Math Journeys Texas, Grado 2 (Spanish)

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 TEKS Correlation Guide of the Math Journeys grade 2 program outlines the TEKS corresponding to each of the lessons, including both the content and process standards for educators. The scope and sequence document is organized into sections called “Journeys” and identifies the TEKS and ELPS addressed in each. The Journey Instructional Guide provides a detailed rationale for each journey. For example, section 2 of the guide provides the vertical rationale for how the current journey builds upon the previous one and how it prepares students for subsequent concepts. The A2 Journey Instructional Guide, which focuses on identifying numbers and counting from 1–100, extends the concepts of counting, comparing, ordering, and estimating from the previous journey, which involved numbers 1–20. The horizontal rationale is provided in section 3, which explains how instruction progresses from concrete to representational to abstract models of number sense.

The “Alcance y secuencia” scope and sequence document of the Math Journeys grade 2 program outlines the TEKS, process standards, and mathematical concepts corresponding to each grade 2 session throughout the curriculum. Additionally, the scope and sequence is organized to show how concepts are connected and developed across lessons within the grade level. The materials provide a detailed progression of mathematical learning by demonstrating how foundational grade 2 skills are introduced and extended in later sessions. For example, early sessions focus on foundational number sense and representations, while later sessions build toward more complex mathematical reasoning and problem-solving. The vertical alignment within the scope and sequence demonstrates how each concept builds upon previous learning and prepares students for future mathematical understanding. The horizontal alignment is reflected in the connections between concepts, process standards, and multiple representations used throughout the lessons and activities.

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 Program Guide of the Math Journeys grade 2 program comprehensively explains how to implement the curriculum based on the three-step framework of “build,” “consolidate,” and “practice.” Each lesson is designed to start with an educator-led, small-group lesson followed by logsheets for students to complete independently with educator feedback and then optional further practice on Atlas Math, an adaptive digital platform. In addition, the “Lesson Internalization and Planning” section explains how to plan for variability among students. This section includes explanations for multiple entry points, just-in-time supports, extensions, and multiple representations and modes of expression.

The Guía del programa outlines strategies and usage recommendations for adapting instruction across a variety of instructional settings and contexts. In addition, the guide supports differentiated instruction and flexible lesson implementation throughout the grade 2 curriculum. Guidance for personalized learning is provided through the adaptive digital platform Atlas Math, which allows students to work at their own pace while engaging in support or extension activities based on individual learning needs. The implementation guidance shows how educators can adapt instruction to support varying levels of student understanding while keeping students engaged with grade-level mathematical concepts and processes.

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

The TEKS Correlation Guide of Math Journeys Spanish recommends skill entry points based on the results of diagnostic assessment. The program aligns journeys and lessons with the TEKS content and process standards. The TEKS Correlation Guide helps educators implement instruction by connecting lessons and activities to specific standards within each journey. The materials also include a diagnostic assessment and placement report, which recommends skill entry points and helps educators identify appropriate instructional starting points, targeted interventions, and differentiated learning opportunities based on the performance data of individual students.

The Guía del programa outlines strategies and usage recommendations for adapting instruction across a variety of instructional settings and contexts. In addition, the guide supports differentiated instruction and flexible lesson implementation throughout the grade 2 curriculum. The materials include “Práctica adicional” through the adaptive digital platform Atlas Math, which allows students to practice, review previously taught concepts, and learn new concepts based on individual learning needs. “Informes del progreso” provide updates on individual student progress as well as performance on TEKS-aligned activities. The implementation guidance shows how grade 2 educators can monitor student learning and adapt instruction to support varying levels of understanding while keeping students engaged with grade-level mathematical concepts and processes.

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

Math Journeys provides protocols and guidance for internalizing both units and lessons through the “Lesson Internalization and Planning” section of the Program Guide. In the “Preparing for a Journey” section, educators learn how each journey builds upon prior learning, review lesson objectives and mastery criteria, identify scaffolds and enrichment opportunities, gather materials, and analyze learning progression before starting instruction. The materials also contain lesson internalization protocols in the sections “Preparing for a Building Session,” “Preparing for a Consolidating Session,” and “Preparing for an Additional Practice Session.” These sections help educators clarify objectives, anticipate students’ thinking and misconceptions, prepare materials, identify opportunities for formative assessment, analyze student responses, and use progress-monitoring data to inform future instruction.

The Math Journeys grade 2 program contains journeys, which are labeled with a letter to identify the cluster or unit and a number to identify the lesson. Each journey serves as a guide for educators, outlining the learning objectives, TEKS, vocabulary, teaching resources, and sequence of lesson activities throughout instruction. The materials provide teaching strategies and organized lesson components that help educators understand the progression of concepts and prepare for instruction. The implementation guidance shows how grade 2 educators can preview lessons, internalize instructional objectives, and adapt their teaching practices to support varying student needs while keeping students engaged with grade-level mathematical concepts and skills.

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

The Math Journeys grade 2 program provides resources to help instructional leaders assist educators with implementing the program. The “Hands on Partnership” section in the Program Guide contains examples of how a math success manager can partner with and provide guidance to instructional leaders. Examples include “facilitation of PLC [professional learning community] sessions, student work and progress-monitoring analysis, aligning instructional practices, and developing a long-term tier two math model.”


The Latin American Spanish (es-LA) edition of the Math Journeys Coaching Guide for Instructional Leaders provides resources and explicit guidance for instructional leaders to help grade 2 educators implement Math Journeys as designed. The “How to Use It” section establishes a clear coaching protocol that instructional leaders use during classroom observations, post-observation conversations, and when collaboratively planning the next lesson with the educator. The guide also describes four stages of implementing Math Journeys and emphasizes that educators initially use the program’s primary components as designed and put them into practice with fidelity. For example, during a grade 2 classroom observation, an instructional leader can use the Stage 1 Observation Tool to verify that the educator has followed the intended lesson structure, prepares and uses manipulatives appropriately, uses program resources when indicated, provides adequate time for consolidating and discussing logsheets, and meets the lesson objectives. Following the observation, the leader can use the self-reflection and modeling rubric to guide a coaching conversation about successful strategies, student misconceptions, and specific improvements. Next, the leader can use the lesson preparation guide to collaboratively plan subsequent instruction, including objectives, TEKS, prerequisites, anticipated student errors and strategies, materials, manipulatives, routines, and instructional adjustments.

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 Guía del programa breaks down the instructional components within each journey lesson and suggests timeframes for each part of the lesson. The components include educator-led instruction, student exploration, discussion, and practice activities to support consistent implementation of the program as designed. Additionally, the Guía del programa describes multiple resources for assessment, including diagnostic and progress-monitoring tools. The digital practice progress report specifically provides TEKS-aligned assessment data by identifying student performance for each TEKS to support instructional decision-making and monitor student growth.

The Math Journeys grade 2 program contains lesson plans outlining the learning objectives, TEKS alignment, vocabulary, educator and student materials, instructional resources, and lesson components throughout the curriculum. Additionally, instruction is organized into lesson sections such as the “Planteamiento” (“Warm-up”), “Nudo” (“Development”), and “Desenlace” (“Wrap-up”), which guide educators through the progression of instruction and student learning. A sequence of instructional activities is aligned with the lesson objectives and the TEKS, helping educators understand how concepts are introduced, developed, and reinforced during the lesson. For example, in journey B3, session 6, the learning objective focuses on practicing forward jumps on the number line between 1 and 100, while the warm-up, development, and wrap-up activities provide aligned instructional guidance to support students throughout the learning process. This guidance shows how grade 2 educators can internalize lesson expectations, prepare instructional materials, and facilitate instruction aligned with grade-level mathematical concepts and skills.

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 Math Journeys grade 2 program provides guidance on lesson planning through clearly organized lesson components within the program’s structure, including the three-step framework of “build,” “consolidate,” and “practice,” along with suggested timeframes for each part of the lesson to support effective pacing and implementation. Additionally, the lesson framework is designed to help educators deliver instruction in a consistent, purposeful way while providing students with a structured learning routine. The organization of the lesson components helps educators manage their instructional time effectively and ensure that each stage of learning is addressed throughout the lesson.

The Math Journeys grade 2 program contains lesson plans outlining the learning objectives, TEKS alignment, vocabulary, educator and student materials, instructional resources, and lesson components throughout the curriculum. In addition, instruction is organized into lesson sections called the “Planteamiento,” “Nudo,” and “Desenlace,” which guide educators through the progression of instruction and student learning. A sequence of instructional activities aligned with the lesson objectives and the TEKS helps educators understand how concepts are introduced, developed, and reinforced during the lesson. For example, in journey B4, session 16, the learning objective focuses on practicing addition and subtraction with numbers between one and 1,000 within a productive practice context, while the warm-up, development, and wrap-up activities provide aligned instructional guidance to support students throughout the learning process. This guidance shows how grade 2 educators can internalize lesson expectations, prepare instructional materials, and facilitate instruction aligned with grade-level mathematical concepts and skills.

Evaluation for 1.2c
Materials contain support for families in Spanish and English for each unit, with suggestions on supporting the progress of their student(s).

The Math Journeys grade 2 program contains family resources within each journey to help caregivers support students’ learning at home. The family letter in Spanish offers guidance, questions, vocabulary, and suggested activities connected to the lesson concepts being taught in class. In addition, the language of the family letter can be changed using the language toggle located in the top right corner, allowing families to access the information in their preferred language. The family letter is designed to strengthen the connection between school and home by providing caregivers with specific strategies and conversation prompts to reinforce student understanding outside of the classroom.

The Math Journeys grade 2 program contains a family letter in Spanish that supports families throughout each journey or unit within the curriculum. The family letter provides information about students’ learning goals, mathematical concepts, and strategies that families can use to support learning at home. The materials also include guidance and activities that reinforce grade-level skills and encourage family involvement in student learning outside of the classroom. This guidance shows how grade 2 families can support students’ progress and strengthen the connections between classroom instruction and learning at home.

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

The Math Journeys grade 2 program contains resources for summative assessment to evaluate student mastery of journey content and related mathematical skills. The materials provide the “Prueba del final de journey” assessment, which includes the intended purpose and use of the assessment within the instructional program. In addition, educators receive guidance on administering the assessment, interpreting the results of student performance, and using performance levels to support instructional decision-making. For example, grade 2 educators use the assessment guide to determine whether students are ready to move on to the next journey or require additional support and review. The materials also support educators in monitoring student mastery and planning targeted interventions based on assessment outcomes.

The Math Journeys grade 2 program contains resources for instructional assessment to support ongoing monitoring of student learning throughout instruction. The materials provide the definition and intended purpose of formative assessments, which are integrated throughout the lesson activities to support instructional decision-making. In addition, educators receive guidance on activating prior knowledge, conducting checks for understanding, identifying misconceptions, and making real-time instructional adjustments to support student learning. For example, grade 2 educators use formative evaluation strategies embedded within lesson plans to monitor students’ understanding during instruction and provide targeted support as needed. The materials also help educators respond to student performance through opportunities for ongoing practice in formative assessment during the learning process.

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

The Math Journeys grade 2 program guides educators to administer assessments both consistently and accurately using the Guía de implementación for the “Prueba de nivel.” The materials explain the assessment’s purpose and characteristics, describe its components and question types, and outline clear administration procedures and expectations for the testing environment. This guidance helps educators implement assessments uniformly across all grade 2 classrooms and establish an appropriate testing environment. For example, grade 2 educators follow the guide to understand assessment procedures, prepare students for the testing environment, and administer the diagnostic evaluation according to program expectations. The materials also help educators implement assessment practices consistently so that they gather meaningful data on student performance.

