Math Journeys Texas, Grade 1

Evaluation for 1.1a
Materials include an alignment guide outlining the TEKS, ELPS, and concepts covered, with a rationale for learning paths across grade levels (vertical alignment) and within the same grade level (horizontal alignment) as designed in the materials.

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

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

Evaluation for 1.1b
Materials include an implementation guide with usage recommendations and strategies for effective educator use in various contexts, such as just-in-time supports, advanced learning, or as a course.

The materials in Math Journeys include a Program Guide that provides comprehensive educator guidance for implementation, including a 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 additional practice in Atlas Math, an adaptive digital practice. Additionally, the “Lesson Internalization and Planning” section provides guidance on planning for learner variability, including explanations for multiple entry points, just-in-time supports, extensions, and multiple representations and modes of expression.

The materials in group 1 include an implementation guide with recommendations and strategies for effective educator use across various contexts, such as implementing the materials for just-in-time supports, advanced learning, or as a course. For example, the materials list 10 practices for effective math intervention in the program overview. These practices guide educators to “identify each student’s starting point, set realistic and meaningful goals, [and] create a safe environment where students dare to think.” The materials prompt educators to “guide reasoning through modeling, questioning, and feedback,” as ways to foster conceptual understanding.

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

The lessons and journeys in Math Journeys are aligned to the TEKS content and process standards, and materials include a TEKS Correlation Guide that outlines recommended skill entry points based on diagnostic assessment results. The guide provides educators with tools for implementing instruction by connecting lessons and activities to specific standards within each journey. The TEKS Correlation Guide alone does not provide a recommended skill entry point.

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

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

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

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

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

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

Additionally, on-demand video resources in the training materials provide guidance on specific strategies, such as “Let’s Add by Breaking Down.” The videos are not specifically for instructional leaders, but can help educators and leaders who may need more guidance on a specific strategy.

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

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

In the grade 1 Math Journeys, the ELPS are included in each lesson. For example, lesson A2, “Acoustic Counting Forward and Backward (1–50),” includes a Lesson-Level ELPS Companion. The lesson provides educator guidance to teach students to “count forward and backward within 50; identify the number before and after; skip count by 10s; order numbers.” The ELPS focus for the lesson includes listening (E), speaking (B, E), and writing (C). The expected oral output includes, “The next number after ___ is ___. When I count by 10s, the 1s stay the same and the 10s change.” The expected written output noted in the lesson is, “Missing-number patterns and ordering numbers from least to greatest.”

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

Evaluation for 1.2b
If designed to be adaptive, materials include responsive learning objectives, lesson components with suggested timeframes, and assessment resources aligned with the TEKS and ELPS.

The materials in Math Journeys include guidance for lesson-planning through clearly organized lesson components within the program structure. To support effective pacing and implementation, the materials outline the instructional sequence of “build, consolidate, and practice,” along with suggested time frames for each part of the lesson. Additionally, the lesson framework is designed to help educators deliver instruction in a consistent and purposeful manner, while providing students with a structured learning routine. The organization of the lesson components supports educators in managing instructional time effectively and ensuring that each stage of learning is addressed throughout the lesson.

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

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

Each math journey provides a family letter to help caregivers support learning at home. These letters may include questions to ask, vocabulary to use, and specific activities to support the student. Educators can change the letter’s language to Spanish or English using the language toggle in the top right corner.

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

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

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

The Placement Test Implementation Guide contains clear and detailed guidance for educators to administer the diagnostic assessment consistently and accurately. This guidance includes the estimated length of the test, the role of the instructor during administration, and the suggested materials. For example, the “Administration Guidance” section outlines that “paper and pencil are recommended to support student thinking and working memory during the assessment.” This level of detail ensures that all educators administer the diagnostic assessment in a consistent and accurate manner across classrooms.

Additionally, the End-of-Journey Test: Instructions and Guide shows educators how to lead the assessment and have students respond individually. The guide walks educators through how to check information before test day, administer the test, and review the results. The guide also specifies the approximate length, estimated testing time, materials needed (digital and external), number of assessment items, and examples of response types.

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

The materials help educators administer the digital end-of-journey test by offering printable versions of all assessment components. The End-of-Journey Test: Instructions and Guide gives educators downloadable links to printable PDFs, including the administration instructions, journey tests, and answer key. With these resources, educators can flexibly give assessments in classrooms with limited digital access or when they prefer paper-based testing.

Educators cannot enable or disable text-to-speech for individual students on the digital platform. Rather, only students themselves can independently activate audio support at any time. Educators can change the language of instruction, but this is the only type of language support provided. Furthermore, the digital interface does not provide calculators, which means educators must supply and manage calculators during assessments.

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

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

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

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

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

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

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

For example, the Journey Test A2 answer key gives educators detailed rationales for both correct and incorrect responses in the “Item-by-Item Guide” section. These rationales help educators understand student thinking and spot potential misconceptions. For instance, question 3 asks, “Where is 24 represented?” The correct rationale explains that the top left abacus, with two beads on the $10 rod and four beads on the $1 rod, shows that “two $10 units and four $1 units total 24.” The rationales for the incorrect responses state, “This shows 42, not 24,” “This shows 6, not 24, because there are no tens,” and, “This shows 35, not 24.”

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 instructional materials include a placement test report to provide educator guidance for responding to student performance trends. The “Placement in Journeys” section explains how assessment results can be used to support instructional decision-making and student placement. Specifically, the placement test report assists educators in grouping students for targeted instruction and determining appropriate placement within the Math Journeys program. Based on students’ assessment performance, the report generates suggested starting points for each student within the journey progression. This allows educators to differentiate instruction according to demonstrated levels of understanding and academic readiness.

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

Evaluation for 2.2c
Materials include tools for teachers to track student progress and growth, and tools for students to track their own progress and growth.

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

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

Evaluation for 2.2d
If designed to be static, materials provide prompts and guidance to support educators in conducting frequent checks for understanding at key points throughout each lesson or activity.

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

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

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

Furthermore, the Program Guide describes adaptive sequences of activities designed to reinforce concepts that were introduced during instruction, and are aligned to each student’s individual learning needs. Throughout these adaptive activities, students receive consistent, immediate, and responsive feedback that supports learning consolidation and promotes continued understanding of mathematical concepts. The adaptive learning pathway uses data-driven insights to adjust instruction in real time, which allows the sequence of activities to evolve based on each student’s performance and demonstrated needs. This individualized approach supports differentiated instruction by providing students with targeted learning experiences and ongoing feedback throughout the program.

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 materials include educator guidance for scaffolded activities designed to support students who have not yet demonstrated proficiency with grade-level concepts. Each lesson within the program contains a representation page, accompanied by either a support or extension logsheet that provides differentiated instructional opportunities based on student needs. For example, in Journey B, “Counting with the Bead String II,” educators provide explicit support during the wrap-up by having students record what they learned. In the wrap-up, students represent different numbers on the 50-bead string in their logbooks. If students count beads one by one, educators encourage them to use the colored beads to represent tens.

The support logsheets incorporate scaffolds to promote student understanding, such as selecting from a set of options, counting, matching, and using visual representations. These supports reduce the level of abstraction by providing concrete and visual models that help students develop a deeper understanding of grade-level concepts while working toward the intended learning outcomes.

Evaluation for 3.1b
Materials include explicit educator guidance for language supports, including pre-teaching and embedded supports for developing academic vocabulary and unfamiliar references in text.

The materials include linguistic accommodations for each math journey. Within these accommodations, a Journey Language Bank provides suggestions for general language support strategies and routines. Examples of these supports include using sentence frames and discourse starters to scaffold the use of technical language during classroom discussions. Suggestions also include options for discourse and writing prompts to use during specific lessons.

