

In the grade 2 Math Journeys, the ELPS are included in each lesson. For example, in lesson B3.1, “Addition: Jumping on the Bead String,” the ELPS focus includes listening (E), speaking (E), and writing (C, F). The language objective is, “Students will explain how they break apart an addition jump to reach the next ten on a 50-bead string.” The language demand in the lesson provides guidance for students to “listen to oral prompts, sequence a strategy, and describe tens-and-ones reasoning with a visual model.”

Additionally, the materials provide guidance on how to use the companion by using one short section per lesson to add a compact ELPS layer, without crowding the main guide. Each lesson note names the language objective, language demand, expected oral and written output, and a simple placement note for classroom use.

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.

The materials in Math Journeys include guidance for lesson planning through clearly organized lesson components within the program structure. The materials support effective pacing and implementation by outlining the instructional sequence of “build, consolidate, and practice,” along with suggested time frames for each part of the lesson. Additionally, the lesson framework is designed to help educators deliver instruction in a consistent and purposeful manner as they provide students with a structured learning routine. The organization of the lesson components helps educators manage instructional time effectively and ensures that each stage of learning is addressed throughout the lesson.

The Math Journeys materials give educators detailed lesson plans for each station, including a summary and learning objectives aligned to the TEKS. The cluster overviews list the ELPS language goals and each lesson’s wrap-up features TEKS-aligned checks for understanding. For example, in the Journey A1, lesson 1, wrap-up, educators ask students, “Some friends are sitting around the table, and another one arrives. How many are there in total?” This question checks whether students understand the concept of addition.

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).

Each math journey provides a family letter in Spanish to help caregivers support learning at home. The letter suggests questions to ask, vocabulary to use, and specific activities caregivers can use at home to support their student’s learning. Educators can change the letter’s language to English with the language toggle in the top right corner.

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

In the Program Guide, the “Assessment and Progress Monitoring” section clearly defines each assessment and explains its purpose. Educators use the diagnostic assessment at the start of instruction to identify students’ prior knowledge and decide which journey fits each student. Additionally, educators use formative assessments, such as warm-ups, logsheets, and embedded checks for understanding, to adjust instruction in real time. Educators use summative assessments, including end-of-journey tests and cumulative progress reports, to evaluate student mastery of targeted skills and determine if students are ready to advance in the instructional pathway.

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

The materials in Math Journeys include educator guidance to ensure consistent and accurate administration of instructional assessments, including the Placement Test Implementation Guide. This guide includes the estimated length of the test, the role of the instructor during administration, and suggested materials. For example, the “Administration Guidance” section notes that “paper and pencil are recommended to support student thinking and working memory during the assessment.” This level of detail ensures that all educators administer the diagnostic assessment in a consistent and accurate manner across classrooms.

The End-of-Journey Test: Instructions and Guide shows educators exactly how to administer the end-of-journey assessment. The guide lists step-by-step procedures to help educators prepare before the test, lead students during testing, and complete tasks after the test day. On test day, educators make sure students have individual devices, help them find the assessment, enter the access code, and confirm that they submit their work correctly. These detailed steps help educators run the assessment consistently and efficiently.

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.

Materials provide educators with resources that give flexibility for assessments in classrooms with limited digital access or when paper-based testing is preferred. The materials help educators administer the digital end-of-journey test by offering printable versions of all assessment components. The “End-of-Journey Test: Instructions and Guide” gives educators downloadable links to printable PDFs, including administration instructions, journey tests, and answer key.

However, the materials do not include tools that educators can enable or disable to support individual students. For example, educators cannot enable or disable text-to-speech for individual students on the digital platform. Educators can change the language of instruction, but this is the only type of language support provided. Only students have the ability to independently activate audio support at any time. The digital interface also does not provide calculators, which means educators must supply and manage calculators during assessments.

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

The materials include diagnostic assessments with TEKS-aligned tasks and questions. In the placement test report sample, the diagnostic assessment identifies student performance across multiple mathematical strands, then processes and connects results to specific instructional pathways within the Math Journeys progression. The diagnostic assessment incorporates three levels of Depth of Knowledge (DOK) to measure students’ understanding and reasoning skills. For example, one assessment item asks, “How many fruits are there?” which aligns with DOK 1 because it requires students to demonstrate factual knowledge and basic recall. Another item asks, “What is the result of this operation: 43 + 26?” which reflects DOK 2 because students must apply procedural knowledge and mathematical computation skills. Additionally, the assessment includes higher-level questions such as, “Which of these numbers will be in the 5th position of the following sequence?” This question aligns with DOK 3 because it requires reasoning, pattern recognition, and problem solving skills. Collectively, these assessment tasks demonstrate that the diagnostic assessment measures student understanding across more than two levels of cognitive complexity.

Additionally, the materials include diagnostic assessments with interactive item type questions and tasks. In the placement test for grades K–2, students demonstrate their mathematical thinking in different ways as they move through item types such as multiple-choice, numerical-response, and number line placement questions. For example, in questions 1 and 2, students select a multiple-choice answer. In questions 3–8, students generate numeric responses independently. In questions 13 and 14, students place responses accurately on a number line. The inclusion of these varied item types supports a more comprehensive evaluation of student learning because it measures conceptual understanding, procedural accuracy, and mathematical reasoning across multiple formats.

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 materials also include interactive formative assessment item types with varying complexity levels. For example, student logsheets and digital activities include multiple-choice questions, number entry, text entry, and number line activities. Educators use wrap-up assessments to check learning throughout each lesson. One assessment item asks, “Which number do you hear?” This item aligns with DOK 1 because students demonstrate factual knowledge and basic recall. Another item asks, “What number is shown?” This item reflects DOK 2, as students apply procedural knowledge and mathematical computation skills to identify the number from visual images. The assessment also includes higher-level items, such as, “Which number is missing?” This DOK 3 question requires students to reason, recognize patterns, and use problem solving skills to determine the missing number in a sequence. Together, these assessment tasks demonstrate that the formative assessments measure student understanding across more than two levels of cognitive complexity.

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

The materials provide educators with detailed scoring information for interpreting student performance data through the placement test report sample. The instructional assessment report displays each student’s score and identifies the corresponding performance category, including low, medium-low, medium-high, and high achievement levels. In addition to reporting performance outcomes, the sample report offers recommendations for instructional placement based on assessment results. This comprehensive approach supports educators in making informed and individualized instructional decisions aligned with student learning needs.

For example, in the Journey Test B3 answer key, the “Item-by-Item Guide” section presents detailed rationales for both correct and incorrect responses. These rationales help educators understand student thinking and identify potential misconceptions. In question 1, students add 43 and 26. The rationale for the correct answer explains, “43 + 26 combines four tens and three ones with two tens and six ones. That gives six tens and nine ones, or 69.” The rationale for the incorrect answer of 62 states, “It is missing six ones from the second addend.” The rationale for the incorrect answer of 49 notes, “It adds only the six ones to 43 and does not include the two tens.” For the final incorrect response of 68, the rationale states, “68 is one less than the correct sum, and does not satisfy the expression.” This active language helps educators recognize student misconceptions.

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 placement test report guides educators on how to respond to student performance trends. For example, the “Placement in Journeys” section explains how educators can use assessment results to support instructional decision-making and student placement. Specifically, the placement test report helps educators group students for targeted instruction and determine appropriate placement within the Math Journeys program. Based on students’ assessment performance, the report generates suggested starting points for each student within the journey progression. This allows educators to differentiate instruction according to demonstrated levels of understanding and academic readiness.

The instructional materials in the End-of-Journey Test Answer Key and Formative Guide shows educators how to use activities and instructional supports in response to student performance. The guide details each assessment item, describes possible student misconceptions, and includes related skills and standards. The guide also includes “the student may…” statements and recommendations for additional support. Together, these components help educators analyze student responses and identify areas where students misunderstand concepts or lack skills. Additionally, the guide suggests targeted instructional support and interventions so educators can address student needs and promote academic growth based on assessment results.