The Math Journeys grade 2 program provides resources for summative assessment to help educators administer assessments effectively and make instructional decisions. The Instrucciones y guía for the “Prueba del final de journey” contain guidance on how to use manipulatives and other instructional supports to implement the assessment successfully. Additionally, educators receive guidance on administering the assessment, understanding intended use cases, and interpreting student performance data from the summative assessment.

Evaluation for 2.1c
Digital assessments include printable versions and accommodations, including text-to-speech, content and language supports, and calculators, that educators can enable or disable to support individual students.

The Math Journeys grade 2 program provides digital supports to address the accessibility needs of individual students during assessment. These include text-to-speech functionality, content and language supports, and calculators on the digital assessment platform. Additionally, students can access accessibility features to support equitable participation during digital assessments. For example, grade 2 students can use embedded digital supports while completing assessment activities within the platform. However, educators cannot independently change students’ language settings or manage individualized accessibility features within the platform’s settings.

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

The Math Journeys grade 2 program provides resources for diagnostic assessment to measure students’ understanding of grade-level mathematical concepts and skills through TEKS-aligned tasks. Interactive assessment activities contain different levels of complexity that require students to apply mathematical reasoning and problem-solving skills. Additionally, numeric response tasks help students demonstrate understanding of place-value concepts and computation strategies through practical application. For example, students solve computation problems as well as real-world word problems through numeric response tasks that require place-value understanding and problem-solving skills. The materials also help educators monitor students’ comprehension and identify instructional needs through structured activities for diagnostic assessment.

The Math Journeys grade 2 program provides resources for summative assessment to measure student mastery of TEKS-aligned mathematical concepts and skills through a variety of levels of complexity. For example, the questions on the end-of-journey assessments involve factual knowledge, procedural understanding, and problem-solving. Additionally, educators receive guidance and access to reporting tools that help them interpret student performance data and make instructional decisions. For instance, the digital Journey Test B4 contains assessment items aligned with the TEKS, while the “Muestra de informe de prueba” displays journey levels aligned with the TEKS and identifies student performance levels. The materials also help educators use assessment reports to strategically choose supports that students may need and determine whether they are ready to advance to the next journey.

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 Math Journeys grade 2 program provides TEKS-aligned assessment resources to measure students’ application of mathematical reasoning and problem-solving skills. The assessment items require students to apply conceptual understanding through multiple mathematical representations and problem-solving strategies. Additionally, students have opportunities to analyze mathematical models and explain the operations used to solve problems. For example, students solve a multi-step addition problem and interpret a number-line model to determine the operation used, supporting conceptual understanding of addition and subtraction. The materials also help educators monitor students’ reasoning skills and identify instructional needs through TEKS-aligned assessment tasks.

The Math Journeys grade 2 program provides educators with resources for formative assessment to help students at different levels of mathematical understanding. Educators use “Hojas de registro” for each journey to prompt students to answer questions and show what they know during lessons. The program also offers differentiated support. For example, educators assign “Hojas de registro de apoyo” to students who need extra help and “Hojas de registro de ampliación” to students who are ready for extension activities. These resources help educators differentiate instruction and respond to student performance through formative assessment tasks at varying levels of 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 Math Journeys grade 2 program equips educators with resources for scoring assessments that help them interpret student performance and make instructional decisions. The Guía de puntuación a nivel de evaluación gives them performance levels, score ranges, and detailed descriptions of student understanding so they can identify students’ strengths, misconceptions, and instructional needs. The “Muestra de informe de la prueba de nivel” helps educators analyze assessment results and use student data to plan instruction. For example, educators review performance reports to find areas where students need extra support or targeted intervention. These resources help educators monitor students’ progress and plan instruction based on assessment outcomes.

The Math Journeys grade 2 program provides resources for scoring assessments to help educators interpret student performance and make instructional decisions. The Instrucciones y guía of the “Prueba del final de journey” include printable assessment resources, while the Solucionario o clave de respuestas y guía formativa contain the answers. Additionally, educators receive guidance through answer rationales, achievement levels, scoring information, and information on formative assessment to support instructional planning. For example, grade 2 educators can use the answer key and formative guide to analyze correct and incorrect responses, identify possible student misconceptions, review related TEKS, and determine additional instructional supports needed after Journey Test B4. The materials also help educators use assessment data to decide on their next instructional steps and targeted interventions.

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 Math Journeys grade 2 program provides resources for assessment reporting to help educators respond to trends in student performance and make instructional decisions. The “Ubicación en trayectorias (journeys)” report helps educators analyze student assessment data and identify learning needs. Additionally, educators receive guidance on grouping students as well as selecting targeted instructional tasks and activities to provide focused support and intervention. For example, educators can use student performance results from the “Ubicación en trayectorias” report to place students into appropriate instructional pathways and determine differentiated learning supports. The materials also help educators monitor students’ progress and plan targeted instruction based on assessment data.

The Math Journeys grade 2 program provides resources for instructional support to help educators respond to trends in student performance on assessments and provide targeted intervention. The Instrucciones y guía of the “Prueba del final de journey” include printable assessment resources, while the Solucionario o clave de respuestas y guía formativa contain the answers. Additionally, educators receive guidance to identify student misconceptions, review related TEKS, determine areas needing reinforcement, and select additional instructional supports and activities. For example, educators can use the guide following the Journey Test B4 to analyze students’ responses, identify learning gaps, and implement targeted activities to help them in specific skill areas. The materials also help educators make instructional decisions and provide differentiated interventions 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 Math Journeys grade 2 program provides
The Math Journeys grade 2 program provides resources for monitoring progress to help educators track students’ growth and make instructional decisions. The “Progreso general” dashboard on the “Classroom Manager” platform contains data on weekly progress, completed activities, time spent, course grades, and levels of content mastery. Additionally, the materials help educators monitor grade 2 student performance and analyze growth data to guide instruction and intervention decisions. For example, educators can use the dashboard to review student activity completion, monitor mastery of mathematical concepts, and identify areas where additional instructional support may be needed. However, the program does not include tools that allow students to independently track or monitor their own progress and growth.

The Math Journeys grade 2 program provides digital tools for monitoring progress to enable students to view performance information during interactive math activities. They have access to scores and feedback within the “Atlas Math Biblioteca de applets,” which students use to practice Math Journeys skills and concepts. Additionally, the materials help students view results immediately after completing applet activities. For example, students can see their scores after finishing an activity within the digital applets. However, the scores are not stored or displayed over time, making it difficult for students to independently track their long-term progress and growth across activities.

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 Math Journeys grade 2 program provides guidance on formative assessment to help educators conduct checks for understanding throughout lesson activities. Educator prompts, observation opportunities, and discussion questions help educators monitor students’ understanding of mathematical concepts and problem-solving strategies. Additionally, educators receive guidance on how to encourage students to explain their thinking, justify their responses, and analyze mathematical errors during instruction. For example, in a given activity, students analyze whether an operation is solved correctly, identify where the error occurred, and use a number line to correct their mistake and justify their reasoning using mathematical language. To encourage students to explain their thinking and support opportunities for formative assessment throughout the lesson, educators can use prompts such as “¿Entiendes qué hace que esta solución sea incorrecta?” and “¿Podrías explicar tu proceso para encontrar y corregir el error?”

The Math Journeys grade 2 program provides guidance on formative assessment to help educators conduct frequent checks for understanding throughout lesson instruction. Targeted questions, observation opportunities, and discussion prompts help educators monitor students’ understanding and identify misconceptions during learning activities. Additionally, educators receive guidance on how to analyze student performance, observe multiple problem-solving strategies, and determine whether lesson objectives have been met. For example, in journey B4, session 1 in the “Desenlace,” educators are given targeted questions and observation prompts to identify misconceptions, analyze student responses, observe different methods that students use to solve problems, and determine mastery of the learning objectives. The materials also help educators use ongoing practices in formative assessment to guide instructional decisions and provide targeted support as needed.

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

The Math Journeys grade 2 program provides resources for formative assessment to ensure frequent checks for understanding throughout lesson activities. Interactive digital applets on the Atlas Math platform enable students to solve math problems and receive immediate feedback during instruction. Additionally, milestone trackers and response indicators support ongoing opportunities for formative assessment and help students monitor their understanding while completing activities. For example, in applet A39, students solve addition problems using visual models and number line strategies while receiving immediate feedback after submitting their responses, with correct answers marked by a green check and incorrect answers identified with a question mark.

Targeted questions, observation opportunities, and discussion prompts help educators monitor students’ understanding and make instructional adjustments during lessons. Additionally, educators have ongoing opportunities to analyze students’ responses and identify areas where additional support may be needed. For example, in journey B4, session 1, educators receive multiple opportunities throughout the lesson to conduct checks for understanding through targeted questions and student observations in order to adjust instruction as needed. The materials also help educators use formative assessment practices to guide instruction and respond to students’ learning needs during lesson activities.

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 Math Journeys grade 2 program explicitly explains how to scaffold lessons and activities for students who have not yet reached proficiency in prerequisite or grade-level concepts and skills. Various supports help educators provide additional representations and hands-on learning experiences to strengthen students’ understanding of key mathematical concepts. For example, in the lesson “Sumamos por descomposición: llevadas hasta 1,000,” the “Apoyo” section guides educators to provide base 10 blocks so that students can solve addition problems manipulatively. This scaffolded support helps students develop a conceptual understanding of place value and addition with regrouping while engaging in grade-level tasks.

Various supports help educators provide additional representations, language supports, and structured problem-solving opportunities based on students’ needs. For example, in lesson B3, session 16, the “Hoja de actividad de apoyo” has scaffolded activities to help students reach proficiency while comparing subtraction strategies. The student “Cuaderno” contains equations and word problems with an empty number line, while the support logsheet provides number representations alongside the equations, identifies the subtrahend on the number line, and includes language supports such as bolded words and separated sentences within the word problems. These scaffolded supports strengthen students’ understanding of subtraction strategies while providing access to grade-level learning.

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 Math Journeys grade 2 program provides educators with explicit guidance on language supports to help students acquire and use academic vocabulary and understand mathematical concepts. The “Vocabulario clave” section introduces academic terms such as descomponer, salto, recta numérica, estrategia, and decenas. In addition, interactive applets, number lines, visuals, educator modeling, and guided discussions support students’ understanding of mathematical concepts and problem-solving strategies.

Math Journeys B3 Language Bank provides educators with explicit guidance on grade 2 pre-teaching and embedded language supports that enable students to develop their academic vocabulary and address unfamiliar references in the text. The guide outlines specific routines that educators can use before or during instruction to build students’ mathematical language, including language related to the next or previous ten, decomposition, tens and ones, regrouping, equivalent strategies, efficiency, and justification. The pre-teaching routines describe explicit actions for educators to take and identify when each support should be used. For example, before students record decomposition work in B3.9–B3.12, the educator has students state the total number of tens and ones and then record that same mathematical language in their written work. In addition, routine 6, “Unfamiliar Reference Quick Bridge,” directs educators to pre-teach the context of an unfamiliar song, story, game, or object by showing an image, real object, or brief clip, briefly explaining the reference, having students repeat key terms, and then returning to the math without pre-teaching the mathematical concept. The lesson-by-lesson guidance identifies specific unfamiliar references and provides an explicit bridge for each. For example, before Math Journeys B3.17, the educator introduces the unfamiliar context of a movie theater by showing the image, explaining the rows of seats and which seats are occupied or empty, and having students identify an empty seat and repeat key terms before starting the mathematical task. Together, these supports provide grade 2 educators with explicit guidance for helping students build their academic language as well as pre-teaching unfamiliar references so that students can access and engage with Math Journeys lesson content.