The materials include a Journey Language Bank and redirections for each journey. Journey Language Banks include a lesson-by-lesson table that names the unfamiliar references in each lesson, as well as the bridge to use before the lesson to help educators pre-teach the context of the text. For example, the Journey A2 Language Bank and redirections add extra pre-teach routines, discourse moves, writing prompts, and redirection options that educators can use selectively. In lesson A2.3, the unfamiliar reference in the text is “numbers shown with 7 segments, the way digits appear on a digital clock or other device.” Then the quick bridge before the lesson suggests that educators “show a digital clock display and say, ‘These numbers are made with small bars called segments. You see them on clocks and other devices.’” Students repeat the segment and point to one bar.

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

The materials offer enrichment and extension activities in Journey A2, “Identify Numbers and Counting, 1–100,” and provide instructions on how to facilitate the process and assess student responses. The Journey A2 Enrichment and Extension Guide states, “How to use this guide: grade-level extension, the student is ahead within the journey’s content. Decide who qualifies using the signals in section two; facilitate and assess with section three (Extension logsheets) and section four (Extension tips), during the session and at wrap-up.” For above-content extension, the guidance notes state that if “the student is ahead of the journey itself, the pattern of signals across sessions and tests (section two, third signal) triggers the early End of Journey Test. If the student scores above 75%, they advance to the next journey (section five).”

Additionally, the materials include enrichment and extension in “Introducing the Bead String.” For quantities hidden on the bead string, educators ask, “How many beads are under the tunnel?” Students then complete the missing numbers along the string. The intent of this section is to support and extend on learning for part–whole reasoning on a linear model. In the Enrichment and Extension Guide, educator guidance states that students reach mastery when they can “state hidden quantities from structure (two full tens and three more) and explain the complement relation: the tunnel hides what is missing between what I can see and what there must be in total.”

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

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

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

The grade 1 materials let students show their understanding of mathematical concepts in multiple ways. Math Journeys lessons intentionally use the concrete, pictorial, abstract (CPA) instructional sequence to offer students different ways to demonstrate understanding, such as using their bodies, manipulatives, Atlas Math digital applets, or writing. Multilevel logsheets help students consolidate learning by recording hands-on experiences. Lesson plans explicitly guide educators through each sequence by highlighting when to use manipulatives or prompts. Additionally, lesson plans provide ready-made slides to encourage mathematical thinking and discourse. In the lesson “Representing Numbers to 100,” activity 1, educators have students form a circle and place 20 to 30 snap cubes in the center. Educators invite a student to build as many towers of 10 snap cubes as possible, and state the total number of snap cubes. Educators then ask how to write this number and highlight that the first digit represents the number of towers of 10 snap cubes, while the second digit represents the remaining snap cubes.

Additionally, practice sets and quizzes let students demonstrate their understanding of mathematical concepts. For example, in Journey B4, lesson 14, “Consolidating Addition and Subtraction II,” students count backward by tens and ones in a circle as a class to approach zero. They work with digital and concrete manipulatives and record their representations on individual papers. Students also communicate their ideas using multiple representations, such as base ten blocks, written equations, diagrams, symbols, and spoken language. Students justify their use of the equal sign to show that both sides have the same value.

Evaluation for 3.2a
Materials include explicit (direct) prompts and guidance for educators to build knowledge by activating prior knowledge, anchoring big ideas, and highlighting and connecting key patterns, features, and relationships through multiple means of representation.

The materials provide explicit prompts and guidance for educators to build prior knowledge. For example, the warm-up anchors big ideas by activating students’ prior knowledge at the start of each session. For instance, in lesson A2.11, the 100-bead string is introduced and students work together to create a group string. This activity builds on their previous experience with smaller 20- and 50-bead strings to establish a foundation for larger numbers, up to 100. The development then continues to support the transition to more abstract representations by connecting physical models to the two-color number line.

The materials include explicit prompts and educator guidance to build student understanding by using multiple means of representation to highlight and connect key patterns, features, and relationships. For example, in lesson 13, “Representing Numbers to 100,” students use snap cubes to build towers of 10 from various given quantities. Through this activity, students develop an understanding of key relationships by identifying that the first digit in a two-digit number represents the number of tens towers, while the second digit represents the remaining ones cubes. The lesson then extends student understanding by incorporating $10 and $1 bills to model the tens and ones digits. This supports students in recognizing patterns in place value representation across concrete and symbolic models. Students continue to use both the snap cubes and dollar bills to represent educator-provided quantities, which reinforces key features of two-digit numbers through multiple representations and hands-on practice.

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

The materials in the grade 1 Math Journeys program include educator guidance for effective lesson delivery and facilitation by way of various instructional approaches. These approaches include whole-group instruction, collaborative learning opportunities, oral counting routines, movement-based activities, hands-on use of manipulatives, visual representations, independent practice, and mathematical discourse. The materials also provide step-by-step facilitation guidance, educator questioning prompts, and differentiated supports through embedded supports and application sections to encourage student engagement and mathematical understanding. For example, in the lesson “Acoustic Counting Forward and Backward (1–50),” guidance in the warm-up prompts educators to “ask students to form a circle and have them select two movements and alternate them while doing a Choral Count forward from 0 to 20.”

The materials guide educators to deliver lessons effectively with various instructional approaches. For example, lesson 4, “Cardinal Counting (up to 20),” encourages student discourse and guides educators to transition between whole-group, small-group, and independent activities. The lesson incorporates written responses and explanations to justify thinking, and promotes hands-on exploration with math manipulatives. Educators connect lessons to real-world problems and scenarios to teach mathematical concepts.

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

Intervention lessons within the materials offer small-group, collaborative, and individual opportunities, and guide educators to facilitate lessons with different types of practice. Educators typically lead the warm-up as a whole-group discussion, then combine whole-group and small-group work to provide hands-on exploration and student discourse. The wrap-up assigns individual work for consolidation, followed by a group debrief. This variety lets educators implement different tiers of support within a single lesson. For example, in one lesson, educators instruct students to use an abacus and “encourage the students standing at the board to arrange themselves from least to greatest and record the order with the corresponding sign on the board: 7 < 16 < 25 < 34 < 43 < 52 < 61 < 70.”

The materials provide placement test reports to help educators group students by proficiency level. Educators review this data to plan targeted instruction, place students on the right learning paths, and offer small-group interventions to address specific learning gaps. For example, the grade 1 placement test report organizes each journey and pinpoints students who would benefit from instruction in that journey based on their learning needs.

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

The materials in Math Journeys for grade 1 include enrichment and extension methods that support a variety of student engagement opportunities throughout the lessons. The materials provide differentiated supports through support and extension sections embedded within instructional activities. These tools allow educators to extend or scaffold learning based on individual student readiness and performance. The lessons also include explicit educator guidance for effective implementation through partner discussions, questioning prompts, manipulatives, number lines, visual models, and independent practice opportunities. For example, students use multiple strategies to calculate distances on number lines, compare solution methods, and justify their mathematical reasoning through whole-group, partner, and individual activities. These scaffolded supports and enrichment opportunities equip educators with the tools needed to differentiate instruction for grade 1 students while maintaining meaningful engagement with grade-level mathematical concepts and skills.

The materials also provide extension activities that promote student engagement, along with instructional guidance for each task. For example, in Journey A2, lesson 3, students extend their thinking by finding numbers that add up to 7, 11, and 13. They compare results with classmates to identify which case has the most solutions and examine patterns on a hundreds chart. Students also create numbers using a set number of digital segments and analyze their results to determine which segments are used most and least frequently.