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 instructional materials provide an educator dashboard that automatically compiles real-time student assessment data to help educators monitor progress and make instructional decisions. In the digital practice section, the general progress dashboard details weekly student performance by reporting hours spent on activities, the number of activities completed, overall grades, and performance data aligned with the TEKS standards for both the class and individual students. For example, the dashboard displays scores for each TEKS standard and uses a color-coded system—dark green, light green, orange, and red—to indicate varying levels of student performance and mastery. This feature enables educators to quickly identify strengths, areas of concern, and trends in student achievement to inform targeted instruction and intervention.

The instructional materials provide a digital platform in which students progress through the Math Journeys program based on their assigned placement levels. During activities, students receive immediate, real-time feedback on their responses through visual indicators, such as a checkmark for correct answers and a question mark for incorrect answers. While this feature supports immediate response validation and engagement during practice activities, the program does not provide students with tools to independently monitor or track their overall academic progress and growth over time. As a result, students have limited opportunities to engage in self-monitoring or reflect on long-term performance trends within the program.

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.

The instructional materials include educator prompts designed to support student reasoning and mathematical discourse. For example, in the lesson plan for “Addition: Jumping on the Bead String,” “Development: Activity 1” section, students hold up their pads with each answer after the educator’s cue. Guided by materials in “Development: Activity 2,” educators prompt students to explain why jumping to 40 first makes this addition equation easier, and how they know that 43 is a reasonable answer for 38 + 5. These prompts support student communication, critical thinking, and opportunities for verbalizing mathematical understanding.

The materials in the Math Journeys program guide educators to conduct checks for understanding throughout lesson activities. For example, in Journey B3, “Consolidating Addition and Subtraction I,” “Addition: Jumping Without Bridging” section, educators remind students that the empty number line in these activities shows the section with the numbers for each addition operation, and does not represent either the beginning or the end of the number sequence. Educators tell students before they start to mark the reference tens between which the addition numbers fall on the number line. This guidance supports educators in checking what students know and promoting efficient thinking strategies.

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

The digital Atlas Math Applet Library provides multiple opportunities for frequent checks for understanding throughout instructional activities. For example, in activity A1, “Words and Numerical Digits: Let’s Identify,” students listen to a number spoken orally and select the correct response from three answer choices. The activity provides immediate feedback based on student responses. If a student selects the correct answer, a green check mark appears and the next question is displayed. If a student selects an incorrect answer, the chosen response turns red and a question mark appears. The same question is then repeated orally with a reduced number of answer choices to support student understanding and provide another opportunity for success. If a student answers correctly after an initial incorrect response, the progress bar turns green but still includes a question mark to indicate that the first attempt was incorrect. If the student answers incorrectly a second time, the correct response is automatically identified, and the progress bar displays green stripes to indicate two incorrect attempts on the same question. These features provide educators with ongoing opportunities to monitor student understanding, identify misconceptions, and respond to student needs during instruction.

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 support logsheets in each lesson provide explicit, data-driven support and additional visual scaffolding. For example, Journey B, “Acoustic Counting Forward,” includes explicit support in the wrap-up where students record what they have learned. In the wrap-up task, students use the standard algorithm to complete three-digit addition problems, such as 547 + 238 and 545 + 240. Students answer, “Which addition seemed easier for you? Explain why they had the same result.” For students who are struggling, the guidance states, “students do not need to represent numbers with squares, bars, and crosses if they do not need them. For the second addition, some students may not need the green box.”

A support logsheet within the resources section of each lesson provides targeted assistance for students who require additional support to meet grade-level expectations. The support logsheet incorporates scaffolds in which students count, match, and use visual representations. These supports reduce the level of abstraction through concrete and visual models to help students develop a deeper understanding of grade-level concepts while working toward the intended learning outcomes.

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 materials in each math journey provide linguistic accommodations, including a Journey Language Bank that suggests general language support strategies and routines. Educators use sentence frames and discourse starters to help students use technical language during classroom discussions. The suggestions also offer discourse and writing prompts for specific lessons. The materials provide a Lesson-Level ELPS Companion with brief planning notes for each lesson. These companions support language development by identifying the language objective, language demands, expected oral and written responses, and suggestions for when to use the support during instruction. For example, in the Journey A1, lesson 3, “Writing Numbers to 100,” ELPS Companion, students use subtraction language to explain a verse of a song and identify how many numbers are left after one falls. Also in the companion, students respond to oral or visual clues, count aloud, and explain how many more are needed to make five. The materials provide an expected oral response with the sentence frame, “This group has a ___ more/fewer than ___.” The materials also provide an expected written response in the wrap-up where students draw a model and record the matching quantity. These supports help students develop academic language while engaging with grade-level math content.

The materials provide a Journey Language Bank and redirections for each journey. The Journey Language Bank includes routines, quick bridges for unfamiliar references, a lesson-by-lesson table that names unfamiliar references in each lesson, and the bridge to use beforehand to pre-teach the text’s context. The B3 Journey Language Bank and redirections offer additional pre-teach routines, discourse moves, writing prompts, and redirection options that educators can use selectively. For example, in lesson B3.1, the unfamiliar reference is “bead string: the two-color beaded tool the lesson assumes students already know (named in the title, never in Key Vocabulary).” The quick bridge for this lesson instructs educators to “hold up the bead string before the first jump and say, ‘This is a bead string. The beads change color every ten beads, so we can see the tens.’ Students point to one group of ten and repeat bead string and ten.”

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 materials in the Journey B3 Enrichment and Extension Guide include additional learning opportunities and grade-level extensions for students who are “ahead within the journey’s content.” In section two, educators facilitate and assess which students could benefit from extended learning opportunities. Sections three and four included extension logsheets and tips with links to each tool. The materials reinforce that enrichment and extension opportunities are ideal for students who are “ahead of the journey itself. The pattern of signals across sessions and tests (section 2, third signal) triggers the early End of Journey Test; above 75% the student advances to the next journey (section 5).”

The materials include enrichment and extension materials, as in the lesson “Addition: Jumping and Bridging Through 10 II,” in which students complete two rounds of additions. Educators tell students, “Add by representing along the number line and complete the rectangles with your answers.” Educators tell students to look at the numbers from task one and the answers from task two, then ask, “What do you notice?” The Enrichment and Extension Guide also supports educators by stating that mastery is met if the student “bridges through the ten deliberately on every item and states the pattern connecting task one and task two in general terms, then uses it to check or anticipate an answer without recomputing.” Additionally, mastery is not met if student work has “correct answers obtained by counting on in ones, and a literal reading of the two lists at the closing question, with no relationship proposed.”

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 digital materials do not include the ability for educators to enable or disable text-to-speech and content and language support. Additionally, digital materials do not include digital calculators.

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.

Math Journeys lessons intentionally use the concrete, pictorial, abstract (CPA) instructional sequence to encourage students to use their bodies, manipulatives, digital applets, or writing to show their understanding in multiple ways. Multilevel logsheets help students consolidate learning by recording hands-on experiences from each session. Lesson plans provide prompts and ready-made slides to encourage mathematical thinking and student discourse. Lesson plans also highlight when educators need to use manipulatives. In the lesson “Connecting Subtraction: Same Result,” activity 1, educators lead guided group discussions and use base ten blocks as visual aids. Students analyze subtraction pairs like 21 – 15, 22 – 16, and 19 – 13 to understand mathematical relationships. By comparing snap cube towers and number line distances, students observe that adding or removing the same amount from both numbers preserves the difference. Students then explain why equivalent subtraction expressions produce the same result. The lesson guides educators to ask questions such as, “What do you notice happens to the difference when we add the same number of cubes to both towers?”

Additionally, materials provide opportunities for students to demonstrate understanding of mathematical concepts in various ways. For example, in Journey B4, lesson 14, “Consolidating Addition and Subtraction II,” students count backwards by tens and ones in a circle and try to work as a class to get close to zero. Students use digital and concrete manipulatives and write their representations on individual papers. They communicate their ideas through physical base ten blocks, written equations, diagrams, symbols, and spoken language. Students justify their use of the equal sign to show that both sides have the same value.

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 materials provide explicit prompts and guidance for educators to build on prior knowledge. For example, the warm-up anchors big ideas by activating students’ prior knowledge at the start of each session. In lesson B4.11, students use their understanding of place value to order addition expressions from least to greatest without calculating. Students have opportunities to represent relationships in multiple ways, including through oral discourse or the use of manipulatives.