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 Math Journeys B3 Enrichment and Extension Guide provides educators with explicit guidance on grade 2 enrichment and extension activities for students who have shown proficiency in current and above-level content and skills. The guide mentions three observable indicators for determining which students should receive extension, including completing the core task with correct reasoning and time remaining, accurately completing the standard logsheet without support and justifying one’s responses, and demonstrating sustained proficiency with standard and available extension activities across three consecutive sessions. The guide also contains annotated Extension logsheets that identify the purpose of each task, what educators should listen for, evidence of mastery, and indicators that a student is not yet showing mastery. For example, in journey B3.6, students extend their learning by analyzing addition across a ten and identifying the relationships between two series of problems. Students demonstrate mastery when they use composed jumps across the ten, explain the relationship between the two sets of numbers, and use that relationship to anticipate an outcome before representing it. When a student shows sustained proficiency for three consecutive sessions, the guide directs the educator to administer the B3 end-of-journey assessment early. A score above 75 percent advances the student to journey B4, providing access to content above the student’s current placement.

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 Math Journeys Spanish program does not provide digital accommodations to support individual students’ needs such as text-to-speech functionality, content and language supports, or calculators that educators can enable or disable. As a result, the materials do not contain embedded supports for digital accessibility as required by this indicator.

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

The Math Journeys grade 2 program explains how to offer options and supports to students so they can show their understanding of mathematical concepts in various ways, including performing, expressing, and representing mathematical thinking. Students have opportunities to demonstrate their learning through verbal explanations, movement activities, equations, manipulatives, and number-line representations. In addition, guided questioning, visual models, step-by-step educator modeling, and collaborative discussions help students express and represent their mathematical thinking in multiple formats.

Students have opportunities to demonstrate their learning through digital tools, manipulatives, verbal explanations, and visual and written representations. For example, in lesson B3-3, students begin by using applet A31 to model jumps on a number line and find solutions. Students then use a color-coded number line or a 50-bead string to make jumps and identify changes in the tens. Finally, students record their thinking in their “Cuaderno” using visual and written representations. The materials help students express and represent mathematical understanding through multiple formats and instructional experiences.

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 Math Journeys grade 2 program contains explicit prompts and guidance for educators to help students build their knowledge by activating their prior knowledge, anchoring big ideas, and highlighting and connecting key patterns, features, and relationships through multiple means of representation. Students have opportunities to connect previously learned concepts to new learning through concrete models, visual representations, and oral discussions. For example, students use number lines, bead strings, equations, and place-value strategies to compare, analyze, and solve math problems. The materials also highlight patterns and relationships among numbers and operations, and help students make connections among mathematical concepts through multiple representations.

Students have opportunities to connect concrete models to visual representations and mathematical relationships. For example, in lesson B4.15, development activity 1, students first use snap cubes as concrete representations to explore the relationship between addition and subtraction by discovering that the distance when counting forward and backward is the same. Next, students use number lines to model subtraction and analyze patterns in the answers when the same amount is subtracted from both the minuend and the subtrahend. As a result, the materials help students identify mathematical patterns and make connections among operations through multiple representations.

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

The Math Journeys grade 2 program guides educators on how to effectively deliver and facilitate lessons using various instructional approaches. The materials include whole-group instruction, collaborative learning opportunities, hands-on manipulatives, mathematical discourse, visual models, guided questioning, partner activities, and independent practice. In addition, step-by-step guidance for educators helps students justify their reasoning, analyze the relationships between equations, and represent mathematical concepts through multiple representations. Embedded supports such as “Apoyo,” “Ampliación,” and guidance for emergent bilingual (EB) students help educators differentiate instruction and promote student engagement throughout the lesson.

The Math Journeys grade 2 program contains multiple instructional approaches that help students move from concrete to representational understanding while developing addition and subtraction concepts through decomposition. For example, in lesson B5.5, the warm-up activity is facilitated through whole-group instruction. The development activities incorporate hands-on learning experiences that transition from small-group collaboration to partner work and then to independent practice. Students also receive instruction on how to use base 10 blocks, place-value drawings, magic pads, and visual representations to build mathematical understanding through multiple instructional approaches.

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 Math Journeys grade 2 program provides multi-tiered intervention methods through a variety of instructional practices and teaching structures to support students’ diverse learning needs. Through whole-group, partner, and individual teaching structures, guided, collaborative, independent, and educator-supported opportunities for practice are embedded throughout the lessons. In addition, educators receive guidance on implementation through questioning prompts, manipulatives, number-line models, visual representations, support options, and extension opportunities. For example, grade 2 students solve subtraction and distance problems using number lines, cubes, equations, and multiple subtraction strategies while educators guide mathematical discussions, scaffold reasoning, and encourage students to explain and compare solution methods. Moreover, differentiated supports and independent application tasks allow educators to monitor students’ understanding and provide targeted intervention as needed.

The Math Journeys grade 2 program provides assessment data, instructional recommendations, and flexible grouping options that help educators identify students’ needs and select appropriate intervention supports. For example, the “Muestra de informe de la prueba de nivel” placement test report provides educators with student performance data that they can use to make instructional decisions, reteach specific skills in whole-group settings, create intervention groups, or assign individualized learning pathways based on students’ needs. The materials help educators implement targeted interventions to address learning gaps and promote student growth.

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

The Math Journeys grade 2 program provides enrichment and extension methods that support a variety of opportunities for student engagement throughout the lessons. Differentiated supports in the “Apoyo” and “Ampliación” sections, embedded within instructional activities, allow educators to extend learning based on student readiness and performance. Additionally, the lessons guide educators on effective implementation through questioning prompts, manipulatives, number lines, partner discussions, visual models, and independent practice opportunities. For example, students solve subtraction problems using multiple strategies, calculate distances on number lines, compare solution methods, and justify their mathematical reasoning through whole-group, partner, and individual activities. Moreover, scaffolded support and enrichment opportunities help educators differentiate instruction while keeping students engaged with grade-level mathematical concepts and skills.

The Math Journeys grade 2 program provides students with opportunities to extend their learning through hands-on activities, multiple problem-solving strategies, and challenging extension tasks. For example, in lesson B4-9, students engage with manipulatives such as applets, base 10 blocks, and magic pads to explore mathematical concepts. In addition, extension tips encourage students to demonstrate different strategies and complete “Actividades de ampliación,” which provide more challenging activities for students who are ready to deepen their understanding.

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

The Math Journeys grade 2 program provides educators with prompts and guidance to support timely feedback during lesson delivery in grade 2 lessons such as “Restamos: calculamos la distancia.” Educators have access to questioning routines, discussion prompts, sentence stems, and opportunities for students to explain and justify multiple subtraction strategies throughout the lesson. For example, students solve subtraction problems using number lines, distance models, and decomposition strategies while educators monitor their understanding and facilitate discussions about efficient problem-solving methods. In addition, guidance statements help educators address misconceptions, validate different solution strategies, and encourage students to explain why one strategy may be more efficient than another. The lessons also provide bilingual supports, such as the “Apoyo” and “Ampliación” options, and reflective discussion prompts allow educators to provide immediate, responsive feedback based on students’ understanding during instruction.

Anticipated responses, misconceptions, and redirection strategies help educators respond to students’ thinking and address misunderstandings during instruction. For example, the “B4 Banco de lenguaje y redirecciones” includes a “Banco de respuestas previas, ideas erróneas y redirecciones” section that suggests feedback and redirection ideas based on lesson content. In lesson B4.1, if a student changes the starting number by 1 but keeps the same landing number on the number line, then the educator may prompt students to reconsider the change by asking, “Si el inicio es 1 más, ¿dónde debemos llegar?” The materials help educators provide immediate, targeted feedback that enables students to refine their mathematical reasoning and understanding.

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.

This guidance does not apply because the program is not designed to be static.

Evaluation for 3.3b
If designed to be adaptive, materials include embedded linguistic accommodations for all levels of language proficiency [as defined by the English Language Proficiency Standards (ELPS)], which are designed to engage students in using increasingly more academic language.

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

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

The Math Journeys grade 2 program provides educators with implementation guidance to help them use the materials in bilingual/ESL programs effectively through the “Complemento ELPS a nivel de lección.” The materials include lesson-level language objectives, linguistic demands, expected oral and written production, and suggested implementation supports aligned with the TEKS and ELPS. For example, the B4 ELPS companion provides guidance on supporting students’ listening, speaking, and writing skills through sentence stems, opportunities for mathematical discourse, and instructional notes that help educators integrate language acquisition strategies during math instruction.

The Guía de implementación and the “Anexo de Journey B4” provide model-specific implementation guidance aligned with the mathematical content and language demands of each session. The materials also include differentiated support based on the type of bilingual or ESL program. For example, for transitional bilingual early-exit and late-exit programs, the materials recommend using the home language to support students’ understanding of place-value concepts before transitioning to English for mathematical reasoning. In lesson B4.2, “Puente al 10,” educators preview terms such as descomponer and hacer puente, narrate the jumps in English, and provide extended opportunities for bilingual rehearsal before students explain their thinking in English.

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 program provides embedded guidance to help EB students develop their academic vocabulary, increase their comprehension, build background knowledge, and make cross-linguistic connections through oral and written discourse. Key vocabulary, sentence stems, structured partner discussions, and written response opportunities support language development during math instruction. For example, in the lesson focused on decomposing numbers to make ten, students use academic terms such as descomposición, decena, and unidad while explaining their mathematical thinking both orally and in writing. The “Estudiantes bilingües emergentes” support section contains sentence stems and opportunities for guided discourse that help students explain how numbers change when decomposing and recomposing quantities during collaborative discussions.

Academic vocabulary, structured group discussions, supports for EB students, and guiding questions provide students with opportunities to explain their mathematical thinking both orally and in writing. For example, in lesson B4.1, “Sumamos y restamos: saltos sin reagrupación,” students review and practice terms such as hechos derivados, salto, hacia adelante, hacia atrás, recta numérica, and hechos relacionados, discuss strategies for representing addition and subtraction through jumps on a number line, and record their representations in their “Cuaderno.” The materials help students develop their mathematical language and conceptual understanding through both oral and written discourse.

Evaluation for 3.3e
If designed for dual language immersion (DLI) programs, materials include resources that outline opportunities to address metalinguistic transfer from English to the partner language.

This guidance does not apply 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 Math Journeys grade 2 program contains practice opportunities and instructional assessments throughout the broader learning pathway that require students to demonstrate a depth of understanding aligned to the TEKS. In lesson 17, “Situaciones contextualizadas de suma y resta: estrategia libre,” students engage in “Nudo: actividad 1—Inventamos situaciones” and “Nudo: actividad 2—Resolvemos situaciones contextualizadas,” where they create and solve real-world addition and subtraction situations using strategies such as decomposition and number-line jumps. Students justify their reasoning, compare solution methods, and connect operations to contextualized scenarios involving movie theaters, airplanes, buses, and farms. In the “Desenlace,” titled “Registramos lo que aprendimos,” students independently solve contextualized problems, select and apply appropriate strategies, explain their reasoning, and create their own subtraction situation for 27 − 15. This closure activity serves as an instructional assessment that requires students to show a depth of understanding aligned to the TEKS through problem-solving, mathematical reasoning, and written responses.

Journey B4.7, “Sumamos y restamos por descomposición,” provides students with opportunities to demonstrate their understanding of addition and subtraction through using manipulatives, representations, and mathematical discussions. In “Nudo: actividad 1,” students use base 10 blocks to model the addition of 243 + 315, represent the operation in vertical form, and create a pictorial representation of their work. Students decompose the numbers by place value and add hundreds, tens, and ones separately (200 + 300 = 500, 40 + 10 = 50, and 3 + 5 = 8) before composing the partial sums to determine the total of 558. In activity 2, students apply the same process to subtraction, using place-value understanding to decompose numbers and subtract hundreds, tens, and ones. By connecting concrete models, pictorial representations, and numerical procedures, students develop a conceptual understanding of how addition and subtraction operate within the base 10 system. These activities require students to apply place-value reasoning, compose and decompose numbers, and justify solution strategies, demonstrating a deep understanding of the mathematical concepts addressed in the lesson.