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

Each lesson overview in Math Journeys grade 1 provides educators with methods to give timely feedback during lessons. A section within each overview contains specific prompts and guidance for educators to pause at key moments during the lesson to check student understanding, address misconceptions, and give immediate, meaningful feedback in real time. This support equips educators to deliver responsive instruction and keep students on track toward lesson objectives. For example, in activity 2, the educator guidance states, “How can I reduce how often students ask me questions? Minimize questions by staying in the center of the classroom during the first few minutes of the tasks. Only accept questions from groups and redirect individuals with ‘What did your group say?’”

The materials include guidance to support educators in providing timely and responsive feedback through the Journey Language Banks. These banks identify anticipated student responses or misconceptions, explain what those misconceptions may indicate about student understanding, and provide suggested educator redirections. For example, in lessons A2.7 and A2.8, the materials identify a potential misconception in which students count every bead starting from one, or begin counting from the incorrect end of the bead string. The language bank explains that this misconception may indicate that students have not yet developed a secure understanding of orientation and reference points on the bead string. To address this misunderstanding, the materials guide educators to “anchor the start point,” locate benchmark numbers such as 5, 10, or 15 first, and then support students in counting on from those benchmarks to strengthen number sense and counting accuracy.

Evaluation for 3.3a
If designed to be static, materials include educator guidance on providing and incorporating linguistic accommodations for all levels of language proficiency [as defined by the English Language Proficiency Standards (ELPS)], which are designed to engage students in using increasingly more academic language.

The specific ELPS focus, language objective, language demand, expected oral and written output, and suggested supports of each journey are outlined in a table within the Lesson-Level ELPS Companion. Each lesson provides embedded linguistic accommodations for all levels of the previous ELPS. For example, in Journey C2, station 2, the lesson includes supports for reading word problems at each proficiency level. The proficiency levels are aligned with beginner, intermediate, advanced, and advanced high, rather than pre-production, beginning, intermediate, high intermediate, and advanced.

The materials provide a digital Teacher Guide with embedded linguistic accommodations for all current levels of the ELPS. In Journey B2, “Addition: Counting on II,” activity 1, the bilingual tip includes a suggestion for each of the five proficiency levels. For example, the lesson guides the educator to prompt pre-production students with the task, “Show the hidden cubes with fingers while a partner counts-on task.” For the same task, the advanced suggestion states, “Counting on from ___ is faster than counting all: ___ + ___ = ___.”

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

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

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

Journey Language Banks in the Math Journeys grade 1 program guide educators to use the materials effectively in bilingual and ESL programs. The materials offer language routines, discourse supports, sentence stems, and writing supports to help emergent bilingual (EB) students participate in math discussions and explain their thinking. For example, the A2 Journey Language Bank guides educators to use pair conversations, quick writing activities, instructional routines, and prompts that build oral language, academic vocabulary, and language acquisition during math instruction.

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

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

The materials in the Math Journeys program include embedded guidance to help EB students use oral and written discourse as they develop academic vocabulary, increase comprehension, build background knowledge, and make cross-linguistic connections. The materials include academic vocabulary, structured partner discussions, oral language routines, and opportunities for students to use precise mathematical language to explain mathematical thinking. For example, in the lesson “Acoustic Counting Forward and Backward (1–50),” students practice vocabulary such as sequence, next, and previous while they order numbers, justify responses, and participate in counting discussions. The “Emergent Bilingual Students” section provides sentence stems, repeated oral practice, and collaborative discourse opportunities that help students strengthen comprehension and mathematical language development during instruction.

Journey A2, lesson 4, begins with a warm-up that guides educators to build on students’ background knowledge as they learn to represent teen numbers. In activity 1.2, “Number Talk 1,” educators help EB students develop academic vocabulary through oral discourse and introduce teen-number language, including ones, tens, greater than/less than, counting, and place value. Additionally, educators make cross-linguistic connections by comparing how English and Spanish teen-number names signal “one ten and some ones.” Educators highlight that in English, eleven and twelve are exceptions to the regular naming pattern. In the compare-and-connect routine, educators prompt students to explain how numbers like 13, 15, 16, and 18 build from “one ten and some ones.” Students work in pairs to build 13 and 15 with snap cubes, discuss whether they started with a tower of 10 or counted one by one, and explain their reasoning. Educators note that Spanish teen-number names, like trece and quince, signal diez more clearly than English eleven and twelve, while thirteen through nineteen follow a ten-plus pattern.

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

This guidance is not applicable because the program is not designed for dual language immersion (DLI) programs.

Evaluation for 4.1a
Practice opportunities throughout learning pathways (including instructional assessments) require students to demonstrate depth of understanding aligned to the TEKS.

The Math Journeys grade 1 materials include practice opportunities and instructional assessments throughout the learning pathway that require students to demonstrate depth of understanding aligned to the TEKS. In lesson B3, “Consolidating Addition and Subtraction I,” activity 2, the educator asks pairs of students to use snap cubes in ten frames to represent 8 + 5. Students move cubes to form a group of 10, then write the new equation 10 + 3 = 13. This process helps students understand and demonstrate the concept behind the math, not just recall facts. Students also use the example of moving eggs from one carton to another to explain how breaking apart numbers connects to the making 10 strategy. The wrap-up logsheet has students fill in ten frames and write matching equations, which allows educators to assess each student’s understanding in line with TEKS 1.3.D.

The grade 1 materials provide multiple opportunities throughout the learning pathways for students to demonstrate depth of understanding aligned to the TEKS. For example, in lesson 12, “Connecting Addition and Subtraction,” students use snap cubes and a part-part-whole frame to identify all possible decompositions of the number 13. This activity aligns with TEKS 1.3.D in that it provides opportunities for students to apply basic fact strategies to add and subtract within 20. The lesson further supports TEKS 1.3.B by providing additional practice activities in which students apply these strategies and use concrete objects and pictorial models to solve word problems. In the lesson’s “Wrap-Up” section, to extend their understanding, students solve word problems that require the use of basic fact strategies before they explain their mathematical thinking. Collectively, these activities provide opportunities for practice, application, and formative assessment while supporting students’ conceptual understanding and procedural fluency aligned to the targeted TEKS.

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

The Math Journeys grade 1 materials include questions, tasks, and extension materials that increase in rigor and complexity to help students achieve grade-level and above grade-level proficiency in the mathematics TEKS. For example, a lesson titled “Acoustic Counting Forward and Backward (1–50)” has an extension tip in which students create a sequence that is six units long and ends at a number between 30 and 50. This is an example of an accessible enrichment task at grade level. Additionally, a dedicated extension logsheet offers a written above grade-level resource for students who need further challenge. In activity 2, students are given number cards from 1–50 and arrange them from least to greatest. Students then use precise mathematical language—such as tens, ones, least, and greatest—to describe why one number is smaller or larger than another and defend the order they chose. The Teacher Guide, “Wrap-Up” section also explicitly outlines an extension opportunity that prompts educators to “ask students to create a sequence that is six units long, ending at a number between 30 and 50. The challenge is to determine the starting point.” Across the lesson, students answer questions, complete tasks, and use extension materials that increase in rigor and complexity. This supports student achievement of grade-level and above grade-level proficiency in the mathematics TEKS.