The materials provide explicit prompts and guidance to help educators build on prior knowledge and connect key mathematical ideas. In Journey B4, lesson 10, educators activate prior knowledge to help students develop fluency with basic addition and subtraction facts. Students connect simple addition and subtraction facts to larger numbers, multiples of 10, and multiples of 100. Students use base ten blocks, apply the standard algorithm to add multi-digit numbers, and solve real-life problems that require these skills. Students share strategies and solve problems together. These activities help students recognize patterns and relationships between concrete, representational, and abstract approaches to problem solving and allow them to represent their thinking in multiple ways.

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

The materials offer educators a variety of instructional approaches, including collaboration, structured conversation, and direct instruction. Educators typically deliver the warm-up in a whole-group discussion before utilizing a combination of whole-group and small-group work to provide students with multiple opportunities for hands-on exploration and student discourse. The wrap-up includes individual work for consolidation, followed by a group debrief. Each session is structured to transition seamlessly from guided discovery where educators facilitate hands-on exploration, to formalization. The warm-up prompts the educator to “have students form a circle and ask one student to choose a number between 90 and 100.”

The materials guide educators to deliver lessons effectively with multiple instructional approaches. In lesson 1, “Add and Subtract: Jumping without Bridging,” educators activate prior knowledge by asking students to solve 53 + 24 on a number line with their Magic Pad. After solving the problem, students review and discuss answers as a class before tackling related equations like 52 + 24 and 54 + 24. Educators prompt students to analyze patterns in the equations and discuss how the results change by one. The next activity extends this reasoning to subtraction equations and encourages students to collaborate and apply similar strategies. During the wrap-up, students independently solve more addition and subtraction problems on the number line, which reinforces the lesson’s strategies.

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 lesson materials outline small-group, collaborative, and individual opportunities for intervention and guide educators to facilitate different types of practice. Educators typically lead the warm-up as a whole-group discussion, then combine whole-group and small-group work to provide hands-on exploration and student discourse. The wrap-up assigns individual work for consolidation, followed by a group debrief. This approach lets educators implement different tiers of support within a single lesson. For example, in one lesson, educators instruct student pairs to calculate the distance on a number line. Educators first hand out a Magic Pad to each pair and generate two cards with the number cards widget. Students place the smallest number on the far left of the number line and the largest on the far right, then calculate the distance between the two numbers by jumping as many times as needed.

The materials include placement test reports that help educators group students based on their current proficiency levels. By reviewing this data, educators can plan targeted instruction, place students on appropriate learning paths, or provide small group interventions to address specific learning gaps. For example, the grade 2 placement test report organizes each journey and identifies which students would benefit from instruction within that journey based on their current learning 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.

Math Journeys grade 2 materials include enrichment and extension methods that support a variety of student engagement opportunities throughout the lessons. Support and extension sections embedded within instructional activities provide differentiated supports that allow educators to extend or scaffold learning based on individual student readiness and performance. The lessons also include explicit educator guidance for effective implementation through questioning prompts, manipulatives, number lines, partner discussions, visual models, and independent practice opportunities. For example, students solve problems using multiple strategies, calculate distances on number lines, compare solution methods, and justify their mathematical reasoning through whole-group, partner, and individual activities. These scaffolded supports and enrichment opportunities equip educators with the tools needed to differentiate instruction for students while maintaining meaningful engagement with grade-level mathematical concepts and skills.

Additional extension activities engage students and include instructional guidance for each task. For example, in Journey A2, lesson 3, students find numbers whose digits sum to 7, 11, and 13. They compare results with classmates to identify which case has the most solutions and examine patterns on a hundreds chart. Students also create numbers using a set number of digital segments and analyze which segments they use most and least frequently.

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

Within the Math Journeys materials, each lesson overview provides educators with specific prompts and guidance to use with students during lessons to provide timely feedback. These prompts guide educators to pause at key moments during the lesson to check for student understanding, address misconceptions, and provide immediate and meaningful feedback to students in real time. This support ensures that educators are equipped with the tools needed to deliver responsive instruction and keep students on track toward meeting the lesson objectives. In activity two, educators ask students, “What are some different ways we could use the snap cubes to solve this problem? Could you explain which strategy makes more sense to you and why?”

The materials provide language banks for each journey that help educators give timely feedback during instruction. These banks offer pre-teach routines, discourse supports, writing prompts, and guidance for redirecting misconceptions. For example, the B4 Journey Language Bank names specific lessons for pre-teach routines and supplies sentence frames for partner discussions, quick writes, and revising explanations. The language bank also includes a section on misconceptions and redirection to help educators interpret student responses and deliver corrective feedback.

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.

Each journey provides a Lesson-Level ELPS Companion with a table that outlines the ELPS focus, language objective, language demand, expected oral and written output, and suggested use for every lesson. This is present in session C1.1, “Exploring Doubles I,” “Development: Activity 2,” in which educators ask questions such as, “Could you explain what happens to the tens and ones when you double 24?” and “How does that relationship help you find the double of a different number, such as 37?”

The materials provide a digital Teacher Guide with embedded linguistic accommodations for all current levels of the ELPS. In Journey A8, “Rote Counting,” activity 2, the bilingual tip includes a suggestion for each of the five proficiency levels. For example, the educator prompt for pre-production students states, “Say a number: the student steps to it and points, no talking.” Additionally, the advanced suggestion states, “Stepping forward adds 1 and stepping backward subtracts 1, every time.”

The materials provide a digital Teacher Guide with embedded linguistic accommodations for all current levels of the ELPS. In Journey C1, “Exploring Doubles I,” activity 2, the bilingual tip includes a suggestion for each of the five proficiency levels. For example, the educator prompt for pre-production students states, “The student builds the double or half with blocks while a partner says it.” Additionally, the advanced suggestion states, “To halve ___, I exchanged one ten for ten ones because ___.”

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.

The digital materials offer text-to-speech, visual manipulatives, and a support button to help with content, but do not provide linguistic accommodations. For example, in applet 95, “Numbering and Calculation,” when students select the wrong equation, the help button prompts, “Listen to the number and select the correct response.” Students can use this prompt to find the number they hear, but the materials lack linguistic accommodations for students who do not understand due to language barriers.

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

In the Math Journeys grade 2 program, educators use the Lesson-Level ELPS Companion to implement materials effectively in bilingual and ESL programs. These materials outline lesson-level language objectives, linguistic demands, expected oral and written production, and suggested supports aligned to the TEKS and ELPS. For example, the B4 Lesson-Level ELPS Companion shows educators how to use sentence stems, mathematical discourse opportunities, and instructional notes to support students’ listening, speaking, and writing development. These materials help educators integrate language acquisition strategies during math instruction.

Additionally, the Texas Bilingual/ESL Implementation Guide includes educator guidance on instruction for emergent bilingual (EB) students. The guide is organized into two sections: part one, “Reusable Core for All Math Journeys,” and part two, “Journey Addendum.” The guide identifies the frequent use of visible models and hands-on materials—such as objects, drawings, number paths, ten frames, graphs, cubes, cards, and movement-based activities—as an important feature.

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 Math Journeys grade 2 materials include embedded guidance to support EB students as they develop academic vocabulary, increase comprehension, build background knowledge, and make cross-linguistic connections through oral and written discourse. The materials include key vocabulary, sentence stems, structured partner discussions, and written response opportunities to support language development during math instruction. For example, in the lesson “Addition: Making 10,” students use academic vocabulary, such as decomposition, sum, total, and addition, to explain mathematical thinking orally and in writing. During collaborative discussions, the “Emergent Bilingual Students” section provides sentence stems and guided discourse opportunities to help students explain how numbers change when decomposing and recomposing quantities.

The materials throughout the Math Journeys program include embedded guidance to support EB students as they develop academic vocabulary, increase comprehension, build background knowledge, and make cross-linguistic connections through both oral and written discourse. Each lesson includes a key vocabulary section that identifies cognates to support language development. For example, in lesson 16, “Productive Practice: Addition within 20,” the listed cognates include equivalent/equivalente, compare/comparar, and equation/ecuación. The lesson builds background knowledge during a warm-up routine called “Which Does Not Belong?” in which students analyze and discuss mathematical representations, apply the same routine with equations, and justify why one equation does not belong with the others. Students then extend their understanding as they discuss, solve, and record equations related to additional mathematical problems. These activities provide opportunities for students to engage in mathematical discourse, strengthen academic language, and make connections between conceptual understanding and written mathematical representations.