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 Math Journeys grade 2 program contains questions and tasks, including enrichment and extension materials, that increase in rigor and complexity, leading to grade-level and above-grade-level proficiency in the mathematics TEKS. In lesson B2.16, “Práctica productiva: suma hasta 20,” students engage in the “Planteamiento” titled “¡Qué! Encontramos el intruso” and “Nudo: actividad 1,” where they analyze groups of representations and addition expressions, identify an intruder, and justify their reasoning using mathematical evidence. To explain and defend their thinking, students respond to educator prompts such as “¿Podrías usar palabras concretas para explicar por qué este no encaja?” and “¿Puedes describir exactamente qué hace que este elemento sea diferente de los demás?” Students are encouraged to consider multiple valid solutions and justify the attributes used to support their conclusions. In “Nudo: actividad 2—Hacemos sumas de dígitos,” students create sums, identify equivalent expressions, and generate multiple equations that produce the same outcome. The educator increases rigor by asking students to explain why different equations produce the same sum and to justify how they know their solutions are equivalent. These tasks require students to analyze number relationships, compare solution strategies, and construct mathematical arguments. During the “Desenlace,” titled “Registramos lo que aprendimos,” students independently identify combinations that sum up to 10, complete equations, and apply their understanding of addition relationships. “Ampliación” opportunities extend learning by prompting students to explore all possible sums that can be created with a given addend, encouraging pattern recognition, generalization, and mathematical reasoning beyond the expectations of the core lesson.

Journey B3.11, “Resta por descomposición: sin reagrupación,” provides activities that progressively increase the rigor and complexity of subtraction through decomposition while supporting students’ understanding of procedures that lead to more efficient methods. In “Nudo: actividad 1—Comenzamos a restar con bloques base 10,” students solve problems such as 45 − 23 by using base 10 blocks, pictorial models, and vertical notation. Students decompose the numbers into tens and ones, subtract by place value (40 − 20 = 20 and 5 − 3 = 2), and then combine the partial differences to determine the final answer of 22. The activity increases in complexity by requiring students to represent the subtraction in multiple ways and connect concrete models to symbolic procedures. The enrichment activity deepens their learning by showing how subtraction relates to both taking from and combining situations when only one part of the whole is known. During the “Desenlace,” the “Ampliación” activity pushes students to think further by having them use number cards from 0–9 to create two-digit by two-digit subtraction equations that yield answers within a specific range, such as 30–40. These tasks prompt students to 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 Math Journeys grade 2 program demonstrates coherence across concepts horizontally within the grade level by connecting patterns, big ideas, and relationships. In lesson B4.11, “Comparación de estrategias de suma y resta,” students connect place-value understanding, estimation, and strategy selection when ordering addition expressions from least to greatest without calculating the sums. In “Nudo: actividad 1—Argumentamos si algunas sumas y restas están resueltas correctamente,” students analyze subtraction situations represented on number lines and use visual models to determine whether solutions are correct. Students then connect number-line reasoning, decomposition, and derived-fact strategies by analyzing equations such as 33 − 20 = 13 and 32 − 19 = 13, explaining why different methods produce the same outcome. Students justify the relationships among numbers and compare multiple solution strategies, reinforcing the big idea that equivalent representations yield equivalent results. During activity 1.3, students connect decomposition strategies to equations such as 47 + 65 = 100 + 12 = 112, linking place-value reasoning, decomposition, and computation. Across the lesson, students make connections among place value, estimation, number-line reasoning, decomposition, derived facts, and equivalent representations, showing coherence across mathematical concepts within the grade level.

Another illustration of this can be seen in journey B4.4, “Restamos: calculamos distancias,” where students connect manipulatives, number lines, addition, and subtraction to develop a coherent understanding of number relationships within the grade level. In “Nudo: actividad 1—Planteamos dos estrategias para representar una resta,” students use cubes and number lines to represent subtraction situations, such as 18 − 16, by showing backward jumps and determining the difference between the two numbers. Through educator-guided discussions, students explore how counting the units between 16 and 18 on a number line can also be used to find the difference. Students discover that measuring the distance between two numbers gives the same result as subtracting and offers an efficient strategy when the numbers are close together. In activity 2, “Calculamos la distancia entre dos números sobre la recta numérica,” students pick two two-digit number cards and find the distance between them by making forward or backward jumps on a number line. They connect these representations to both addition and subtraction and realize that the distance stays the same no matter which direction they use. These connected experiences help students build relationships among subtraction, addition, distance, and number-line representations, supporting a coherent understanding of mathematical concepts at this grade level.

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

The Math Journeys grade 2 program demonstrates coherence vertically across concepts and grade bands by connecting patterns, big ideas, and relationships. In the “Vista general de tramo–B: pensamiento aditivo,” the “Progresión de contenidos” section outlines how students build from a foundational understanding of number relationships, counting, and place value to increasingly sophisticated addition and subtraction strategies. The overview connects prior learning about composing and decomposing numbers to future work with additive reasoning, mental computation, and problem-solving. The “Contexto matemático” section further demonstrates vertical coherence by showing how representations and strategies evolve throughout the learning progression, including number lines, decomposition, place-value reasoning, and derived facts. The overview highlights how students progress from concrete and pictorial representations to more abstract strategies, connecting composing and decomposing numbers, number-line reasoning, and place-value concepts to future additive thinking and computation. The materials explain how these models are revisited and extended across journeys to help students make connections among number relationships, addition, subtraction, and increasingly efficient computation strategies. These explicit connections help students understand how mathematical ideas build across learning experiences and prepare them for more advanced work in subsequent grade levels. By explicitly linking prior knowledge, current learning, and future mathematical concepts through a documented learning progression, the materials show vertical coherence across concepts and grade bands.

Similarly, journey C1.1, “Explorar los dobles I,” establishes vertical coherence by connecting students’ prior experiences with finding doubles of one-digit numbers to current grade-level work involving doubles of numbers from 0–50. The lesson also lays the foundation for future learning by connecting doubles to repeated addition and later multiplication concepts. During the “Planteamiento,” students review strategies for finding doubles using their fingers, snap cubes, ten frames, and other familiar representations. In “Nudo: actividad 1—Descomponemos para hallar dobles y mitades,” students use base 10 blocks and place-value understanding to decompose numbers into tens and ones and determine their doubles. Students find the doubles of each part separately and then combine the results to determine the total double. Throughout this process, students build on previously learned strategies while developing an understanding of decomposition and repeated addition. These experiences support future learning in later grade levels, where students use decomposition strategies and multiplicative reasoning to solve more complex problems in section C3 and beyond.

Evaluation for 4.2c
Materials demonstrate coherence across lessons or activities by connecting students’ prior knowledge of concepts and procedures to the mathematical concepts to be learned in the current grade level and future grade levels.

The Math Journeys grade 2 program shows coherence across lessons and activities by connecting students’ prior knowledge of concepts and procedures to current and future mathematical learning. In lesson B3.9, “Suma por descomposición: sin reagrupación,” students build on prior conceptual knowledge of place value, number relationships, and representing numbers with tens and ones. In “Planteamiento,” students analyze multiple representations of quantities, including base 10 blocks, money, and numerical representations, to identify mathematical relationships among the representations. In “Nudo: actividad 1—Comenzamos a sumar con bloques base 10,” students apply previously learned procedures for representing and decomposing numbers into tens and ones to solve addition problems such as 24 + 15. The materials explicitly connect these procedures to current grade-level addition concepts by having students combine tens and ones separately and justify their reasoning using place-value concepts. In “Nudo: actividad 2—Representamos las primeras sumas,” students transition from concrete models to pictorial and symbolic representations by decomposing numbers and recording sums vertically. This progression connects current learning to future mathematical concepts and procedures, including multi-digit addition, efficient computation strategies, and standard algorithms. Through explicit connections among prior knowledge, current learning, and future mathematical concepts and procedures, the materials demonstrate coherence across lessons and activities.

Journey B4.7, “Sumamos y restamos por descomposición,” connects students’ prior experiences using manipulatives and pictorial representations to add and subtract with new learning involving decomposing numbers into hundreds, tens, and ones. In “Nudo: actividad 1,” students use base 10 blocks to model the addition of 243 + 315, represent the operation in vertical form, and create a pictorial representation. Students decompose the numbers by place value and add the hundreds, tens, and ones separately (200 + 300 = 500, 40 + 10 = 50, and 3 + 5 = 8) before combining the partial sums to determine the total of 558. In activity 2, students apply the same process to subtraction, using place-value understanding and multiple representations to solve problems. These activities build on strategies introduced in section B3 while supporting future learning in section B5, where students transition toward using standard algorithms for addition and subtraction. Through this progression, students connect concrete models, pictorial representations, and symbolic procedures, strengthening their understanding of place value and computation.

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

The Math Journeys grade 2 program provides students with opportunities to develop and apply their mathematical knowledge and skills through distributed practice over time. In lesson B3.9, “Suma por descomposición: sin reagrupación,” students retrieve previously learned knowledge of place value, number decomposition, and representing numbers with tens and ones. During “Nudo: actividad 1—Comenzamos a sumar con bloques base 10,” students apply these concepts and procedures by representing numbers such as 24 and 15 with base 10 blocks, decomposing the numbers into tens and ones, and combining the quantities to determine a sum. The lesson prompts students to explain their reasoning through questions such as “¿Podría explicar cómo te ayuda descomponer los números en decenas y unidades para sumar?” and “¿Cómo muestran tus barras y cruces que 50 + 40 = 90 y 1 + 3 = 4?” In “Nudo: actividad 2—Representamos las primeras sumas,” students continue applying decomposition strategies to solve addition problems such as 51 + 43 using concrete, pictorial, and symbolic representations. The distributed practice continues in the “Desenlace,” where students independently solve numerical and contextualized addition problems using the same strategy. Through repeated opportunities to retrieve, apply, and extend previously learned concepts and procedures across multiple activities, the materials support distributed practice over time.

Another opportunity for retrieval practice is provided in journey B3.16, “Comparamos estrategias de resta,” where students revisit and apply subtraction strategies introduced earlier in section B3. Previously throughout the broader learning pathway, students have used methods such as making backward jumps on a number line and drawing pictorial representations with base 10 blocks to solve subtraction problems. In activity 1, students subtract numbers within 100 using both a number line and base 10 block drawings and then discuss and compare the solutions generated by each strategy. In activity 2, students apply these same approaches to subtraction problems that require regrouping. By revisiting familiar strategies in new contexts, students retrieve and strengthen previously learned concepts while developing a deeper understanding of subtraction. These spaced retrieval opportunities help students connect prior learning to new mathematical ideas throughout section B3.

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

The Math Journeys grade 2 program provides opportunities for interleaved practice with previously learned skills and concepts across the learning pathways. In the “Vista general de tramo—B: pensamiento aditivo,” the “Progresión de contenidos” and “Contexto matemático” sections describe how students revisit and apply previously learned concepts, including number relationships, place-value understanding, decomposition, and additive reasoning, while developing increasingly sophisticated addition and subtraction strategies. Students must draw on multiple previously learned skills such as number-line reasoning, decomposition strategies, and place-value methods when solving new mathematical situations. Rather than practicing strategies in isolation, students repeatedly apply and connect concepts and procedures developed in earlier sessions to support flexible problem-solving and efficient computation. The learning progression highlights how additive thinking develops by integrating multiple strategies and representations across the general pathway, requiring students to select, compare, and apply previously learned approaches in new contexts. Through opportunities to revisit, integrate, and apply previously learned skills and concepts across the broader learning pathway, the materials provide opportunities for interleaved practice.