The materials include questions, tasks, and extensions that increase in rigor and complexity to support grade-level and above grade-level proficiency in the mathematics TEKS. For example, in Journey B2, lesson 7, activity 1, students complete ten frames before they advance and learn to use an addend to transform expressions like 9 + 6 into 10 + 5. This task increases rigor toward grade-level TEKS 1.3.D. For example, in activity 2, student pairs physically move snap cubes, record the transformed equation, 10 + 3 = 13, and explain their strategy to deepen conceptual demand. The session’s progression from concrete ten frame completion to written transformed equations guides students toward grade-level addition fluency. These activities also provide a solid foundation for TEKS 2.4.B, where students use various strategies to add and subtract efficiently. For example, in Journey B2, lesson 7, the wrap-up has students mark items that are being subtracted with a line, rather than erase them, to solve the difference in a subtraction sentence. As an extension, students are given the difference and determine the number of items that are being subtracted. This activity requires higher-level thinking and offers a solid foundation to prepare students for multistep word problems in TEKS 3.4.A.

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

The materials for Math Journeys grade 1 provide a horizontal layout that builds on previous scopes within the grade level. For example, the making 10 strategy connects decomposition, place-value structure, and addition within a single lesson. The strategy shows students how breaking apart an addend reveals the big idea that 10 is a landmark. The activity links ten frame models to transformed equations, like 10 + 3 = 13, to connect patterns across representations. For example, the activity 1 educator guidance states, “Decomposing 10 is essential for completing the first ten frame. Students must know how many more eggs are needed in the first ten frame to make 10. Students need to know how to decompose numbers into digits to determine how many eggs will remain in the second ten frame after moving eggs to complete the first ten frame. The goal is to introduce a new strategy and help students make sense of it.” Educators then project the addition expression 9 + 6 using the ten frame widget. Students answer, “How many eggs need to move from the second ten frame to the first one to fill it?” and “What new addition expression do we get by moving 1 egg from the second ten frame to the first one? (10 + 5).”


The materials for grade 1 demonstrate coherence across concepts horizontally within the grade level by connecting patterns, big ideas, and relationships. For example, Journey B2, lesson 12, ties the decomposition of numbers into part-part-whole relationships to both addition and subtraction equations. This connects the big idea that these operations are inverse. Activity 3 guides educators to present the word problem, “Tayler’s cousin is 9 years old, and Sofia’s cousin is 20. How much older is Sofia’s cousin than Tayler’s?” After educators present this problem, students share problem-solving strategies and determine what operation they would use to represent the situation in the problem mathematically. The materials note, “Even though students have not yet worked with this type of operation, it is important for them to develop the ability to represent a situation mathematically. In this case, the situation can be represented with either an addition operation (9 + ___ = 20) or a subtraction operation (20 - 9 = ___). This type of situation helps students see addition and subtraction as inverse operations.”

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 1 materials demonstrate coherence vertically across concepts and grade bands from grades K–6 by connecting patterns, big ideas, and relationships. In cluster A, “Counting and Numbers,” the “Learning Progression” section outlines how foundational counting and number concepts develop throughout the learning pathway and support future mathematical learning. The materials connect students’ understanding of counting, cardinality, number relationships, and place value to increasingly sophisticated concepts and strategies introduced in subsequent journeys. The overview also highlights how representations evolve across learning experiences, including with the use of bead strings, number lines, and place-value models to support the development of number sense and computation. The “Mathematical Background” section further explains how these representations are revisited and extended to deepen students’ understanding of counting patterns, number decomposition, and additive reasoning. By explicitly connecting prior knowledge, current learning, and future mathematical concepts through a documented learning progression, the materials demonstrate vertical coherence across concepts and grade bands.

Moreover, Journey B2.9, “Addition: Ten Frame and the Bead String,” establishes vertical coherence by connecting students’ previous experiences with current grade-level learning. For example, students were previously taught how to use cubes and bead strings to represent and add numbers. This lesson includes addition by bridging through 10, which connects students’ previous experiences with current grade-level learning. The lesson also supports future learning in that it prepares students to use bead strings and number lines to represent operations with larger numbers. In activity 1, students move from using two clothespins on a 20-bead string, to using three clothespins to represent the next 10 as they bridge through 10 when adding. In activity 2, students connect bead string representations to ten frames to model addition across a 10. Students also record and label the numbers represented by the clothespins on paper to link concrete and pictorial representations. Through these experiences, students build on previously learned strategies while they develop understandings that support future work with number lines, as well as more advanced addition concepts in later grade levels.

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 1 materials demonstrate coherence across lessons and activities by connecting students’ prior knowledge of concepts and procedures to current and future mathematical learning. Students build on prior conceptual knowledge of number decomposition and the understanding of 10 as a benchmark number. The lesson explicitly states that using the making 10 strategy requires students to understand both the decomposition of 10 and the decomposition of digits. For example, activity 1 revisits prior knowledge of number decomposition through ten frame dot routines before students are introduced to the making 10 addition strategy. Educators use the ten frame widget to present the addition expression 9 + 6, then ask students, “How many eggs need to move from the second ten frame to the first one to fill it? What new addition expression do we get by moving 1 egg from the second ten frame to the first one? (10 + 5).” The E1 note in activity 2 states, “Students engage in process standard 1E when they create and use representations to organize and record the Making 10 strategy. By placing snap cubes in ten frames for 8 + 5, moving 2 cubes to complete the first frame, and writing the new equation 10 + 3 = 13 on their Magic Pads, they translate a concrete action into a number sentence that communicates the mathematical idea.”

Furthermore, Journey 2, lesson 12, “Number Line: From Colors to Empty Line (1–100),” connects students’ prior experiences with new learning. Students previously learned to use bead strings to represent numbers and addition, and new learning in this lesson involves empty number lines. In activity 1.1, students use a clothespin to locate a number on a bead string and determine the result of a forward jump of five units. Students then represent the same addition on an empty number line, which connects a familiar model to a more abstract representation. In activity 1.2, students complete a similar task without the bead string and represent the forward jump directly on the empty number line. Through this progression, students move from concrete and visual models to more abstract representations of addition. These experiences build on previously learned concepts from section A2 and support future learning in sections B2–B5, where students apply number line strategies to add and subtract larger numbers and develop more advanced computational reasoning.

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

The grade 1 Math Journeys materials provide opportunities for students to develop and apply mathematical knowledge and skills through distributed practice over time. In grade 1, lesson 7, “Addition: Making 10,” materials provide spaced retrieval opportunities that let students practice skills from earlier lessons. In the warm-up, students use ten frame subitizing to recall pairs that make 10, a skill they learned in B1. In activity 1, students apply this knowledge to rewrite expressions like 9 + 6 as 10 + 5. The lesson instructions show students how to decompose numbers into digits and determine how many eggs remain in the second ten frame after moving eggs to fill the first. The lesson introduces a new strategy and helps students understand it. By repeatedly revisiting decomposition concepts throughout the B1 and B2 pathway, the materials strengthen students’ ability to break apart addends and use 10 as a benchmark.

The materials give students spaced retrieval opportunities by including review lessons that help them practice and remember key math skills. For example, in lesson 13, “Connecting Addition and Subtraction II,” students connect addition and subtraction with numbers 10–20 to similar operations with numbers 1–10. Students revisit basic single-digit facts and then apply those skills to teen-number problems. When students connect new concepts to what they already know, they deepen their understanding of numbers and learn to solve problems with bigger sums and differences more efficiently. These spaced review opportunities help students remember important math ideas and become fluent with operations. The review activities also help educators check student understanding, spot misconceptions, and adjust instruction to fit students’ needs.

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

The grade 1 Math Journeys materials provide interleaved practice opportunities for students to refresh previously learned skills and concepts across learning pathways. In lesson 13, “Connecting Addition and Subtraction II,” students practice different skills and concepts together through interleaved activities. In activity 1, students begin with “number talk” tasks that combine single-digit addition and subtraction facts from B1 with the teen-number expressions they are currently studying. This method encourages students to use both skill sets simultaneously. Educators use the number cards widget to generate two cards between one and five, then students write and solve the addition operation on the Magic Pad. When working with small numbers, students count forward from the larger number and make as many jumps of one as the smaller number shows. Educators then guide students to repeat this process with different numbers. The lesson connects expressions like 12 + 4 to the related fact 2 + 4, which helps students blend place-value concepts from A2 with additive reasoning from B2. Students also use bead strings and clothespins from earlier lessons to check their answers, which integrates previous representational skills with the new strategy.