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 grade 2 Math Journeys materials include practice opportunities and instructional assessments throughout the learning pathway that require students to demonstrate depth of understanding aligned to the TEKS. For example, in lesson 17, “Addition and Subtraction Word Problems: Free Strategy,” students create a movie theater story for 42 - 13, which allows students to connect subtraction to a familiar real-world situation. Students then check that the numerical answer makes sense within the context. Next, students create a second problem with the same operation, a task that requires conceptual understanding beyond computation. The wrap-up presents multistep situations in which students select operations and justify their choices. For example, students work to solve the word problem, “Lauren blew up 24 yellow balloons and 19 blue balloons for her party. After playing with her friends, some balloons popped. If there are now 18 inflated balloons left, how many have popped?” This closure activity serves as an instructional assessment where students use problem solving, mathematical reasoning, and written responses to demonstrate depth of understanding aligned to the TEKS.

The materials provide practice opportunities that require students to demonstrate depth of understanding aligned to the TEKS. For example, in Journey B4, lesson 11, activities 1.1–1.3, students view worked examples that contain errors. Students then identify the mistakes, correct them, and justify why derived-fact and decomposition strategies produce identical results. Students engage in the TEKS process standard 2.1.G when they use precise mathematical language to explain and justify why the shown solution to 62 - 58 is incorrect. Next, students articulate that eight represents the length of the remaining jump after subtracting five tens, not the final result of the subtraction, and then use a number line to justify that the correct answer is four. Students analyze the different strategies and determine which is most efficient for them. The materials also provide assessment opportunities that require students to demonstrate depth of understanding aligned to the TEKS. In independent work task 2, for example, students use cards to complete inequality expressions. This demonstrates depth because it connects multiple solution paths to symbolic comparison, thus functioning as a formative assessment aligned to TEKS 2.4.B.

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 grade 2 Math Journeys items, including enrichment and extension materials, increase in rigor and complexity as students move through them on the path to grade-level and above grade-level proficiency in the mathematics TEKS. For example, in the warm-up for lesson B2.16, “Productive Practice: Addition within 20,” students identify the number that does not belong. To do so, they analyze groups of representations and addition expressions, identify an intruder, and use mathematical evidence to justify their reasoning. The educator asks students questions that require them to explain and defend their reasoning, such as, “Could you use specific words to explain why this one doesn’t belong?” and “Can you describe exactly what makes this item different from the others?” Students are encouraged to consider multiple valid solutions and justify the attributes used to support their conclusions. In activity 2, students create sums, identify equivalent expressions, and generate multiple equations that produce the same result. To increase rigor, the educator asks students to explain why different equations produce the same sum, and to justify how they know that their solutions are equivalent. To complete these tasks, students analyze number relationships, compare solution strategies, and construct mathematical arguments. Throughout the learning pathway, students independently identify combinations that sum to 10, complete equations, and apply their understanding of addition relationships. The materials include extension opportunities in which students explore all possible sums that can be created with a given addend. This encourages pattern recognition, generalization, and mathematical reasoning beyond the core lesson expectations.

Another example of how grade 2 Math Journeys materials increase in rigor and complexity on the path to grade-level and above grade-level proficiency in the mathematics TEKS is Journey B3, lesson 17, activity 1. The task starts with single-operation movie theater problems for 42 - 13. Activity 2 then moves to a three-quantity bus problem. Activity 3 introduces a multistep farm problem with cows, horses, and chickens, in which students chain together subtraction steps without a prescribed equation structure. In activity 4 of the wrap-up, students extend their reasoning in grade-level applications as they compose an original problem for 27 - 15. This activity requires higher-level thinking, builds a solid foundation, and prepares students for multistep word problems in TEKS 3.4.A. In these tasks, students reason strategically, apply their understanding of place value, and use subtraction concepts flexibly beyond the core lesson.

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

The materials for Math Journeys grade 2 provide a horizontal layout that builds on previous scopes within the grade level. For example, in activity 1.2, student pairs use derived facts to solve a two-digit subtraction problem. This task connects place-value structure to estimation and strategy choice within the same grade-level range. The session then links number line reasoning directly to decomposition, which shows that both models are valid for solving the operation and the answer is the same. This horizontal connection across jumping, decomposition, and derived-facts strategies unifies the big idea that equivalent representations yield identical results.

The grade 2 materials provide multiple opportunities throughout the learning pathways for students to demonstrate depth of understanding aligned to the TEKS. For example, in lesson 11, “Comparing Addition and Subtraction Strategies,” students analyze whether addition and subtraction equations have been solved correctly. Students identify errors in the solutions and then use a more efficient mental strategy to solve two-digit subtraction problems, in alignment with TEKS 2.4.B. The lesson further promotes conceptual understanding as students evaluate mathematical reasoning and justify their corrections. In the lesson’s “Wrap-Up” section, students continue to demonstrate depth of understanding as they analyze an equation, identify any errors, and apply mental strategies to determine the correct solution. Collectively, these activities provide opportunities for practice, mathematical reasoning, and formative assessment while supporting students’ mastery of the targeted TEKS.

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.

The Math Journeys grade 2 materials clearly show how each scope connects across grades. For example, the cluster D overview in “Representing Fractions: Length Model I,” explains how students move from using area and set models in D1, to placing fractions on a number line in D1.11, and finally to working with decimals on the number line in D6. This connects concepts from grade 2 through grade 6. In activity 1.2, students iterate unit fractions along a paper strip. Educator notes explicitly show how this length model prepares students for future number line work. When students iterate unit fractions, they use measurement skills that help them build number line diagrams. The session also shows students that a larger denominator creates a smaller unit fraction, a key idea they will use in fraction comparison, decimal place value, and division in later grades.

In grade 2, Journey C, “Multiplicative Thinking, Cluster Overview,” students move away from counting by ones to thinking in groups. They use rectangular arrays and fixed interval jumps on the number line to understand multiplication as iterated addition. Finally, students use what they learned in previous lessons to move from simple grouping to proportional reasoning and the distributive property.

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.

In the Math Journeys grade 2 materials, students connect concepts from earlier lessons. For example, in activity 1.1, “Addition by Decomposition: No Regrouping,” students return to base ten block grouping from Journey B2. In the activity, students count the rods on one side and the units on the other, which links their prior counting skills to the new decomposition strategy. Educators are given guidance on how to help students reason through problems like 20 + 10 = 30 and 4 + 5 = 9. Educators use these examples to bridge known single-digit addition facts to two-digit addition with decomposition. Later lessons extend this skill up to numbers as large as 1,200. The B3 Journey Instructional Guide explains that this session prepares students for regrouping in B3.10 and for learning the standard addition algorithm in B5.

The materials include lessons and activities that connect students’ prior knowledge of concepts and procedures to learning in the current grade, while it additionally prepares them for future mathematical understanding. In lesson 12, “Subtraction by Decomposition: Regrouping,” students build on their previous experience decomposing numbers in subtraction situations that do not require regrouping, and extend this understanding to problems that involve regrouping. During the lesson, students use manipulatives and visual models to represent the decomposition of a 10 into 10 ones. This allows students to explain both the process and reasoning behind regrouping when subtracting. These hands-on experiences help students connect the conceptual understanding of place value with the procedural steps used in the standard subtraction process. By linking prior knowledge of decomposition to more complex subtraction situations, the lesson develops students’ fluency and understanding of multi-digit subtraction. This learning supports current grade-level expectations and provides a foundation for future work with larger numbers, multi-digit addition and subtraction, and more advanced computation strategies beyond 100.

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

The grade 2 materials in lesson 15, “The Number 10 (Part 2),” give students spaced retrieval opportunities to revisit skills from earlier lessons. In the warm-up students revisit the “Which one doesn’t belong?” routine from previous sessions. In activity 1.1 students return to base ten block representation that they learned in B3.1–B3.8 with bead-string activities. In activity 2 students practice the tens-and-ones skill they developed during the B3 jumping sessions to apply the decomposition strategy to 51 + 43. By bringing back both the grouping concept and the bars-and-crosses procedure throughout the learning pathway, the materials help students practice and remember important skills and concepts.