The Math Journeys grade 2 program provides opportunities for interleaved practice with previously learned skills and concepts across the learning pathways. Throughout section B3, students consolidate their understanding of addition and subtraction using multiple strategies, including base 10 blocks, bead strings, pictorial representations, number lines, and decomposition. Rather than practicing each strategy in isolation, the general learning pathway intentionally revisits and combines previously learned concepts, allowing students to strengthen their prior knowledge while developing new understanding. For example, in journey B3.15, development activity 1, students solve addition problems involving two two-digit numbers using a number line and decomposition while interpreting pictorial representations of base 10 blocks. In activity 2, students apply these same strategies to addition problems that require regrouping, thus extending their understanding to more complex situations. Students have encountered and practiced the strategies used in both activities throughout journeys B3.1–B3.12, providing them with ongoing opportunities to revisit, connect, and apply previously learned concepts and procedures. These opportunities support interleaved practice by integrating multiple representations and strategies across lessons rather than teaching them as isolated skills.

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

The Math Journeys grade 2 program provides students with opportunities to interpret, analyze, and evaluate models and representations of mathematical concepts and situations in journey B4.11, “Comparación de estrategias de suma y resta.” During the “Planteamiento,” students interpret addition expressions and analyze the relationships among numbers to order sums from least to greatest without calculating. In “Nudo: actividad 1.1,” students analyze an incorrect number-line representation of 62 − 58 = 8, identify the error, and use mathematical reasoning to determine the correct solution. To help students justify their thinking and evaluate the accuracy of the representation, the educator uses prompts such as “¿Entiendes qué hace que esta solución sea incorrecta?” and “¿Podrías explicar tu proceso para encontrar y corregir el error?” 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 outcome. In activity 1.3, students interpret and analyze a decomposition model representing 47 + 65 = 100 + 12 = 112, connecting multiple representations of the same mathematical idea. During the “Desenlace,” students complete “Encuentra el error y corrígelo,” evaluating mathematical representations, identifying inaccuracies, and revising incorrect solutions.

Questions and tasks in the Math Journeys grade 2 program provide students with opportunities to interpret, analyze, and evaluate models and representations of mathematical concepts and situations. In journey B3.6, development activity 1, students interpret a number line that represents 37 with two jumps of 10 and one jump of six and then translate the representation into an equation. The educator subsequently models the same addition by decomposing the jump on the ones to bridge through the next ten, helping students connect the visual model to a more efficient addition strategy. Students analyze further problems to determine whether the jump on the ones will cross a ten and how the number line representation should be adjusted. To encourage students to analyze patterns and connections among representations, the educator uses prompts such as “¿Observan alguna forma útil de dividir los saltos cuando pasamos a la siguiente decena?” and “¿Podrían utilizar esta misma estrategia con otros números que también pasan por una decena?” In activity 2, “Comparamos 2 maneras de sumar mediante saltos,” students compare two addition expressions, 45 + 29 and 29 + 45, using jumps on an empty number line. Students evaluate the efficiency of different representations and solution methods by discussing whether it is easier to start at 29 and make four jumps of 10 and one jump of five, or to start at 45 and make two jumps of 10 and one jump of nine. Through educator-facilitated discussions, students compare strategies, justify their reasoning, and evaluate which representation is more efficient while recognizing that both approaches produce the same outcome. These opportunities require students to interpret number-line models, analyze relationships among quantities, and evaluate mathematical representations and strategies for solving addition problems.

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

The Math Journeys grade 2 program provides students with opportunities to create concrete models and pictorial representations of mathematical situations in B3.9, “Suma por descomposición: sin reagrupación.” During “Nudo: actividad 1,” students use base 10 blocks to represent numbers such as 24 and 15, combine the quantities, and model addition using tens rods and ones cubes. Students create concrete models to show how numbers can be decomposed and recomposed to determine a sum. In “Nudo: actividad 2,” students transition from manipulatives to pictorial representations by recording numbers with segments and crosses on their “pizarrita mágica” and using those representations to solve addition problems, such as 51 + 43, through decomposition. Educator guidance emphasizes the connection between the base 10 models and the drawings, helping students represent the same mathematical situation in multiple ways. During the “Desenlace,” students complete addition problems and contextual situations using visual representations and equations. These activities require students to create both concrete models and pictorial representations of mathematical situations.

Questions and tasks in the Math Journeys grade 2 program provide students with opportunities to create concrete models and pictorial representations to represent mathematical situations. In journey B3.12, development activity 1, students solve 75 − 47 using base 10 blocks, creating a concrete model to represent the subtraction situation. As students work through the problem, they exchange one ten rod for ten ones to demonstrate regrouping and physically remove the tens and ones needed to subtract 47. Students then connect the concrete model to a pictorial representation by drawing tens and ones on the board, showing the regrouping process by recording the exchange of one ten for ten ones and crossing out the tens and ones that are subtracted. Through these representations, students model the subtraction situation and visually represent the actions performed with the base 10 blocks. These opportunities help students create and use both concrete models and pictorial representations to represent mathematical situations involving subtraction with regrouping.

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

The Math Journeys grade 2 program provides students with opportunities to apply their conceptual understanding to new problem situations and contexts in B3.17, “Estrategia libre.” During activity 1, students are presented with equations such as 42 − 13 and 80 − 31. They are then asked to invent contextual situations that could be solved using those expressions. Next, students solve the problems using previously learned strategies, including jumps on the number line and decomposition, and explain how their solutions connect to the context. In activity 2, students solve real-world situations involving buses, farms, and other everyday contexts, selecting and applying appropriate strategies rather than following a prescribed procedure. The materials note that students may choose different solution methods and emphasize connecting the numerical outcome to the question being asked. During the “Desenlace,” students continue applying their understanding to new situations involving balloons, money, and basketball scores and create their own contextualized problem to represent 27 − 15. These tasks require students to transfer their conceptual understanding and problem-solving strategies to new mathematical situations and contexts.

Questions and tasks in the Math Journeys grade 2 program provide students with opportunities to apply their conceptual understanding to new problem situations and contexts. In journey B4.13, students apply previously learned concepts of addition, subtraction, and decomposition within 1–1,000 to estimate solutions rather than calculate exact answers. Students use their understanding of place value and number relationships to determine which estimated answer is the most reasonable from a set of options rounded to the nearest hundred. For example, when estimating 133 + 210, students combine the hundreds and tens to determine that the sum is closer to 300 than 400, applying decomposition and place-value reasoning in a new context. Rather than performing the complete calculation, students use estimation strategies to make and justify reasonable predictions. The Teacher Guide includes questions that encourage students to explain how they determined which estimate was most appropriate and why an answer is closer to one benchmark number than another. In activity 2, “Usamos la estimación en la resolución de situaciones contextualizadas,” students extend these estimation strategies to solve addition and subtraction problems embedded in real-world situations. These opportunities require students to transfer and apply their conceptual understanding of operations, decomposition, and place value to new mathematical contexts, deepening their ability to reason about quantities and make reasonable estimates.

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

The Math Journeys grade 2 program contains tasks designed to build the automaticity and fluency students need to complete grade-level mathematical tasks. In journey B2.16, “Práctica productiva: suma hasta 20,” students engage in repeated practice with addition facts and number relationships through a variety of activities. During “Nudo: actividad 1,” students use number cards to create addition expressions, determine sums, and explain their reasoning to their peers. In activity 2, 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 while reinforcing efficient recall of addition facts. During the “Desenlace,” students identify combinations that equal 10, complete missing-addend equations, and generate additional number combinations using given number cards.

The Math Journeys grade 2 program provides tasks designed to build the automaticity and fluency students need to complete grade-level mathematical tasks. In journey B2.17, “Práctica productiva: resta hasta 20,” the warm-up uses applet A87, pack 3 to provide students with repeated opportunities to compare numbers using the symbols =, <, and >, strengthening their fluency with number relationships and comparison. In development activity 1, students use applet A14, packs 12 and 10 to determine missing numbers in part-part-whole boxes. Through repeated practice identifying unknown parts and wholes, students reinforce addition and subtraction relationships and develop automaticity with fact families and missing-addend situations. In activity 2, “Restamos con cartas,” students use number cards (1–20) and symbol cards (−, =, <, >) to create and compare subtraction expressions such as 6 − 2 > 4 − 3. Working together, students take turns selecting cards and mentally solving subtraction expressions to determine the appropriate comparison symbol. Because students repeatedly calculate and compare differences without relying on manipulatives, they build fluency with subtraction facts and develop automaticity in evaluating numerical relationships.

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

The Math Journeys grade 2 program provides students with opportunities to practice applying efficient, flexible, and accurate mathematical procedures throughout the learning pathways. In journey B3.12, “Resta por descomposición: con reagrupación,” students apply decomposition strategies to solve subtraction problems that require regrouping. During “Nudo: actividad 1,” students represent 75 − 47 using base 10 blocks, decompose a ten into ones, and model the subtraction using concrete, pictorial, and symbolic representations. The educator prompts students to explain and justify their thinking with questions such as “¿Podrías explicar tu estrategia empleada sobre 75 − 47?” and “¿Podrías explicar a tus compañeros cómo has resuelto esta estrategia?” Students then apply the same procedure to additional subtraction problems and discuss whether the strategy can be transferred to new situations through questions such as “¿Podrías utilizar lo que aprendiste al resolver 75 − 47 para resolver 62 − 37?” In activity 2, students solve subtraction problems using money representations to reinforce the decomposition strategy with a different model. Through these activities, students practice selecting, applying, explaining, and generalizing efficient and accurate procedures for subtraction with regrouping.

The Math Journeys grade 2 program provides students with opportunities to practice applying efficient, flexible, and accurate mathematical procedures throughout the learning pathways. In journey B4.15, development activity 1, students represent 21 − 15 using snap cubes and a number line to determine the distance between the two quantities. Students then explore equivalent subtraction expressions by adding one cube to each quantity to create 22 − 16 and removing three cubes from each quantity to create 19 − 13, observing that each subtraction results in the same difference. By using manipulatives and number lines, students develop flexibility in their thinking while accurately determining equivalent subtraction relationships. In activity 2, “Buscamos restas con el mismo resultado que nos faciliten el cálculo,” students solve 74 − 48 on an empty number line and determine that the difference is 26. The educator then guides students to transform the expression into the equivalent subtraction 76 − 50, helping them recognize that adjusting both numbers by the same amount preserves the difference while making the calculation more efficient. The educator facilitates discussion by asking students to compare the two subtraction expressions and explain which is easier to solve and why. These opportunities encourage students to analyze and apply efficient procedures, use flexible strategies to transform problems, and verify the accuracy of equivalent subtraction methods while deepening their understanding of number relationships.

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.