The materials create interleaved practice opportunities by having students use related skills and concepts together in one lesson. In lesson 13, “Connecting Addition and Subtraction II,” students learn how addition and subtraction relate when sums are greater than 10, especially by looking at the ones place to find related facts. During the lesson, students solve both single-digit and teen-number problems, so they build fact fluency and practice place-value strategies at the same time. Students connect basic addition facts to multi-digit problems, which helps them see how the operations are linked. By blending these concepts, the lesson helps students use strategies flexibly and strengthens their overall mathematical reasoning.

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 grade 1 materials provide opportunities for students to interpret, analyze, and evaluate mathematical models. For example, “Addition: Making 10,” activity 1, asks students to interpret the ten frame widget showing 9 + 6 and explain how many eggs must move to fill the first frame. Students then analyze how the physical move transforms the expression into 10 + 5, connecting the model to a new equation. The guide prompts, “What pattern do you notice in how we make groups of 10?” These activities require students to interpret, analyze, and evaluate mathematical models and representations throughout the lesson.

The materials guide students to interpret, analyze, and evaluate models and representations through targeted questions and tasks. In Journey A2, lesson 15, activity 1, students use an abacus as a mathematical model. Students determine what number the abacus shows, predict the outcome when they add a bead, and analyze how placing the bead in the tens or ones column changes the value. Students discuss which column increases the number more and justify their reasoning with place-value concepts. Students learn that adding a bead to the tens column increases the number by 10, while adding one to the ones column increases it by one. The educator asks, “What happens to our number when we put a bead in the left column?” This prompts students to connect the visual model to the abstract idea of place value and support their conclusions with mathematical evidence.

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

The materials include questions and tasks that help students create concrete models and pictorial representations of mathematical situations. For example, Journey B2, lesson 7, activity 2, asks student pairs to place snap cubes in ten frames for expressions such as 8 + 5 to build a concrete model of the addition equation. Students manipulate the cubes to model the quantities, compose a 10, and observe how the numbers can be decomposed and recombined to support efficient addition. Students then draw the ten frames and record the transformed equation on their Magic Pads as a pictorial representation. As students write the corresponding transformed equation, they connect the visual representation to symbolic notation. The Teacher Guide explicitly supports this progression by stating that students “translate a concrete action into a number sentence that communicates the mathematical idea.” This helps students move from hands-on modeling to visual and symbolic representations of the same mathematical relationship.

Similarly, the materials include questions and tasks that provide opportunities for students to create concrete models and pictorial representations to represent mathematical situations. In Journey A2.14, “Representing Numbers on the Abacus I,” activity 1, “Identify Numbers on the Abacus I,” students use an abacus to practice representing two-digit numbers. As students model numbers, the educator encourages them to connect the model to the quantity represented. For example, educators “project the Abacus widget and show students how to represent the number 23: place 2 beads in the tens column and 3 beads in the ones column.” In activity 2, “Represent the Number on the Abacus,” students use applet A18, pack 1, to view a symbolic representation of an abacus and work with a partner to identify and record the number shown. In activity 2.2 the educator calls out numbers between 20 and 99 and students work in pairs to represent the numbers using different forms. One student records the numeral while the other creates a pictorial representation by drawing the abacus. Through this sequence of activities, students use the abacus to create and connect concrete models. Additionally, students use drawings to create pictorial representations to represent two-digit numbers and demonstrate their understanding of place value.

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

In Journey B, “Additive Thinking,” students use counting strategies to identify quantities in sets of objects. In activity 1 students transfer conceptual understanding of addition and subtraction to unfamiliar story situations. For example, students apply the bead-string jumping strategy they previously learned to real-world bus and marker contexts. Students write a math sentence and solve it on the bead string so the story context stays visible. The Teacher Guide prompts students to connect their answers to the context in the real-world problem.

Furthermore, the materials provide opportunities for questions and tasks in which students create concrete models and pictorial representations of mathematical situations. For example, in Journey B2, lesson 7, “Number Talk 2,” student pairs apply the making 10 strategy that they first developed with snap cubes on ten frames to new expressions, such as 5 + 9 and 9 + 8. Rather than work with the original examples used during instruction, students make addition more efficient by transferring their understanding that a quantity can be decomposed and recomposed to create a 10. Students write the transformed equation on their Magic Pads to connect the concrete action to a new symbolic context. Educators ask, “How does moving the cubes change the numbers in their equation?” and encourage students to explain the mathematical relationship underlying their strategy. Students learn that while the addends are decomposed and recombined, the total remains unchanged. This requires students to apply their understanding of number composition, decomposition, and equivalence in unfamiliar situations, as opposed to relying on rote memorization.

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

The materials include tasks designed to develop the automaticity and fluency that students need for grade 1 addition tasks. For example, the grade 1 lesson, “Productive Practice: Addition within 20,” has an explicitly stated goal for students to develop addition fluency through productive practice. In activity 2 small groups of students turn over two random number cards numbered one through nine, and independently compute the sum before they compare answers with the group. This is a high-volume, fast-paced activity that generates repeated retrieval of addition facts within 20. Activity 2.2 sustains productive practice across varied expressions by requiring student pairs to find multiple card combinations that produce equal sums. Learning objective A confirms the designed intent to reinforce practice with sums of numbers between one and 20.

Furthermore, the materials include questions and tasks that provide opportunities for students to apply conceptual understanding to new problem situations and contexts. In Journey B2.16, “Productive Practice: Addition within 20,” activity 2, “Sum of Digits,” students solve sums within 20 by applying addition strategies and number relationships they previously developed in lessons B2.7–B2.15. As the activity progresses, students encounter new situations that extend their understanding of equality. For example, students use number cards and operation symbols to identify two different addition expressions that result in the same sum, such as 4 + 7 and 5 + 6, and then represent the relationship as 4 + 7 = 5 + 6. Rather than use the equal sign to show the answer to a calculation, students apply their conceptual understanding in a new context by interpreting the equal sign as the representation of a balance or equivalence between two expressions. The Teacher Guide prompts students to discuss and justify why both sides of the equation are equal and how they know the expressions represent the same quantity. These opportunities require students to transfer previously learned addition concepts to a new mathematical situation, which deepens their understanding of equality and the meaning of mathematical symbols.

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

The grade 1 Math Journeys materials provide opportunities for students to practice the application of efficient, flexible, and accurate mathematical procedures throughout learning pathways. For example, the lesson “Addition: Counting On I,” provides efficient, flexible, and accurate mathematical procedures by guiding students from conceptual understanding to application. The lesson’s learning objectives are explicitly framed around students learning to use efficient procedures, such as recognizing that addition is more efficient when starting with the larger addend, and understanding that changing the order of addends can be an efficient strategy. Activity 1.2 directly contrasts two approaches, counting on from three to reach nine versus counting on from six. Educators ask students, “Which handkerchief would you lift first and why?” and guides students to identify the more efficient method. Additionally, activity 2 provides repeated practice opportunities for students to apply this flexible, efficient procedure across multiple number pairs.