In another example, students revisit skills they learned earlier in the B3 and B4 learning pathway. In the warm-up students practice ordering-by-sum reasoning from B3.15 without doing calculations. In activity 1.1, students identify and correct an error in a number line solution, which helps them strengthen the procedural skills they practiced in B3.3–B3.8. Students actively use their prior skills in new situations within these tasks.

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

In cluster overview A, “Counting and Numbers,” students practice different skills and concepts together through interleaved activities. For example, in activity 1.1 students order addition expressions without calculating. In activities 1.2 and 1.3, students apply three previously learned concepts in sequence. Students analyze a subtraction problem solved with derived facts and an addition problem solved by decomposition. For independent work, in task 2 students use number cards to fill in blanks for both addition and subtraction inequalities, which utilizes skills from B4.2–B4.9. This lesson structure avoids blocked practice and encourages students to choose strategies flexibly for both operations during one session.

The materials provide interleaved practice opportunities by incorporating multiple related skills and concepts within the same lesson. For example, in lesson 11, “Comparing Addition and Subtraction Strategies,” the learning objective focuses on students’ ability to use different strategies to solve addition and subtraction equations within 100. Throughout the lesson, students examine, compare, and discuss different solution strategies, then apply those strategies to solve a variety of addition and subtraction problems. Students deepen their understanding of number relationships and develop strategic competence as they move between operations and evaluate multiple approaches to problem solving. This intentional integration of skills promotes flexible thinking, encourages students to select efficient strategies, and strengthens their ability to apply mathematical concepts across different types of problems.

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 grade 2 Math Journeys, B4.11, “Comparing Addition and Subtraction Strategies,” students interpret, analyze, and evaluate models and representations of mathematical concepts and situations. During the warm-up students interpret addition expressions and analyze relationships among numbers to order sums from least to greatest without calculating. In activity 1, students analyze an incorrect number line representation of 62 - 58 = 8. They then identify the error and use mathematical reasoning to determine the correct solution. Educators ask questions such as, “Do you understand what makes this solution incorrect?” and “Could you explain your process for finding and fixing the error?” Students justify their thinking and evaluate the accuracy of the representation. In activity 1.2 students analyze derived fact representations and compare number line models to explain why 33 - 20 = 13 and 32 − 19 = 13 produce the same result. In activity 1.3 students interpret and analyze a decomposition model representing 47 + 65 = 100 + 12 = 112, a task that connects multiple representations of the same mathematical idea. During the wrap-up, students complete a “find and fix the error” task, evaluate mathematical representations, identify inaccuracies, and revise incorrect solutions.

The materials provide educators with guidance and recommendations for using various instructional approaches to deliver effective lessons. For example, lesson 4, “Cardinal Counting (up to 20),” offers opportunities for student discussion and explains when and how to transition between whole-group, small-group, and independent activities. In activity 1 students count their snap cubes as they first make a group of 10 and place the extras to the side. This task emphasizes place value and supports cardinal counting of numbers greater than 10. In another example, 13 represents one group of 10 and three more. In activity 1.2 students work in pairs and use snap cubes to build 16 and 11, and 18 and 12. Students should understand that the smaller number appears earlier when counting forward, and later when counting backward.The lesson encourages students to write responses, justify their thinking, and explore math concepts hands on with manipulatives. It also connects mathematical concepts to real-world problems and scenarios.

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

In Math Journeys grade 2 students create concrete and pictorial models of mathematical situations. For example, in Additive Journey B3, activity 1.1, students represent numbers with rods and units of base ten blocks on a tray, creating concrete models before any written work begins. In activity 2, students represent numbers on the side with bars and crosses to symbolize the rods and units, which produces a pictorial record on the Magic Pad. Both steps are tied to the same addition expression and connect the concrete manipulation directly to its drawn equivalent.

The materials include questions and tasks that provide opportunities for students to create concrete models and pictorial representations. In lesson 10, “Reviewing Addition and Subtraction,” students use base ten blocks to create concrete representations of numbers such as 423 and 216, placing each quantity on separate trays to model place-value concepts. The educator asks questions about the quantities represented and to determine the total value when the collections are combined. Students manipulate the base ten blocks to model addition as they physically join hundreds, tens, ones, and regroup as needed to find the sum. They also use the blocks to model subtraction situations and demonstrate the action of decomposing and regrouping quantities. After they work with the concrete materials, students create pictorial representations as they draw base ten blocks to record and explain their addition and subtraction strategies, including regrouping. Through these activities, students connect hands-on models to visual representations, deepen their understanding of place value and operations, and make their mathematical thinking visible through multiple forms of representation.

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

In Journey B3.17, “Addition and Subtraction Word Problems: Free Strategy,” students apply counting strategies to identify quantities in sets of objects. In activity 1 students create a movie theater word problem for 42 - 13 and 80 - 31, then invent contextual situations that can be solved using those expressions. Next, students use previously learned strategies to solve the problems, including jumps on the number line and decomposition, and explain how their solutions connect to the context. Activity 2 then presents a multistep bus problem in which students decide which operation fits an unfamiliar situation. Students solve real-world situations that involve buses, farms, and other everyday contexts as they select and apply appropriate strategies, rather than following a prescribed procedure. Students may choose different solution methods and emphasize connecting the numerical result to the question being asked. The wrap-up independent tasks extend this further, where students make up a problem to solve 27 - 15. These tasks require students to transfer conceptual understanding and problem-solving strategies to new mathematical situations and contexts.

The grade 2 materials include questions and tasks that provide opportunities for students to apply conceptual understanding to new problem situations and contexts. In lesson 12, “Development: Activity 1,” students apply their understanding of addition strategies as they use base ten blocks to solve the expression 134 + 47. Students analyze the relationship between 134 + 47 and 131 + 50 by recognizing that moving three ones from the first addend to the second creates a more efficient computation while preserving the sum. Students then extend their understanding as they describe a real-world situation in which this addition expression could be applied. The lesson continues by having students apply the same reasoning to subtraction expressions and adjust numbers to create easier problems, while maintaining the same difference. The use of manipulatives supports conceptual understanding and helps students develop flexible strategies that transfer to paper-and-pencil calculations in new mathematical contexts.

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

The materials in grade 2, Journey B2.16, “Productive Practice: Addition within 20,” include tasks designed to develop the automaticity and fluency that students need for grade-level math. For example, in activity 2.1 students place number cards face down, flip two at random, and independently write the sum before they reveal answers to their group. This builds rapid recall of sums within 20. In activity 2.2 each student finds two pairs of cards with equal sums and records them as equations, which reinforces flexible fluency with the equal sign as equivalence. Students identify different combinations of numbers that produce the same sum and record multiple equivalent equations, such as 3 + 2 = 1 + 4 and 4 + 7 = 5 + 6. Students discuss and compare strategies as they reinforce efficient recall of addition facts. In the wrap-up, students work independently to identify combinations that equal 10, complete missing addend equations, and use given number cards to generate additional number combinations. Through repeated opportunities to compose numbers, recognize equivalent sums, and apply addition relationships, students develop the automaticity and fluency needed to support grade-level mathematical problem solving and computation.

Atlas Math systematically sequences related subtraction facts derived from known results. For example, the materials present 37 − 5 = 32 followed by related problems such as 37 − 6 and 37 − 16, encouraging students to use known differences rather than recalculating each time. The platform continuously monitors accuracy and response time and adjusts pacing and difficulty to support the development of true automaticity alongside conceptual fluency. Students who respond quickly and accurately advance to more complex derived-fact relationships, while those who need additional time receive repeated exposure to similar fact chains. This adaptive structure builds automaticity with basic subtraction facts and promotes flexible fluency across the 1–100 range, in alignment with the expectations of TEKS 2.4.B and 2.7.B.

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

The materials provide efficient, flexible, and accurate mathematical procedures throughout learning pathways as they guide students from conceptual understanding to application. In the lesson “Comparing Addition and Subtraction Strategies,” activity 1.1, student pairs order expressions by sum without calculating to practice efficient estimation procedures across the learning pathway. Furthermore, in activities 1.2 and 1.3 students identify errors in the number line and derive facts and solutions, which builds accurate procedural checking. For independent work, students find and fix the error, which prompts flexible selection among jumping, decomposition, and derived-facts strategies.