The Math Journeys grade 2 program provides students with opportunities to evaluate mathematical representations, models, strategies, and solutions for efficiency, flexibility, and accuracy throughout learning pathways. In journey B4.11, “Comparación de estrategias de suma y resta,” students analyze and compare multiple strategies for solving addition and subtraction problems. During “Nudo: actividad 1,” students evaluate whether the subtraction problem 62 − 58 has been solved correctly on a number line, identify the error, and justify their reasoning. Students then compare Count Back strategies with finding the distance between two numbers. The materials explicitly state that “el alumnado reflexione y concluya que es más eficiente calcular la distancia entre ambos números que colocarse en el 62 y dar un salto de 58 unidades hacia atrás,” prompting students to evaluate the efficiency of different solution methods. In activity 1.2, students analyze the compensation strategy by comparing expressions such as 33 − 20 = 13 and 32 − 19 = 13. To encourage students to evaluate the effectiveness of alternative approaches, the materials state that “aunque nos sirva para comprobarlo, no es una estrategia tan eficiente como convertir 32 − 19 en una resta más fácil de resolver.” During the “Desenlace,” students identify and correct errors in completed addition and subtraction solutions. Through these activities, students evaluate mathematical representations, strategies, and solutions for efficiency, flexibility, and accuracy while justifying their mathematical thinking.

The Math Journeys grade 2 program provides students with opportunities to evaluate mathematical representations, models, strategies, and solutions for efficiency, flexibility, and accuracy throughout the learning process. In journey B4.3, development activity 1, students analyze an addition situation involving 44 snap cubes represented as four towers of 10 and four individual cubes stored in an opaque bag. After the educator adds two additional towers of 10 and students determine that the total is 64, the educator introduces a change to the problem by explaining that only 19 cubes (rather than 20) should have been added. Students are encouraged to evaluate different solution strategies and reason flexibly about how to adjust their answer. For example, students may recognize that 44 + 20 = 64 and then subtract 1 to find 44 + 19 = 63, while others may choose to add 19 directly. To encourage students to compare strategies and evaluate their efficiency, the Teacher Guide includes prompts such as “¿Qué técnica para resolver 44 + 19 te parece más fácil y por qué?” and “¿Por qué sumar 20 y luego quitar uno puede ser una estrategia útil para sumar 19?” Students then represent the same addition on a number line by locating 44, making two jumps of 10 forward, and one jump of one backward. By solving the problem using manipulatives, mental strategies, and number-line representations, students evaluate the efficiency, flexibility, and accuracy of different approaches while recognizing that they can use multiple representations to arrive at the same solution.

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

The Math Journeys grade 2 program contains guidance to help students select increasingly efficient approaches to solve math problems. In journey B4.5, “Suma y resta: agrupamos saltos de 10,” students use number lines to solve addition and subtraction problems and are guided to refine their strategies for greater efficiency. During “Nudo: actividad 2.1,” students solve 43 + 45 using jumps on a number line and then compare alternative approaches. To encourage students to replace multiple jumps with a more efficient representation, the materials explicitly state, “Esperamos que propongan cambiar los 4 saltos de 10 por un solo salto de 40.” In activity 2.2, students solve subtraction problems and are guided to combine jumps of 10 into a single larger jump. To help students select more efficient solution methods, the materials state, “pedimos al alumnado que registre la solución de manera que todos los saltos de 10 unidades queden aglutinados en un solo salto más largo.” Through these prompts and representations, students learn to evaluate and refine their strategies by grouping jumps and using more efficient procedures for addition and subtraction.

The Math Journeys grade 2 program contains guidance to help students select increasingly efficient approaches to solve math problems. In journey B3.6, development activity 1, students locate 37 on a number line and determine where they will land after making two jumps of 10 and one jump of 26 forward. As students represent 37 + 26 = 63 on the number line, they are encouraged to use a more efficient strategy by decomposing the jump on the ones and bridging through the next ten. To help students analyze and refine their approaches, the Teacher Guide includes prompts such as “¿Observan alguna forma útil de dividir los saltos cuando pasamos a la siguiente decena?” and “¿Podrían utilizar esta misma estrategia con otros números que también pasan por una decena?” Students learn that after making two jumps of 10 to reach 57, they can efficiently decompose the remaining six into two jumps of three, moving from 57 to 60 and then from 60 to 63. In activity 2, “Comparamos dos maneras de sumar mediante saltos,” students compare the addition expressions 29 + 45 and 45 + 29 using empty number lines. Students represent the sums using different starting points and jump patterns and then discuss which approach is easier to use. The Teacher Guide prompts students to compare strategies and justify their reasoning, leading them to recognize that starting with the larger addend can result in a more efficient solution path. These opportunities help students select increasingly efficient approaches by decomposing numbers, bridging through tens, comparing solution methods, and analyzing the effectiveness of different addition strategies.

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

The Math Journeys grade 2 program explicitly states how the conceptual and procedural emphases of the TEKS are addressed in the “Vista general de tramo—B: pensamiento aditivo.” The overview identifies the conceptual emphasis by describing 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. The overview also identifies the procedural emphasis by outlining the skills students will practice throughout the broader learning pathway, including solving addition and subtraction problems, decomposing numbers, representing operations with equations and models, and applying efficient strategies to determine solutions. Through the “Vista general de tramo—B: pensamiento aditivo,” the Math Journeys grade 2 program clearly communicates both the conceptual understanding and procedural skills addressed within the TEKS.

The Math Journeys grade 2 program explains how the conceptual and procedural emphases of the TEKS are addressed. In journey B3.10, development activity 1, students link their conceptual understanding of place value and decomposition with the procedural process of regrouping during addition. Students use base 10 blocks to solve 28 + 35 by representing tens and ones and determining the total number of each. As students combine the ones and find that the total exceeds 10, they exchange 10 ones for one ten rod, reinforcing the place-value concept that ten ones are equivalent to one ten. Students then represent the same process using drawings of base 10 blocks and symbolic notation on the board. The educator helps students connect the concrete and pictorial representations to the abstract algorithm by ensuring that the symbolic representation reflects the regrouping that occurred. For example, students represent 20 + 30 = 50 and 8 + 5 = 13, then decompose 13 into 10 + 3, regroup the additional ten, and combine it with the existing tens to show that 20 + 30 + 10 = 60, resulting in a final sum of 63. Through these experiences, students develop a conceptual understanding of why regrouping works while simultaneously learning the procedural steps needed to accurately solve addition problems with regrouping.

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.

Questions and tasks in the Math Journeys grade 2 program provide students with opportunities to use concrete models, pictorial representations, and abstract models as required by the TEKS. In journey B3.11, “Resta por descomposición: sin reagrupación,” students use multiple representations to develop an understanding of subtraction through decomposition. During “Nudo: actividad 1,” students start with concrete models by representing numbers such as 45 using base 10 blocks and physically removing tens and ones to model subtraction. Students then transition to pictorial representations by drawing bars and crosses to represent tens and ones and crossing out the quantities being subtracted. To help students connect the visual models to the subtraction process, the materials state that “estas cajitas recogen los resultados de restar las unidades y las decenas cuando operamos con números de dos cifras.” In activity 2, students represent subtraction problems such as 67 − 42 using segments and crosses on their “pizarrita mágica,” reinforcing pictorial representations alongside the subtraction process. Students also use abstract representations by recording the subtraction in vertical form and decomposing the numbers into tens and ones to calculate partial differences. During the “Desenlace,” students solve contextualized subtraction problems using the same representations and record their solutions numerically. Through these activities, students use concrete models, pictorial representations, and abstract representations to deepen their understanding of subtraction and place-value relationships.

The Math Journeys grade 2 program contains questions and tasks that provide students with opportunities to use concrete models, pictorial representations, and abstract models as required by the TEKS. In journey B3.10, development activity 1, students use base 10 blocks to represent and solve 28 + 35, providing a concrete model of the addition situation. As students combine the tens and ones, they determine that the total number of ones exceeds 10 and exchange 10 ones for one ten rod, demonstrating regrouping through a hands-on model. Students then create a pictorial representation by drawing the base 10 blocks and recording the regrouping process. Finally, students connect these representations to an abstract model by recording the addition using a vertical decomposition method and symbolic notation. The educator ensures that the symbolic representation accurately reflects the exchange of 10 ones for one ten and helps students connect the regrouping shown in the concrete and pictorial models to the written algorithm. These opportunities help students use and connect concrete models, pictorial representations, and abstract mathematical representations to build their understanding of addition with regrouping.

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 Math Journeys grade 2 program provides students with supports to connect, create, define, and explain concrete and representational models to abstract concepts as required by the TEKS. In journey B3.12, “Resta por descomposición: con reagrupación,” students use base 10 blocks and visual representations to model subtraction with regrouping and connect these models to the standard written algorithm. During “Nudo: actividad 1,” students represent 75 with base 10 blocks and model the subtraction of 47 by physically exchanging four tens bars for 40 unit cubes. To help students understand why regrouping is necessary, the materials explicitly state, “Pretendemos que se dé cuenta de que tiene que quitar cuatro barras y siete cubos pequeños de la bandeja, pero que solo hay cinco cubos pequeños.” Students then create representational models by drawing bars and crosses and recording the subtraction process on the board. The lesson connects these concrete and pictorial models to abstract representations through vertical subtraction and partial differences, showing how 75 − 47 can be represented as 20 + 8 = 28. To help students define and explain the relationship between the models and the numerical procedure, the materials further clarify that “estas cajitas recogen los resultados de restar las decenas y las unidades cuando operamos con números de dos cifras.” In activity 2, students apply the same strategy using money models with $10 and $1 bills, further connecting the regrouping concept to real-world representations. Through these supports, students connect, create, define, and explain concrete and representational models as they deepen their understanding of subtraction with regrouping.

The Math Journeys grade 2 program provides students with supports to connect, create, define, and explain concrete and representational models to abstract concepts, as required by the TEKS. In journey B3.10, “Sumamos por descomposición: llevadas en las unidades,” the Teacher Guide provides questions, discussions, instructional supports, and a video resource to guide students through the progression from concrete models to pictorial representations and abstract mathematical concepts. In development activity 1, students use base 10 blocks to represent and solve 28 + 35, counting the tens and ones in each addend and combining them to determine the total. The Teacher Guide explains that when the total number of ones exceeds nine, students may exchange 10 ones for one ten rod, reinforcing the relationship between ones and tens within the base 10 system. Students then create pictorial representations by drawing the base 10 blocks and recording the regrouping process, and they connect these representations to an abstract vertical addition model using decomposition. A supporting video further reinforces the concept by demonstrating addition problems in which the ones digits total more than nine and require regrouping. As students share and explain their representations, the educator ensures that the symbolic notation accurately reflects the exchange of 10 ones for one ten and prompts students to explain how the concrete model, drawing, and written algorithm represent the same mathematical process. These supports help students connect, create, define, and explain the relationships among concrete models, visual representations, and abstract mathematical procedures while developing a conceptual understanding of addition with regrouping.

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

The Math Journeys grade 2 program provides students with opportunities to develop academic mathematical language using visuals, manipulatives, and other language development strategies. In the “Vista general de tramo—B: pensamiento aditivo,” the materials include dedicated vocabulary sections that introduce terms related to addition, subtraction, decomposition, regrouping, place value, and mathematical strategies. The overview incorporates visual representations such as base 10 blocks, number lines, additive boxes, equations, and pictorial models that help students develop and use academic mathematical language. Throughout the broader learning pathway, students use these representations to discuss solution strategies, explain the relationships between quantities, compare methods for solving problems, and justify their mathematical reasoning. Students engage in mathematical conversations using precise vocabulary while connecting concrete and pictorial models to symbolic representations. Through these opportunities to listen, speak, read, and write about math, the Math Journeys grade 2 program helps students develop academic mathematical language aligned with the TEKS.