The materials provide opportunities for students to practice the application of efficient, flexible, and accurate mathematical procedures throughout learning pathways. In the lesson “Addition: Making 10,” activity 1, the materials introduce the making 10 strategy as an efficient procedure for solving addition problems. Students are encouraged to decompose an addend and use a transformed equation such as 10 + 3 = 13 rather than counting all. In activity 2 students use snap cubes and ten frame models to flexibly apply this strategy to new expressions, such as 8 + 5 and 5 + 9. This activity reinforces students’ ability to adapt an efficient method across different problems. Students then record the resulting equations on their Magic Pads to ensure accurate representation of both the decomposition process and the final sum.

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 materials in grade 1 Math Journeys provide opportunities for students to evaluate mathematical representations, models, strategies, and solutions for efficiency, flexibility, and accuracy throughout learning pathways. For example, Journey B2.3, “Addition: Counting On I,” asks students which handkerchief to lift first and why, which requires them to evaluate counting-on strategies for efficiency. Students compare starting from the larger versus smaller addend and judge which approach reaches the total faster. In activity 2 students use cubes to continue solving addition before they discuss how starting with the larger addend can make finding the sum more efficient. Students then reflect on their solutions and identify which addition problem seemed easiest as they discuss the efficiency of different strategies. Through these activities, students evaluate mathematical procedures and solution strategies for efficiency, flexibility, and accuracy.

The materials guide students to actively evaluate mathematical representations, models, strategies, and solutions for efficiency, flexibility, and accuracy. In Journey B2.15, “Adding Three Numbers,” activity 1, students use snap cubes, number cards, and operation symbols to represent and solve addition expressions with three addends, such as 3 + 4 + 5 = 12. Students try different ways to find the sum and compare strategies, such as decomposing numbers to make a 10. For example, students might break seven into 4 + 3 to turn 6 + 7 into 6 + 4 + 3, then use the making 10 strategy to solve more efficiently and accurately. In activity 2 students analyze an image that represents 3 + 4 + 6 and explain which numbers they added first and why. The Teacher Guide prompts students to compare solution methods, identify pairs of numbers that make 10, and discuss how rearranging addends can simplify the calculation. Through these discussions, students evaluate which strategies are most efficient and recognize that combining 6 + 4 first to make 10, then adding 3, leads to a faster and more accurate solution. These activities help students develop efficient, flexible, and accurate approaches to computation by evaluating and choosing among various models, representations, and strategies.

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

The grade 1 materials contain guidance to support students in selecting increasingly efficient approaches to solve mathematics problems. For example, learning objectives in Journey B2, “Introducing Addition and Subtraction (1–20),” are explicitly framed around efficiency, such as recognizing that addition is more efficient when starting with the larger addend. Educators first ask students to observe both approaches, including lifting the handkerchief that hides three and the one that hides six. Educators ask, “Which handkerchief would you lift first and why?” before they guide students to identify the most efficient strategy and encourage them to use it in their work. This provides structured guidance that moves students from free exploration toward deliberate selection of the more efficient procedure.

Furthermore, in Journey B2.10, “Subtraction: Ten Frame and the Bead String,” activity 1, students use clothespins on a 20-bead string to solve subtraction problems such as 12 − 5. Rather than count back one bead at a time, students use a more efficient strategy by decomposing five into two and three. This allows students to make a jump of two to reach 10, and then a jump of three to reach seven. Educators ask students, “If we make a jump backward from 5, how do we decompose 5 to go through 10?” and “Can you find another way to break apart the number 5 to make the subtraction operation easier?” This encourages students to analyze and compare solution strategies. In activity 2 students use ten frames to represent the same subtraction problem and connect the strategy of bridging through 10 across different models. Educators further support students’ understanding with questions such as, “Could you explain how bridging through 10 works the same way on the ten frame and the bead string?” and “How do the color changes help you find 10 in both tools?” Through these opportunities, students compare representations, justify their reasoning, and recognize that decomposing numbers to bridge through 10 is a more efficient approach than counting back one at a time. These supports help students select increasingly efficient strategies to solve subtraction problems as they develop conceptual understanding across multiple mathematical models.

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

The grade 1 Math Journeys materials explicitly state how the conceptual and procedural emphasis of the TEKS are addressed in cluster overview B, “Additive Thinking.” The overview identifies the conceptual emphasis by describing that students will learn to understand addition and subtraction relationships, compose and decompose numbers, and make connections between different representations and strategies used to solve additive situations. For example, students use concrete, pictorial, and symbolic models to build understanding of part–whole relationships and represent addition and subtraction equations. The overview also identifies the procedural emphasis by outlining the skills students will develop throughout the learning pathway, including how to solve addition and subtraction problems, use counting strategies, represent operations with models and equations, and apply strategies to determine unknown quantities. The “Learning Progression” section in the cluster overview states, “Students stop counting by ones and start thinking in groups. Through the additive box, they master the decomposition of all the numbers up to 10 . . . while they practice addition and subtraction.”

The materials explicitly state how the conceptual and procedural emphasis of the TEKS are addressed within the lessons. In lesson 7, “Addition: Making 10,” students focus on the concept of making 10 to develop addition strategies. Students use snap cubes and ten frames to model the addition problem 8 + 5, which shows them how to visually and physically represent the quantities. Students then move two cubes from one group to complete a full set of 10, which builds their conceptual understanding of composing numbers and recognizing equivalent quantities. After students model the action, they apply the procedural strategy by learning to rewrite the problem as an equivalent expression with the making 10 strategy, then learn to record it as a number sentence. This progression from hands-on modeling to symbolic representation supports students in balancing conceptual understanding with procedural fluency while they develop an understanding of addition as the action of joining quantities.

Evaluation for 5.3b
Questions and tasks provide opportunities for students to use concrete models, pictorial representations, and abstract models as required by the TEKS.

The grade 1 lesson, “Representing Numbers with Base 10 Blocks I,” includes opportunities for students to use concrete objects, pictorial models, and abstract strategies throughout the scope. For example, in activity 1 students use physical flats, rods, and units as concrete models to build numbers while they use base ten blocks to represent quantities like 36. In activity 2 students draw squares, bars, and crosses on the Magic Pad as pictorial representations of the same numbers. Students then write expanded form notation, such as 80 + 7, on their pads to connect the concrete and pictorial work to abstract symbolic representation.

In lesson 3 students develop an understanding of the making 10 strategy for adding single-digit numbers through a progression of connected representations. Students first use snap cubes and ten frames as concrete models to represent an addition expression and to demonstrate how numbers can be decomposed and recomposed to create a group of 10. Students then transition to pictorial representations by using the Magic Pad to draw the snap cubes and ten frame model, which visually represents the strategy students use to solve the problem. Finally, students move to abstract representation by learning to record the addition equation as a number sentence. This progression from concrete manipulation to pictorial modeling and abstract notation provides students with meaningful opportunities to build conceptual understanding of addition while developing procedural fluency through multiple engaging representations.

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

In cluster overview A, “Counting and Numbers,” students connect concrete and pictorial models to algorithms. For example, in activity 2 students sequence through all three representational levels, with explicit educator prompts to mark each transition. For example, at the concrete level, educators ask students, “How many snap cubes from the second ten frame must go into the first ten frame to complete it?” Student pairs place snap cubes directly into printed ten frames for 8 + 5, then physically move two cubes from the second frame to the first. At the representational level, the ten frame printable serves as a visual bridge for students to see the two frame structure shift from 8 + 5 to 10 + 3. This makes the composition visible as a spatial rearrangement before students commit anything to writing. At the abstract level, each student pair records 10 + 3 = 13 on their Magic Pads after the educator asks, “How does writing 10 + 3 = 13 help you show what you did with the snap cubes?” This anchors the symbolic sentence back to the physical movement. Students translate a concrete action into a number sentence to communicate the mathematical idea, which explicitly addresses process standard 1E. Additionally, educators hand out manipulatives and the printable model representation for students to connect abstract to concrete models, as is outlined in the “Wrap-Up” section.