The grade 2 materials provide opportunities for students to practice the application of efficient, flexible, and accurate mathematical procedures. The lesson 11 objective explicitly states that students will learn to “analyze the strategies used to solve addition operations.” To begin, students use estimation to order expressions from least to greatest. Students then analyze errors represented on a number line as they check the accuracy of addition and subtraction procedures. At the same time, students identify and correct misconceptions. Throughout the lesson, students evaluate multiple problem-solving strategies, which promotes flexible thinking and deeper understanding of different approaches to computation. These activities strengthen procedural fluency and accuracy while building a strong foundation for students to solve increasingly complex mathematical problems in future learning.

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.

Throughout the grade 2 Math Journeys learning pathways, students evaluate the efficiency, flexibility, and accuracy of mathematical representations. For example, in Journey B4, “Consolidating Addition and Subtraction II,” activity 1.1, students evaluate whether the subtraction problem 62 - 58 has been solved correctly on a number line. Students then identify the error and justify their reasoning. Next, students compare counting-back strategies to find the distance between two numbers. The materials explicitly state that, “since the minuend and subtrahend are close to each other, students should reflect and conclude that calculating the distance between the two numbers is more efficient than starting at 62 and jumping back 58 units. Students evaluate the efficiency of different solution methods before they evaluate decomposition against distance calculation, and finally judge which is more efficient for close numbers. In the wrap-up independent work students directly evaluate the accuracy of presented solutions to find and fix the error.

The materials give students opportunities to evaluate mathematical representations, models, strategies, and solutions for efficiency, flexibility, and accuracy. In Journey B3, lesson 15, activity 1, one partner uses the number line to solve 35 + 42, while the other partner uses decomposition. Students compare their results to see if both strategies produce the same sum. If the sums differ, students identify and explain the error. Students evaluate accuracy as they decide which representation correctly models the problem, and whether each step matches the intended value. In activity 2, which introduces regrouping, students evaluate flexibility and efficiency to determine which strategy they find easier and why. When the educator asks, “Could you explain your method step by step?” students justify their reasoning and evaluate how clear and efficient their chosen strategy is. Throughout these tasks, students assess not only correctness but also how useful different representations and procedures are.

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

The grade 2 Math Journeys materials support students as they select increasingly efficient approaches to solve mathematical problems. For example, in Journey B4.5, “Add & Subtract: Grouping Jumps of 10,” activity 2.1, students use jumps on a number line to solve 43 + 45 and then compare alternative approaches. The Teacher Guide instructs educators to “ask students if there is a way to perform the jumps more efficiently,” then demonstrate the consolidated jump on the jumping strategy widget. This scaffolds students from many small jumps toward a single grouped jump to build increasingly efficient number line reasoning.

The materials structure opportunities for students to select increasingly efficient approaches to solve a given problem and evaluate which is most effective. For example, in Journey B4, lesson 11, activity 1.1, students use number relationships and estimation to order expressions, rather than calculation. Students determine which strategy they find easier after they compare number line and decomposition solutions side-by-side, which prompts students to reflect on the relative efficiency of different approaches. Educators “ask students if they can think of a more efficient strategy” and encourage students to consider alternatives beyond an initial method. In particular, students learn to recognize that when numbers are close together it may be more efficient to calculate the distance between them rather than use a longer counting or decomposition process. Throughout the lesson, students repeatedly compare methods and discuss why one strategy may be preferable in a particular situation. This develops students’ ability to select strategies intentionally based on efficiency, rather than apply the same procedure to every problem.

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

The grade 2 Math Journeys materials explicitly state how the conceptual and procedural emphasis of the TEKS are addressed in cluster overview B, “Additive Thinking.” The overview describes how students develop an understanding of addition and subtraction, place-value reasoning, decomposition, and the relationships among numbers and operations. For example, the materials explain how students use representations and strategies to understand additive situations, compare solution methods, and make connections among concrete, pictorial, and symbolic models. To identify the procedural emphasis, the overview outlines the skills students will practice throughout the learning pathway, including learning to solve addition and subtraction problems, decompose numbers, represent operations with equations and models, and apply efficient strategies to determine solutions.

In the lesson, “Subtraction by Decomposition: Regrouping,” students use base ten blocks to exchange one rod for 10 units. This helps students understand why regrouping does not change the value of a number. Through hands-on modeling, students build an understanding of the relationship between tens and ones and why regrouping is necessary in subtraction. Additionally, materials explicitly address the procedural emphasis of the TEKS by guiding students to use decomposition and regrouping to solve subtraction problems. Students first model the process with manipulatives and then record their work, which supports both understanding and accurate application of the procedure.

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.

The materials include opportunities for students to use concrete objects, pictorial models, and abstract strategies to model equations. In the lesson, “Subtraction by Decomposition: No Regrouping,” students work in pairs to represent 45 with physical rods and units, creating concrete base ten models before recording. In activity 2 students draw bars and crosses on their Magic Pads to produce pictorial representations of the same decomposition. Students then write the vertical equation 51 + 43 = 94 with place value notation, which completes the abstract step aligned to TEKS 2.4.B.

Furthermore, similar to the lesson mentioned above, in the “Subtraction by Decomposition: Regrouping” lesson students use concrete, pictorial, and abstract representations to model subtraction with regrouping. In activity 1, to solve problems such as 75 - 47, students use base ten rods and units to create a concrete model and physically exchange one rod for 10 units. In activity 2 students use $10 bills and $1 bills as pictorial representations of the same regrouping process. Students then use the decomposition strategy widget and a standard column diagram to record their work, which connects the concrete and pictorial models to an abstract representation of subtraction.

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 grade 2 Math Journeys materials include supports for students as they learn to connect, create, define, and explain concrete and representational models to abstract concepts, as required by the TEKS. In Journey B3.12 students use base ten blocks and visual representations to model subtraction with regrouping, and connect these models to the standard written algorithm. In activity 1 students represent 75 with base ten blocks and model the subtraction of 47 by physically exchanging four tens bars for 40 unit cubes. To justify their ideas using mathematical language, educators ask students to explain to their partners how they solved the problem. Students describe how they exchanged one rod for 10 units so they could subtract seven ones and explain why the result is 28. Educators ask students, “How can you justify that exchanging 1 ten for 10 ones does not change the value of 75?” Through these supports, students connect, create, define, and explain concrete and representational models as they develop understanding of subtraction with regrouping.

The materials include support for students to connect, create, define, and explain concrete and representational models in relation to abstract mathematical concepts. In lesson 12, “Subtraction by Decomposition: Regrouping,” students build understanding as they use base ten blocks as concrete models to represent subtraction with regrouping. Students physically demonstrate the process of decomposing a number by exchanging one ten rod for 10 individual units. Students then model the regrouping process and record the corresponding subtraction equation as they connect this concrete representation to representational and abstract understanding. Throughout the lesson, students use precise mathematical language to justify their thinking and explain the strategy they used to solve problems, including how exchanging the ten rod for 10 ones allows them to complete the subtraction. This process provides students with opportunities to define and explain mathematical concepts through multiple representations, which supports deeper conceptual understanding as it addresses diverse learning needs and strengthens mathematical communication skills.

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

In the grade 2 Math Journeys materials, students use visuals, manipulatives, and other language development strategies to develop academic mathematical language. In cluster overview B, “Additive Thinking,” dedicated vocabulary sections introduce mathematical terms related to addition, subtraction, decomposition, regrouping, place value, and mathematical strategies. The overview incorporates visual representations such as base ten blocks, number lines, additive boxes, equations, and pictorial models to help students develop their use of academic mathematical language. Sub-section B3, “Consolidating Addition and Subtraction 1,” includes the vocabulary tens, ones, digits, place value, expanded form, and align. Throughout the learning pathway, students engage in mathematical conversations and use precise vocabulary to connect concrete and pictorial models to symbolic representations. Students have many opportunities to listen, speak, read, and write about mathematics, which supports the development of academic mathematical language aligned to the TEKS.