While exploring addition strategies in journey B3.9, “Suma por descomposición: sin reagrupación,” students develop academic mathematical language through visuals, manipulatives, and language development strategies in Math Journeys. Students use base 10 blocks, pictorial representations, and the decomposition strategy to add numbers up to 100 while using academic terms such as descomponer, decenas, unidades, suma, total, and combinar. Students represent tens with bars and ones with crosses, separate each problem into tens and ones, and combine the partial sums to determine the total. To encourage students to explain their strategies using precise mathematical language, the educator asks questions such as “¿Podrías explicar cómo te ayuda descomponer los números en decenas y unidades para sumar?” and “¿Cómo muestran tus barras y cruces que 50 + 40 = 90 y 1 + 3 = 4?” To further help students develop language, the EB guidance provides sentence stems that scaffold mathematical discourse, including “__ más __ es igual a __” for beginning students and “Sumé las decenas: __ más __. Luego las unidades: __ más __” for intermediate students, enabling students to communicate their reasoning with increasingly precise academic vocabulary.

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 Math Journeys grade 2 program provides educators with embedded guidance to scaffold, support, and extend students’ use of academic mathematical vocabulary in context when communicating with peers and educators. The B4 Journey Language Bank (“Banco de lenguaje y redirecciones”) provides educators with sentence stems, discussion prompts, vocabulary supports, and redirection that help students communicate their mathematical thinking using precise academic language. Guidance is offered to discuss addition and subtraction strategies, place-value concepts, decomposition, regrouping, mathematical representations, and problem-solving methods. Educators are given prompts that encourage students to explain their reasoning, justify their solutions, compare strategies, and communicate mathematical ideas during partner, small-group, and whole-group discussions. The Journey Language Banks also include follow-up questions and redirection that extend students’ responses and support deeper mathematical discourse.

Throughout journey B3.11, “Resta por descomposición: sin reagrupación,” students strengthen their use of academic mathematical vocabulary through embedded guidance that scaffolds, supports, and extends mathematical communication with their peers and the educator. Students use base 10 blocks to apply the decomposition strategy as they solve subtraction problems within 100 and communicate their mathematical thinking using terms such as decenas, unidades, descomponer, resta, and diferencia. For example, students solve 45 − 23 by removing rods and unit blocks and explaining each step of the process. To help students connect the concrete model to the subtraction process using precise mathematical language, the educator prompts students to explain their reasoning by asking, “¿Podrías explicar qué nos dicen los bloques sobre los números?” and “Después de retirar 2 decenas y 3 unidades, ¿cómo muestra lo que queda sobre la mesa la respuesta de 45 − 23?” Additionally, the Teacher Guide scaffolds students’ understanding by connecting subtraction to money, encouraging educators to remove the rods first because subtracting larger bills first supports estimation and reinforces place-value concepts. To extend students’ mathematical communication, the lesson applies the decomposition strategy to real-world situations by asking students to solve and discuss problems such as “Tenemos 38 galletas y nos comemos 11. ¿Cuántas quedan?” and “Hemos reunido 26 globos azules y verdes. Si 15 son azules, ¿cuántos globos verdes tenemos?” These contextual problems encourage students to communicate their reasoning using academic mathematical terms in meaningful situations.

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

The Math Journeys grade 2 program provides educators with embedded guidance in order to help students apply appropriate mathematical language and academic vocabulary in discourse. In journey B3.12, “Resta por descomposición: con reagrupación,” students use concrete models such as base 10 blocks to represent 75 and physically exchange one ten rod for ten ones to subtract 47. Students connect the concrete model to representational models by drawing and recording the regrouped tens and ones and using the widget “Estrategia de descomposición.” They then connect these representations to the abstract vertical algorithm to solve 75 − 47 = 28. Embedded guidance for educators includes “Comunicar ideas usando lenguaje matemático preciso” and prompts such as “¿Cómo puedes justificar que cambiar una decena por 10 unidades no cambia el valor de 75?” and “¿Necesitamos cambiar una decena por unidades? Primero podríamos usar una representación como palillos y dar la cantidad de decenas y unidades.” These prompts require students to explain their reasoning using mathematical language. Students justify the regrouping process, describe the relationships between concrete models, visual representations, and symbolic notation, and communicate their mathematical thinking using academic terms such as decena, unidad, reagrupación, descomposición, resta, and valor posicional during mathematical discourse with their peers and the educator.

As students compare addition strategies in journey B3.15, “Comparamos estrategias de suma,” Math Journeys embeds guidance that helps students apply appropriate mathematical language and academic vocabulary during mathematical discourse. During “Nudo: actividad 1—Sumamos y comparamos estrategias,” students work in pairs to solve 35 + 42 by using both an empty number line and the decomposition strategy before comparing the two methods and recognizing that each produces the same sum. To encourage students to explain and compare their strategies using precise mathematical vocabulary, the educator uses prompts such as “¿Podrías explicar tu método paso a paso utilizando palabras matemáticas claras?” and “¿Entiendes por qué ambas estrategias nos dan la misma respuesta exacta?” Later, in activity 2, “Resolvemos sumas que requieren un cambio de decena con las dos estrategias,” students solve 28 + 26 with both decomposition and an empty number line while discussing how each representation models the regrouping process. To further support mathematical discourse, the EB guidance identifies strategy/estrategia, decomposition/descomposición, and equivalent/equivalente as English–Spanish cognates and provides sentence stems at multiple levels of proficiency, including “Di un salto de __ decenas y __ unidades y llegué a __” (Intermedio) and “La recta numérica muestra __ y la descomposición muestra __, pero ambas dan __” (Avanzado). This enables students to communicate their mathematical reasoning with increasingly precise academic vocabulary.

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

The Math Journeys grade 2 program provides embedded guidance to facilitate mathematical conversations in B3.12, “Resta por descomposición: con reagrupación.” Students discuss and justify their strategies for solving subtraction problems with regrouping using base 10 blocks, drawings, and symbolic notation. To encourage students to explain their reasoning, compare strategies, and make mathematical connections, the educator uses prompts such as “¿Observas algo parecido en la manera de resolver estas restas diferentes?” and “¿Podrías utilizar lo que aprendiste al resolver 75 − 47 para resolver 62 − 28?” Math Language Routine (MLR) 4 helps students exchange mathematical information with their peers by discussing how regrouping is represented in the models and explaining how exchanging one ten for ten ones affects the subtraction process. Throughout the lesson, students share, validate, and refine mathematical explanations while connecting concrete and symbolic representations. These embedded opportunities for discussion help students hear, refine, and use mathematical language with their peers.

Through collaborative learning experiences in journey B3.1 “Suma: saltamos en el collar de bolas,” Math Journeys facilitates mathematical conversations that allow students to hear, refine, and use mathematical language with their peers. Students solve addition problems using the Bridging through Ten strategy on the 50-bead string by decomposing addends and explaining their thinking. For example, students solve 38 + 5 by recognizing that they first jump two to reach 40 and then jump three more to reach 43, explaining how decomposing five makes the addition more efficient. To prompt students to justify their strategies and respond to one another’s ideas using precise mathematical language, the educator encourages mathematical discussions by asking, “¿Podrías explicar por qué saltar primero al 40 facilita esta suma?” and “¿Cómo sabes que 43 es una respuesta razonable para 38 + 5?” To strengthen their mathematical communication, the EB guidance recommends the “collect and display” strategy by asking students to record their explanations with visual supports, including drawings of the jumps on the 50-bead string. The educator models explanations such as “Para sumar 5 a 38, primero saltamos dos para llegar a 40 y luego saltamos tres más.” Students use this model to discuss additional problems with their partners, refine their explanations based on peer conversations, and communicate their mathematical thinking with increasing precision.

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 Math Journeys grade 2 program contains embedded guidance to help educators anticipate a variety of student answers, including exemplar responses to questions and tasks, as well as guidance to support and redirect inaccurate student responses. In lesson B3.12, “Resta por descomposición: con reagrupación,” students use base 10 blocks, drawings, and equations to solve subtraction problems that require regrouping. The materials provide anticipated student reasoning and exemplar solutions, including representations showing how one ten is decomposed into ten ones to solve problems such as 75 − 47 = 28. The embedded guidance for educators identifies expected strategies related to place value and decomposition. Moreover, to elicit mathematical reasoning, the educator uses prompts such as “¿Podrías explicar a tu compañero cómo lo resolviste usando tu estrategia?” and “¿Cómo ayuda justificar que cambiar una decena por 10 unidades no cambia el valor de 75?” Educators provide support for redirection through questioning prompts, manipulatives, and scaffolded representations that help them address misconceptions and guide students toward an accurate understanding of regrouping and subtraction.

Throughout journey B4.6, “Repasamos saltos sobre la recta numérica,” embedded guidance enables educators to anticipate a variety of student responses, includes exemplar answers, and helps educators address inaccurate responses. Students represent numbers from one to 1,000 and model addition and subtraction on an empty number line by making forward and backward jumps. As students place 327 on the number line, the Teacher Guide anticipates an appropriate response by explaining that students should place the number between 300 and 400 and closer to 300 than 400, rather than expecting an exact location. This guidance helps educators give feedback that reinforces students’ understanding of number magnitude. Later, as students solve 423 − 152, the Teacher Guide provides exemplar solution paths by describing each jump, including how to bridge through hundreds, and explains how educators can respond to student thinking. For example, to help educators redirect students who struggle with efficient subtraction strategies, the guide notes, “En el caso de la resta 423 − 152, después de restar 100, podemos descomponer el salto de 50 en dos saltos más pequeños para hacer una parada próxima al 300.” Finally, students determine the most efficient strategy for solving 315 − 280 by deciding whether to jump backward from 315 or represent both numbers on a number line and find the distance between them. In providing educators with guidance to reinforce efficient mathematical reasoning while supporting and redirecting student responses as needed, the Teacher Guide anticipates students’ reasoning by stating, “Esperamos que razonen que, al tratarse de dos números cercanos, lo más eficiente es situarlos en la línea numérica y descubrir el salto que debemos dar para llegar de uno a otro.”

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

The Math Journeys grade 2 program integrates TEKS mathematical process standards appropriately within grade-level content instruction. In lesson B3.17, “Estrategia libre,” students apply math to solve and create contextualized problem situations while selecting and justifying solution strategies. During the lesson, students generate real-world situations that can be represented by operations such as 42 − 13 and 80 − 31, explain how the operation relates to the context, and solve the problems using previously learned strategies, including decomposition and number-line jumps. Students also solve contextualized problems involving 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, and finding the number of chickens on a farm when the numbers of cows and horses are known. Throughout the lesson, students communicate their reasoning, compare strategies, justify their solutions, and choose appropriate mathematical tools and techniques. In the “Closure” section, students solve additional contextualized problems and create their own situations to represent a given operation, demonstrating problem-solving, mathematical communication, reasoning, and strategic thinking embedded within content learning.

While comparing addition strategies in journey B3.15, “Comparamos estrategias de suma,” Math Journeys integrates TEKS mathematical process standard 1.G within grade-level content instruction. During “Nudo: actividad 1—Sumamos y comparamos estrategias,” students solve addition problems by using both the “Jumping along the Number Line” strategy and the decomposition strategy to add numbers within 100. Students engage with process standard 1.G as they represent, explain, and justify their solutions to 28 + 26 using precise mathematical language. They describe how they decompose numbers into tens and ones, explain the regrouping process, and justify why both strategies produce the same sum. To encourage students to communicate and justify their thinking, the educator supports students’ mathematical reasoning by asking, “¿Podrías explicar tu método paso a paso utilizando palabras matemáticas claras?” and “¿Entiendes por qué ambas estrategias nos dan la misma respuesta exacta?” Throughout the rest of the lesson, students continue solving addition problems by representing, comparing, and defending their solution strategies. During the “Desenlace,” students apply process standard 1.G to solve contextualized addition problems using both strategies while explaining why each method leads to the correct solution.