Additionally, the materials include supports for students to connect, create, define, and explain concrete and representational models to abstract concepts, as required by the TEKS. In Journey B2.10, “Subtraction: Ten Frame and the Bead String,” the Teacher Guide provides questions, discussions, and instructional supports that guide students from concrete models to pictorial representations and abstract mathematical concepts. For example, in activity 2 students watch a video that builds a connection between using a ten frame and a string of beads for mathematical problem solving to calculate 12-5. For additional support, educators “provide the 20-bead string and clothespins so students can solve the problems using manipulatives.”

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

Math Journeys gives students many opportunities to use manipulatives and visual supports within the learning pathway. For example, in Journey D1.6, “Representing Fractions: Length Model I,” students use flats, rods, and units to connect the terms tens, ones, and expanded form. Students create base ten block arrangements before they write numerals. In activity 1 students fold and measure paper strips to learn the terms unit fraction, numerator, and denominator, which connects fraction vocabulary to a concrete length model. As students estimate, identify, and explain which strips represent halves or fourths, they repeatedly use academic language to describe equal-length parts and fraction relationships. Educators offer further supports for EB students’ language development by providing the sentence frame, “The strip is divided into ___ equal parts, so ___ is the denominator.” This helps students accurately use mathematical terminology in context. In activity 2 students order unit fractions on a visual fraction strip and justify their reasoning using statements such as, “The larger the denominator, the smaller the piece.” These activities promote mathematical discourse while linking academic vocabulary to visual and hands-on representations of fractions.

In grade 1, lesson F1, “Algebraic Language 2 Visual Patterns,” students use mathematical language as they generalize patterns. This is a key process in algebraic reasoning within a geometric context. During the warm-up activity the educator quickly displays different fences and prompts students to record the segments that make up each one. The educator then asks how many segments will make up the next fence, and students write down the operations they use to find the total number of segments in the second fence. After viewing all the images, the educator arranges the information in a table to help students notice patterns.

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.

In Journey B1, sessions using the Journey Language Bank teach EB students to compare and connect representations. These sessions sequence language demands across four clear proficiency levels as students explain how the bead string and number line show the same position. First, the educator asks, “Could you explain how the beads on the string help you find the number on the line?” Beginning students point to matching sections on each model and name the number. Intermediate students use spatial prepositions, such as between, before, and after, to describe number placement on both models. Advanced students explain how the color change at each 10 appears on both the bead string and the number line. Advanced high students justify approximate placement by describing how a number’s position relates to the nearest 10 and the spacing within a section. The scaffold progresses from gesture-and-label to increasingly precise mathematical explanation to provide students at every proficiency level with a differentiated linguistic entry point into the same reasoning. The session explicitly tags process standard 1D, in which students “communicate mathematical ideas using multiple representations.”

The grade 1 materials embed clear guidance for educators to actively scaffold and extend students’ academic mathematical vocabulary throughout lesson activities. For example, in the lesson “Counting and Numbers” students participate in structured mathematical conversations where they explain how bead strings and number lines represent the same number. The materials offer explicit educator support with purposeful questioning strategies, such as, “Could you explain how the beads on the string help you find the number on the line?” and “What do the spaces between marks on the number line represent?” Students use precise mathematical vocabulary to explain relationships between concrete and visual representations. By prompting students to articulate their thinking and compare different representations of numbers, the materials create meaningful opportunities for students to communicate mathematical ideas and strengthen both their conceptual understanding and academic language.

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

The materials include embedded guidance to support students’ application of appropriate mathematical language and academic vocabulary in discourse. For example, in Journey B1, lesson 15, activity 1, students identify and order number pairs while using terms such as addend and decomposition to describe relationships among numbers. The Journey Language Bank provides the sentence frame “___ and ___ make 10” to support students in the task. Activity 2 extends students’ use of academic vocabulary within the context of the lucky escape game, in which students use terms such as addend and total to restate card combinations. This activity reinforces mathematical language as students discuss their strategies and solutions. Through structured partner conversations, sentence frames, and repeated opportunities to explain their thinking, the materials support students in applying appropriate mathematical vocabulary during mathematical discourse.

In Journey B2.11, “Introducing the Additive Part-Part-Whole Frame,” students use mathematical language and academic vocabulary during discussions. For example, in activity 2 students separate snap cubes into all possible pairs and record each arrangement on their Magic Pad, both inside the frame and as an addition equation, such as 5 + 1 = 6 and 1 + 5 = 6. The educator supports mathematical communication by asking questions like, “How do you know you’ve found all the possible pairs?” and “Which strategy could you use to make sure you don’t miss any combinations?” These prompts encourage students to use precise mathematical vocabulary to explain their strategies. For EB students, educators write Spanish cognates—such as decomposition/descomposición, total/total, and equation/ecuación—next to key terms and keep the chart visible while groups compare their lists. Educators prompt students to point to the frame and answer, “The whole is ___, the parts are ___ and ___,” as they confirm each pair.

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

Throughout the pathway, educators lead conversations about math topics and embed guidance that helps students hear, refine, and use mathematical language with peers. In Journey B1, lesson 15, activity 1, students work in small groups with number cards to find and order number pairs that make 10. Students explain combinations such as “eight and two make ten,” and use mathematical vocabulary to compare strategies. In the lesson “Addition: Making 10,” activity 2, student pairs place snap cubes in ten frames and explain how many cubes from the second frame must go into the first to complete it. The educator encourages structured peer talk around decomposition. Additionally, sentence frames prompt EB students to restate a partner’s reasoning, such as, “I know eight and two make ten because eight pins were knocked down and two stayed up.” Students clarify their explanations and deepen conceptual understanding as they link mathematical language to the ten frame model. The educator asks questions like “Who can repeat?” to encourage careful listening, restating of ideas, and use of precise mathematical vocabulary throughout the discussion.

The materials include embedded guidance for educators to facilitate classroom conversations in which students actively use, hear, and refine mathematical language through collaborative interactions with peers. In grade 1 students use number cards to create pairs of numbers that combine to make 10 and then share their combinations with their group, which provides an opportunity for students to hear and discuss multiple ways to compose 10. Educators ask students purposeful questions to help them refine their mathematical language and explain their reasoning. Example educator questions include, “How do these two addends make ten?” and “Can you picture where you saw this before?” Students explain to their peers how they know that their chosen numbers make 10, which reinforces the use of precise mathematical vocabulary. This activity creates a collaborative learning environment where students engage in meaningful discussion, strengthen their mathematical communication skills, and refine their understanding through rich mathematical discourse with others.

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 1 materials include embedded guidance to 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 B2.7, “Addition: Making 10,” students use ten frame representations and manipulatives to apply the making 10 strategy to solve addition problems. The materials provide anticipated responses and exemplar solutions, including identifying that one counter must be moved to transform 9 + 6 into 10 + 5, and that two counters must be moved to transform 8 + 5 into 10 + 3. Educators guide students to explain how the quantities change when counters are moved and how the new equation represents the action shown in the model. The lesson also includes support guidance that encourages the use of ten frames and connecting cubes when students need additional assistance, which helps educators address misconceptions and redirect students toward accurate mathematical reasoning.

The materials guide educators to anticipate a variety of student responses by providing exemplar answers and strategies to redirect inaccurate thinking. In the Journey B4, lesson 11, warm-up, educators review sample reasoning for ordering expressions without calculating in order to prepare for multiple valid approaches. For instance, the guide explains that 42 + 47 will have the greatest sum because it is the only expression with a four in both ten places, which helps educators recognize and validate conceptual reasoning rather than focusing solely on computation. In activity 1 the lesson presents a pre-worked example with a common error, such as a student who interprets eight as the final answer instead of the remaining jump on the number line. Students analyze the mistake, use the number line to find the correct solution, and explain how they corrected the error. Educators ask students, “Could you explain your process for finding and fixing the error?” This prompt encourages students to identify misconceptions, justify their reasoning, and deepen their mathematical understanding.