The grade 2 lesson development activities provide intentional opportunities for students to develop academic mathematical language. For example, in lesson 6, “Representing Fractions: Length Model I,” students engage with key mathematical vocabulary—including unit fraction, numerator, denominator, and equal length—as they explore fractional relationships. Students use visual models and concrete manipulatives, such as ribbons, to represent fractions, then connect these representations to fractional units including halves, thirds, and fourths. Educators support students’ oral language development through structured sentence stems, such as, “The strip is divided into ___ equal parts, so ___ is the denominator.” Students then use discipline-specific vocabulary to explain their mathematical reasoning. By connecting hands-on manipulatives and visual representations to the abstract concepts and symbolic notation of fractions, the materials build a strong foundation for academic mathematical language development, and strengthen students’ ability to use precise mathematical vocabulary to communicate mathematical understanding.

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 grade 2 Math Journeys lesson activities include embedded guidance for educators to scaffold, support, and extend the development of students’ academic mathematical vocabulary. For example, support for EB students at the intermediate level provides tiered sentence frames, such as “I added the tens… then the ones.” Support for students at the advanced high level escalates to justifying the associative property, thus scaffolding vocabulary by proficiency.

Educators incorporate sentence frames to support students as they communicate their mathematical thinking during conversations with peers and educators, such as, “I added the tens: ___ plus ___. Then the ones: ___ plus ___.” These structured language supports help students practice precise mathematical vocabulary as they use place value concepts to explain the process of addition. These materials further strengthen student language development by guiding educators to model and describe the step-by-step process used to find partial sums by adding tens and ones separately. This helps students connect mathematical procedures to academic vocabulary and conceptual understanding. By embedding opportunities for structured discussion, explanation, and justification of mathematical thinking, the materials create meaningful contexts for students to communicate mathematical ideas clearly while building confidence and proficiency in academic mathematical language.

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

The materials provide clear guidance to help students use appropriate mathematical language and academic vocabulary during discussions. For example, in the lesson “Subtraction by Decomposition: Regrouping,” activity 1, students explain their problem solving strategies to partners. During the task, educators encourage students to use precise terms like exchange, tens, and ones. The materials also direct educators to ask, “How can you justify that exchanging one ten for 10 ones does not change the value?”

Additionally, the materials embed guidance that actively helps students use academic language and vocabulary during mathematical discussions. In lesson 4, students practice using precise mathematical language as they explain strategies for combining jumps on a number line. The lesson models this language with examples such as, “I combined four jumps of 10 into one jump of 40,” and “Instead of jumping 10 four times, I made one big jump of 40.” Students then restate and apply this language as they explain their reasoning and discuss strategies with peers. These supports strengthen students’ ability to communicate mathematical thinking clearly, use content-specific vocabulary accurately, and engage in meaningful mathematical conversations.

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

The materials provide prompts and guidance for educators to facilitate conversations about math topics. For example, in Journey B3.12, “Subtraction by Decomposition: Regrouping,” activity 1, students create and share word problems for 42 - 13. The reason for this task is to allow students to hear operation language in authentic story contexts. Educators ask, “Did you and your partner arrive at the same answer? If not, explain your reasoning,” which requires students to refine explanations with precise math language. Additionally, in the routine for EB students, partners generate and discuss questions together to embed repeated use of academic vocabulary, such as difference, total, and operation.

The materials in Journey B3.17, “Addition and Subtraction Word Problems: Free Strategy,” include embedded guidance for educators to facilitate classroom conversations in which students actively use, hear, and refine mathematical language through collaborative discussions. In grade 2 students engage in a warm-up activity where they analyze an image that shows three cubes with five dots on each cube. Another image shows five cubes with three dots on each cube. Students are then asked to explain how the two groups are similar and different. Students focus on comparisons and relationships between the representations to reason mathematically and communicate their thinking. The lesson extends this discourse with a similar task that features an additional image of cubes, for which students also generate multiple justifications to support their reasoning. Through these structured discussions, students listen to the ideas of their peers, apply mathematical vocabulary to explain their thinking, and refine their language as they consider multiple perspectives. This activity fosters a collaborative learning environment where students engage in meaningful mathematical conversations, strengthen communication skills, and participate in rich academic discourse.

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.

The materials in Journey B4.11, “Comparing Addition and Subtraction Strategies,” include embedded guidance to help educators anticipate a variety of student answers, as well as exemplar responses to questions. Additionally, the warm-up activity anticipates student arguments for ordering expressions without calculating, and provides sample reasoning such as, “42 + 47 will have the greatest sum because it is the only expression with a four in both ten places.” Activity 1 presents a pre-worked equation where students identify the error of interpreting eight as a final result, rather than a remaining jump. Students then use the number line to find the correct answer. To redirect inaccurate thinking, educators ask, “Could you explain your process for finding and fixing the error?”

The materials in Journey B4, “Consolidating Addition and Subtraction II,” include embedded guidance to help educators anticipate a variety of student responses. The materials also guide educators on how best to address misconceptions or redirect inaccurate mathematical thinking during instruction. In the warm-up activity the materials include exemplar responses for tasks in which students order expressions based on the value of their sums. Students use addition properties to formulate mathematical arguments, such as explaining that 35 + 32 has a smaller sum than 34 + 39 because if one unit is moved from 39 to 34, the expression becomes 35 + 38. The lesson identifies possible student misconceptions and supplies explanations that help educators recognize and address incorrect reasoning during discussion. These exemplar responses and instructional supports prepare educators to respond effectively to a range of student thinking, guide students toward accurate mathematical reasoning, and strengthen conceptual understanding through targeted feedback and clarification.

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

The materials embed the TEKS mathematical process standards within each scope. For example, in lesson B3.17, “Addition and Subtraction Word Problems: Free Strategy,” activity 1, students create a word problem for 42 - 13. Students connect subtraction to a movie theater context, which integrates process standard 1A because it applies mathematics to everyday life. Students use either the jumping or decomposition strategy to formulate a plan, determine a solution, and evaluate reasonableness to solve the equation. In the wrap-up independent tasks students write and solve novel multistep situations, which sustains standard 1A across the full session. Students explain how the operation relates to the context and use previously learned strategies, including decomposition and number line jumps, to solve the problems. Students also solve contextualized problems with multiple quantities, such as determining how many people are not reading a newspaper when 32 women and 27 men are on a bus and 18 are reading. In another example, students find the number of chickens on a farm once they know the numbers of cows and horses on the farm. Throughout the lesson, students communicate their reasoning, compare strategies, justify solutions, and choose appropriate mathematical tools and techniques.

The materials appropriately integrate the TEKS process standards throughout the lesson. For example, Journey B4, lesson 11, activity 1.1, embeds process standard 1G as students analyze a number line solution for 62 - 58. Students identify the error and explain why the displayed answer is incorrect, then use mathematical language and evidence from the number line to justify their reasoning. This helps students demonstrate their ability to communicate and defend mathematical ideas. Activities 1.2 and 1.3 extend process standard 1G as students apply derived facts and decomposition strategies to solve problems and explain their reasoning. As students work to connect number line models, decomposed numbers, and equations, they communicate how multiple representations illustrate the same mathematical relationships. These opportunities require students to explain, justify, and compare solution strategies, demonstrating meaningful integration of the TEKS process standards throughout the lesson.

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

The grade 2 Math Journeys materials include a description of how the TEKS process standards are incorporated and connected throughout the learning pathways. For example, the B4 Journey Instructional Guide for the “Consolidating Addition and Subtraction II” materials justify the TEKS process standards. These tools include vertical and horizontal alignment explanations and a session-by-session alignment table that identifies where specific process standards are embedded across the journey. The guide explains how students engage in problem solving, reasoning, mathematical communication, representations, and connections across lessons. Additionally, the guide describes how these process standards support the development of additive thinking concepts throughout the learning pathway. The guide also highlights connections between lessons and standards through vertical and horizontal alignment sections, and demonstrates how process standards are intentionally connected across sessions rather than taught in isolation.

The materials include a description of how the TEKS process standards are incorporated and connected throughout the learning pathway. The B4 Journey Instructional Guide describes process standard 1F as an instructional focus across lessons B4.1–B4.15, in which students “analyze relationships to connect mathematical ideas” as they move between number line strategies and decomposition methods to solve problems. The guide explicitly connects process standard 1F to Journey B4, lesson 12, by highlighting how recognizing equivalent expressions, such as 134 + 47 and 131 + 50, develops students’ relational reasoning and reinforces strategies introduced in earlier word problem lessons. This guidance demonstrates that the process standard is not taught in isolation, but is intentionally embedded within individual lessons and continuously revisited throughout the B4 learning pathway. This supports students’ progressive development of mathematical reasoning and connections across concepts.