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

The Math Journeys grade 2 program describes how TEKS mathematical process standards are incorporated and connected throughout the learning pathways. The B4 Journey Instructional Guide justifies the TEKS mathematical process standards, explains the vertical and horizontal alignment, and provides 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 making connections across lessons. Moreover, the guide describes how these process standards support the development of additive thinking concepts throughout the broader learning pathway. In addition, this guide highlights the connections between lessons and standards through sections on vertical and horizontal alignment, showing how process standards are intentionally connected across sessions rather than taught in isolation. These descriptions demonstrate how process standards are incorporated and connected throughout the broader learning pathway.

Across journey B3.12, “Resta por descomposición: con reagrupación,” the Math Journeys grade 2 program describes how TEKS mathematical process standards connect and build throughout the broader learning pathway. The Teacher Guide explicitly identifies process standards 1.F and 1.G, which students apply across multiple lesson activities. In activity 1, “Calculamos restas que son un poco más complejas,” students engage with process standard 1.G as they represent 75 − 47 with base 10 blocks, exchange one ten for ten ones, and explain and justify each step of the regrouping process using precise mathematical language. Students describe why exchanging one rod for ten units allows them to subtract seven ones and explain how the concrete model connects to the symbolic subtraction algorithm. Next, students solve the same subtraction problem using the decomposition strategy and engage with process standard 1.F by analyzing the relationship between the ones digits in the minuend and subtrahend to determine when regrouping is necessary. They recognize that when the ones digit in the subtrahend is greater than the ones digit in the minuend, exchanging one ten for ten ones preserves the value of the number while allowing subtraction to continue. By connecting concrete modeling, symbolic representations, and mathematical analysis, the lesson shows how process standards 1.G and 1.F work together throughout the broader learning pathway.

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

The Math Journeys grade 2 program contains an overview of the TEKS mathematical process standards incorporated into the lesson. In lesson B3.12, “Resta por descomposición: con reagrupación,” the materials explicitly identify process standards, including “1G: justificar ideas usando lenguaje matemático preciso” and “1F: analizar relaciones para conectar ideas matemáticas.” The lesson descriptions explain how students apply these standards throughout instruction as they use base 10 blocks, visual representations, equations, and mathematical discussions to solve subtraction problems with regrouping. Students justify why a ten can be exchanged for ten ones, explain their solution strategies using precise mathematical language, and analyze the relationships between digits and representations to connect subtraction expressions.

Within journey B3.7, “Resta: saltamos sin pasar por el 10,” Math Journeys provides an overview of the TEKS mathematical process standards incorporated throughout the lesson. The Teacher Guide explicitly identifies process standards 1.F and 1.D, helping educators recognize where students apply each standard during instruction. During the “Planteamiento,” students count money using $1 and $10 bills. Process standard 1.F guides students as they analyze the relationships between consecutive amounts by removing one $1 bill at a time from $46 to recognize that each new amount is one less than the previous total. Students then extend this reasoning by removing $10 bills and analyzing how each amount decreases by 10, allowing them to identify and predict numerical patterns. Later, in activity 1, “Aplicamos la estrategia de saltos para resolver situaciones relacionadas con la resta,” process standard 1.D guides students as they communicate mathematical ideas using multiple representations. Students solve 85 − 32 = 53 with snap cubes and an empty number line, explain how removing cubes corresponds to backward jumps on the number line, and demonstrate how both representations model the same subtraction process while communicating their mathematical reasoning.

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

In lesson B3.17, “Estrategia libre,” students analyze, solve, and create real-world addition and subtraction problems. During the “Planteamiento,” students decide if two groups are equal or different and give several reasons for their answers. Throughout the lesson, students answer prompts like “¿Entiendes lo que representa ese número en tu situación contextualizada?” and “¿Podrían proponer otra situación diferente, también relacionada con el contexto del cine?” They solve problems using their own strategies, explain how quantities connect to the context, and invent new math problems that match given operations. The lesson includes group discussions where students share strategies, check their answers, and justify their reasoning. These activities help students persevere in problem-solving and understand math by discussing and applying it to real-life situations.

In journey B3.13, “Relacionamos sumas,” students use manipulatives to see how changing an addend affects the sum. They first solve 18 + 5 = 23. Then, they add 10 blue cubes to the second addend and solve 18 + 15 = 33, discovering that adding the same amount to an addend increases the sum by that amount. Students keep exploring this pattern with more addition problems. During the “Desenlace,” students look at a sequence of related equations like 63 + 7 = __, 63 + 8 = 71, and 63 + 9 = __. They use the known equation to figure out the unknown sums without counting. This activity helps students spot mathematical patterns, solve problems, and understand addition properties. Educators ask guiding questions to help students connect the equations and recognize the pattern when they do not notice it right away.

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

Lesson B3.8, “Resta: saltando y cruzando el 10 II,” helps students understand, explain, and justify that there can be multiple ways to solve problems and complete tasks. Students explore subtraction strategies using the number line, including jumping back by tens and ones, decomposing jumps, and crossing through 10 to solve problems. Students compare different representations and strategies to determine which method is more efficient for solving subtraction problems. To encourage students to explain their process and justify their mathematical reasoning, educators use prompts such as “¿Dónde ubicarían el número 65 y adónde llegarían con un salto de 10 y un salto de siete hacia atrás?,” “¿Qué herramienta utilizaron para resolverlo?,” and “¿Cuál estrategia les ayuda más para resolver la resta? ¿Por qué?” Students participate in discussions where they listen to classmates’ arguments, compare solution paths, and explain why different strategies can lead to the same solution. During independent practice, students select representations that make subtraction easier and apply their chosen strategies, showing that it is possible to solve problems in multiple ways.

In journey B3.15, “Comparamos estrategias de suma,” students compare and connect multiple strategies for adding numbers, including “Jumping along the Number Line” and decomposition. In activity 2, “Resolvemos sumas que requieren un cambio de decena con las dos estrategias,” students work in pairs to solve 35 + 42 using both strategies, check their work, and recognize that both models are valid because they produce the same sum. Box 1G states that students display, explain, and justify their solutions using precise mathematical language. The Teacher Guide contains prompts such as “¿Podrías explicar tu método paso a paso utilizando palabras matemáticas claras?” and “¿Entiendes por qué ambas estrategias nos dan la misma respuesta exacta?” These questions help students explain and justify that they can solve the same problem or complete the same task in different but equally valid ways.

Evaluation for 6.1c
Materials are designed to require students to make sense of mathematics through multiple opportunities for students to do, write about, and discuss math with peers and/or educators.

In lesson B3.17, “Estrategia libre,” students actively do, write about, and discuss math with their classmates and the educator. First, students analyze groups of cubes to decide if they are equal or different and explain their reasoning. They solve real-world subtraction problems like 42 − 13 and 80 − 31 using any strategy they choose. Students use previously learned methods such as “Jumping along the Number Line” and decomposition and invent their own real-world subtraction problems for their classmates to solve. To prompt students to justify their answers, the educator asks questions like “¿Podrías explicar por qué tu respuesta tiene sentido en el contexto de tu historia?” Students record equations and solutions on their “pizarrita mágica,” practice independently during the “Desenlace,” and write their own contextualized problem for 27 − 15. Finally, students explain and defend their strategies during group discussions, compare answers, and show how their methods fit the context of each problem.

In journey B3.12, “Resta por descomposición: con reagrupación,” students practice subtraction with regrouping using base 10 blocks and the decomposition strategy. In activity 1, students model 75 − 47 by exchanging one ten rod for ten ones and explaining how regrouping allows them to subtract seven ones. Next, students solve the subtraction on paper and with a digital widget, connecting hands-on, visual, and digital approaches. Students then solve 62 − 28 using the same regrouping strategy, noticing they must exchange one ten for ten ones when the subtrahend’s ones digit is greater than the minuend’s. To help students compare strategies, explain their reasoning, and connect their learning, Box 1F provides educators with questions such as “¿Observas algo parecido en la manera de resolver estas restas diferentes?” and “¿Podrías utilizar lo que aprendiste al resolver 75 − 47 para resolver 62 − 28?” These activities encourage students to model their thinking, discuss ideas, and make sense of math with their classmates as well as the educator.

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

Embedded instructional routines in lesson B3.12, “Resta por descomposición: con reagrupación,” guide students to share and reflect on their problem-solving approaches by explaining, justifying, and discussing their mathematical thinking with their peers and the educator. Students begin by representing 75 with base 10 blocks and predicting how they will subtract 47 before manipulating the materials. To encourage students to explain why regrouping is necessary and justify how exchanging one ten for ten ones preserves the value of the number, the educator uses prompts such as “¿Podrías explicar por qué cambiar una barra por 10 unidades no cambia el valor de 75?” and “¿Podrías utilizar la agrupación inicial de 75 − 47 para resolver 82 − 28?” Students represent their thinking with base 10 blocks, record the subtraction using symbolic notation, and compare the concrete and symbolic representations. As the lesson progresses, students solve additional subtraction problems using both manipulatives and written representations while discussing the strategies they selected and reflecting on how regrouping helps them subtract numbers with greater accuracy. During the “Desenlace,” students complete independent subtraction tasks, explain how the regrouping process connects to their representations, and share their reasoning as the educator checks for understanding.

In journey B3.2, development activity 2, students solve 33 − 5 using the bead string and apply the strategy previously modeled in activity 1. The Teacher Guide provides step-by-step guidance as students determine how to decompose the subtrahend to make an efficient jump to the previous ten. Box 1F describes the expected reasoning, explaining that students recognize 33 is three away from 30, decompose five into three and two, jump back three to reach 30, and then jump back two more to arrive at 28. To encourage students to explain and justify their strategies, the Teacher Guide includes prompts such as “¿Podrías explicar por qué dar un salto hacia atrás hasta el 30 primero nos ayuda a resolver esta resta?” and “¿Cómo te ayuda la relación entre el 33 y el 30 a decidir cómo descomponer el cinco?” As students solve additional subtraction problems, the educator introduces a part-part-whole box to help students decompose the ones digit and reflect on how choosing different pairs of numbers supports efficient jumps on the bead string, providing opportunities for students to share, explain, and justify their problem-solving approaches.

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

In lesson B3.10, “Suma por descomposición: con reagrupación,” students use base 10 blocks and the decomposition widget to represent 28 + 35. They explain how exchanging 10 ones for one ten changes the model but not the sum’s value. To help students connect concrete models to written equations, the educator uses students’ responses to give feedback, asking questions like “¿Podrías explicar qué representa cada tipo de billete en tu número?” and “¿Cómo muestran los billetes de $10 y los de $1 las decenas y las unidades cuando sumas 28 + 35?” If students overlook regrouping or represent it incorrectly, the educator guides them to compare their models to the written algorithm, explain why exchanging preserves the number’s value, and revise their work based on feedback. These prompts help educators address misconceptions by encouraging students to explain their reasoning instead of just giving the answer.

Moreover, in journey B3.14, development activity 1, students investigate how changes in the minuend and subtrahend affect the difference. In activity 1.1, students solve 37 – 5 = 32 using snap cubes and pictorial representations. The educator then modifies the original problem and asks students to determine how many snap cubes remain if one or 10 additional cubes are removed (37 – 6 = 31 and 37 – 16 = 21). The Teacher Guide explains that students should recognize and articulate that when the subtrahend increases by one or 10, the difference decreases by the same amount. During the “Desenlace,” students analyze related subtraction equations (such as 17 – 5 = 12 and 17 – 6 = __) to apply derived facts instead of recomputing each problem. The Teacher Guide anticipates that some students may calculate each subtraction independently rather than recognize the relationship between the equations and provides guiding questions to help students identify the pattern and explain their reasoning. These guiding questions help educators provide explanatory feedback that addresses anticipated misconceptions and strengthens students’ understanding of subtraction relationships.