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

The materials in Journey B3.12, “Subtraction by Decomposition: Regrouping,” include an overview of the TEKS process standards incorporated into each lesson. The session header tags TEKS 2.4.B and 2.7.B alongside process standard 1G and 1F, giving educators an explicit overview of which process standards are active before instruction begins. The materials state, “Students engage in process standard 1F when they analyze the relationship between the ones digits in the minuend and the subtrahend to determine when regrouping is needed. By comparing expressions such as 75 - 47 and 62 - 28, they recognize that whenever the subtrahend’s ones digit is greater than the minuend’s ones digit, the same exchange of one ten for ten ones applies, connecting one subtraction expression to the next.” This lesson-level tagging allows educators to plan discourse and written outputs aligned to the stated process standards.

The materials include a clear overview of how the TEKS process standards are intentionally embedded within each lesson by explicitly identifying the applicable standards and providing educators with guidance on how to incorporate those standards during instruction. In lesson 17, the TEKS process standard 1A is clearly identified within the lesson plan to support meaningful mathematical application and problem solving. The TEKS process standard 1A, which focuses on applying mathematics to problems that arise in everyday life, is addressed as students create a movie theater scenario to represent the expression 42 - 13. This task connects the subtraction problem to a familiar real-world context. Students apply mathematical reasoning while they interpret the situation, solve the subtraction problem, and evaluate whether their numerical solution makes sense within the context of the story they created. This lesson encourages students to connect mathematical concepts to authentic situations while strengthening their ability to apply mathematics in purposeful and relevant ways. The explicit identification of the process standard and accompanying educator guidance supports consistency in instruction and ensures that educators can intentionally incorporate mathematical application, problem solving, and real-world connections into daily mathematics learning experiences.

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

In grade 2 Math Journeys, lesson 17, students think mathematically, persevere through problem solving, and make sense of mathematics as they analyze, solve, and create contextualized addition and subtraction situations. For example, in activity 1, students create a movie theater story for the expression 42 - 13, which requires them to think mathematically by connecting subtraction to a real-world context. To press students to persevere beyond a single solution path, educators ask, “Is there another way you could have approached the problem?” For example, one word problem states: “On a bus, there are 32 women and 27 men. In total, 18 people are reading the newspaper. How many people are not reading?” To solve the equation, students combine women, men, and newspaper readers. This work demands that students make sense of a multistep additive structure before they select an operation.

The materials provide opportunities for students to think mathematically, persevere through problem solving, and make sense of mathematics. For example, in Journey B4, lesson 15, activity 1, students begin by building towers of 21 and 15 snap cubes. Students then investigate how adding the same amount to both numbers affects the difference between the towers. Students extend this reasoning by testing expressions such as 74 - 48, in which they shift both numbers by an equal amount and then verify that the difference remains 26. Students look for patterns, test conjectures, and persevere in their reasoning as they work through multiple equivalent expressions, rather than rely on a single computation. To encourage students to justify their thinking and develop an understanding of the invariant relationship between the numbers, educators ask, “Can you explain why moving both numbers keeps the distance the same?” This emphasizes conceptual understanding over procedural execution.

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

In grade 2 Math Journeys, lesson B3.8, “Subtraction: Jumping and Bridging Through 10 II,” students learn that they can solve subtraction problems in different ways. The lesson teaches students to try different strategies for subtracting two-digit numbers and to explain and justify their choices. In activity 1 educators draw an empty number line on the board and mark 40, 50, 60, and 70. Educators then ask students where they would place 65 and where they would land if they jumped back 10 and then seven. Educators lead a discussion about whether it is easier to subtract all the units in one jump, or use the bridging through 10 strategy with two jumps. During independent practice, students choose the representations and strategies that make subtraction easier for them to show that there are many valid ways to solve the same problem.

The materials teach students that they can solve problems in different ways. In the Journey E1, lesson 1, wrap-up activity, students fill in missing cards so the sum meets a specific condition. This task offers multiple correct solutions that enable students to try different number combinations until they find answers that work. Students then share and compare their solutions with classmates, explain how each one meets the condition, and justify their reasoning. Through these discussions, students learn that math problems often have more than one solution, and that explaining their thinking helps them evaluate and compare different approaches.

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.

The materials give students many chances to show their math understanding through reading, writing, and discussing. In Journey B3, lesson 17, activity 1, students create a movie theater word problem for 42 - 13, solve the equation on an empty number line, and explain their reasoning to the class. In activity 2 students write equations on their Magic Pads and discuss a bus word problem. Students connect subtraction to a real-world situation and check if their answers make sense in context. Educators ask, “What does each number mean in your story problem?” and “How does your answer make sense in your story?” During the wrap-up activity, students write their own problem for 27 - 15 and share it with a partner. Students then explain and defend their strategies, compare solutions in class discussions, and show how their methods fit the context of each problem.

Additionally, the materials help students make sense of math by doing, writing, and discussing it with peers and educators. In Journey B4, lesson 11, activity 1.1, student pairs order four addition expressions by their sums without calculating, and use place value reasoning instead of memorized procedures. In activities 1.2 and 1.3 students find and fix errors in worked examples and explain why different strategies, like derived-fact reasoning and decomposition, lead to the same answer. In independent work, students complete inequality expressions with given cards and connect different ways of solving to symbolic comparisons. Throughout these activities, students reason, explain, and discuss their thinking in multiple ways to deepen their understanding of math relationships.

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

In lesson 12 educators prompt students to explain their thinking and justify their math strategies. For example, in activity 1 educators ask, “Can you explain to your partners how you solved this using your strategy?” and “How can you justify that exchanging one ten for ten ones does not change the value of 75?” Process standard 1G requires students to show, explain, and justify their regrouping strategy. Additionally, the EB student routine has partners discuss and decide together whether they need to make an exchange before moving on.

The materials help educators guide students to share and reflect on their problem-solving methods. For example, in lesson 15 students order expressions from least to greatest by estimating their sums without calculating exact answers. Rather, students rely on what they know about number relationships to explain and justify the order. As they share their reasoning, students discuss place value and how numbers affect the size of sums. Students also check addition and subtraction equations, spot mistakes, and explain the errors they find. Working with a partner, students talk about their observations and explain the reasoning behind any identified mistakes. Students use precise math language to justify their thinking and suggest more efficient strategies for solving equations. The materials give students many chances to communicate math ideas, evaluate others’ reasoning, identify errors, and improve their problem solving strategies. Through these activities, students build math reasoning, critical thinking, and a deeper understanding of efficient problem solving.

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

In Math Journeys, lesson 10, “Addition by Decomposition: Regrouping Ones,” educators use specific prompts to help students understand regrouping and address common mistakes. For example, when students solve 28 + 26, some might say, “I added 2 + 2 to get four tens, and 8 + 6 to get 14 ones. So the answer is 414.” Educators then guide students to the correct process by saying, “You need to break apart 14 ones into one ten and four ones. Exchange the ten into the tens place, so you have five tens and four ones, or 54.” Students rewrite their explanation using precise place value words, like tens, ones, exchange, and sum, and invite pairs to read their corrected explanations aloud. This routine shows educators exactly how to give feedback when students treat regrouped ones as a separate digit. The lesson also points out that students may forget to exchange 10 ones for one 10, or may represent the regrouped value incorrectly. To fix these errors, educators ask students to compare their models to the written algorithm, explain why the exchange keeps the value the same, and revise their work using feedback. These prompts help educators address misunderstandings by encouraging students to explain and reason through their thinking, not just accept the answer.

The materials include prompts and guidance to support educators in providing explanatory feedback based on student responses and anticipated misconceptions. For example, in the Journey E1, lesson 1, warm-up, the Teacher Guide provides tips, correct solutions, and worked examples for each question. This enables educators to give immediate, targeted feedback to students and clarify misunderstandings by showing correct reasoning alongside common errors, so students can see both what went wrong and how to approach the problem correctly. This structure allows educators to respond to incorrect responses with explanatory feedback that reinforces understanding, rather than simply indicating whether an answer is right or wrong.