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

The grade 1 Math Journeys materials clearly integrate the TEKS process standards into grade-level lessons. In the lesson “Addition: Making 10,” students use the making 10 strategy to solve addition problems with ten frames, connecting cubes, drawings, and equations. Students determine how many counters to move to complete a 10 and represent the sums with models and equations. Throughout the lesson, students explain how moving counters changes numbers, share solutions with peers, and record their reasoning on whiteboards. The lesson connects mathematical representations, problem solving, communication, and reasoning while students use various tools and strategies to solve addition problems. This demonstrates strong integration of the TEKS process standards with content learning. Additionally, the materials embed mathematical process standards from the TEKS in each scope. For example, in lesson 7, activity 1, aligned with standard 1F, students analyze the relationship between decomposing a number and the making 10 strategy. When adding 9 + 6, students see that moving one egg from the second carton to the first creates 10 + 5, which shows how decomposition leads to a more efficient solution. To support this, educators ask, “Could you explain what happens when we move eggs from one carton to another?” and “What pattern do you notice in how we make groups of 10?”

Additionally, the materials appropriately integrate the TEKS process standards throughout the lesson, and the Teacher Guide explicitly identifies process standards 1B and 1G within instruction. For example, in Journey B1, lesson 14, activity 1, process standard 1B is embedded in the pin arrangement task as students analyze the arrangement of 10 bowling pins, develop a strategy for maximizing the number of pins knocked down, test their plan by bowling, and evaluate the results. Students revise their approach when an initial attempt is unsuccessful and engage in an authentic problem-solving cycle of planning, testing, and refining. In the wrap-up process, standard 1G is integrated as students present their representation page to the class. Students use precise mathematical language to explain and justify their drawings, including describing the quantity represented and how it is shown in the illustration. Educators reinforce this expectation by asking, “What exactly did you represent in your drawing, and how can you explain it using precise mathematical language?” and “What part of your representation justifies your answer about the bowling pins that are still standing or have fallen?” These opportunities require students to communicate and justify their mathematical thinking to demonstrate meaningful integration of the TEKS process standards.

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

The materials include a clear description of how process standards are incorporated and connected throughout the learning pathways. For example, the A2 Journey Instructional Guide describes how process standards 1F and 1G are incorporated across A2 sessions. Throughout the journey, students analyze place-value relationships and justify number order. This session is explicitly tagged with 1F and 1G because it connects this session’s skip-counting work to the representation and comparison tasks in A2.13–A2.16. The guide further explains how these process standards build continuously from counting into place-value reasoning.

In Journey B1, lesson 18, the Teacher Guide clearly labels process standards 1F and 1D in both the introduction and the lesson. Standard 1F guides students to analyze the relationship between equal addends and the increasing totals in the doubles song. As they sing, students recognize that doubling equal numbers produces even totals, which helps them identify mathematical patterns across repeated examples and deepen their conceptual understanding. The materials show how standard 1D comes into play when students use multiple representations to communicate the same mathematical idea. Students build two equal snap cube towers, use a tower measurer to find the combined total, and write a matching equation, such as 2 + 2 = 4. Throughout the lesson, the materials link concrete models, visual representations, and symbolic notation to intentionally weave the process standards into instruction and support conceptual understanding and mathematical communication.

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

The Math Journeys grade 1 materials include an overview of the TEKS process standards that are incorporated into the lesson. For example, in lesson B2.12, “Connecting Addition and Subtraction I,” the materials explicitly identify process standard 1B, “Use a problem solving model,” and describe how students apply the standard throughout the lesson. Students use additive boxes, manipulatives, equations, and contextualized situations to represent mathematical relationships, determine missing values, and connect addition and subtraction as inverse operations. Lesson guidance explains that students apply a problem-solving process as they model situations, select representations, communicate mathematical ideas, and justify their solutions to solve increasingly complex tasks. By identifying the process standard and explaining how students engage with it during instruction, the materials provide an overview of the TEKS process standards incorporated into the lesson.

The materials include a clear overview of how the TEKS process standards are intentionally embedded within each lesson by explicitly identifying the applicable standards and providing educators with guidance on how to incorporate those standards during instruction. In lesson 9 the TEKS process standards 1C and 1E are clearly identified within the lesson structure to support purposeful mathematical learning experiences. The TEKS process standard 1C, which focuses on selecting appropriate tools and techniques to solve problems, is addressed as students determine how to use an eight-cube measuring tool to solve measurement tasks and make decisions about the most effective way to complete the activity. The lesson also integrates the TEKS process standard 1E, which emphasizes creating and using mathematical representations, by requiring students to organize, record, and communicate measured lengths using representations that demonstrate their understanding of measurement concepts. Through these embedded instructional opportunities, students actively select mathematical tools, apply strategies, and represent their thinking in meaningful ways. The explicit identification of the process standards and accompanying educator guidance supports consistency in instruction and ensures that educators are able to intentionally incorporate mathematical reasoning, problem solving, and communication skills into daily learning experiences.

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

In the grade 1 learning pathway, Journey B2, lesson 15, students think mathematically and persevere through solving problems as they explore strategies for adding three addends. Students use manipulatives, drawings, and equations to represent sums, investigate how decomposing and reordering numbers can simplify calculations, and explain the reasoning behind their strategies. Educators ask students, “Could you explain how your equation shows what you did with the snap cubes?” and “How do the snap cube colors match the numbers in your equation?” Students participate in whole-group discussions to share and defend their strategies, explain how they represented their solutions, and evaluate different approaches for finding sums. The wrap-up in the Teacher Guide identifies eight valid, distinct solutions, including 1 + 1 + 8, 1 + 2 + 7, and 1 + 3 + 6. Educators are prompted to “ask students to create three distinct options that are not just permutations of the addends’ order,” which requires students to think carefully and persist through multiple attempts. Students who find an obvious combination must keep reasoning to identify non-trivial alternatives, which directly enacts perseverance in problem solving.


In lesson 15 students identify all possible pairs of numbers that add up to 10. As they generate and organize these pairs, students analyze the relationships between the addends. Students recognize patterns, such as when one addend increases by one, the other decreases by one, which keeps the total at 10. This process deepens students’ understanding of number relationships and the concepts of composing and decomposing numbers. In the next activity, students solve problems while playing a game similar to Go Fish, where they strategically create pairs that total 10. The game structure prompts them to apply mathematical reasoning, test their understanding of number combinations, and persist until they find solutions. These problem solving opportunities strengthen students’ conceptual understanding, promote flexible thinking with numbers, and support long-term retention of foundational math concepts.

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

In grade 1 students learn to solve problems in different ways. Students use cubes, number cards, drawings, and equations to model and solve addition problems. During the lesson, students try strategies, like counting all objects and counting on from a known number, and compare these strategies to see which works best. Educators ask questions such as, “Which handkerchief would you lift first and why?” “Why does knowing the first number help you count on?” and “Is it easier to start with 14 and count on three, or start with three and count on 14?” These prompts help students compare counting on from different starting points. After students share their strategies, educators ask which approach was more efficient. Students connect efficiency to the size of the starting number to explain their reasoning.

The grade 1 materials help students understand and justify their math thinking by giving them chances to solve problems in different ways. In lesson A2.15, “Representing Numbers on the Abacus II,” students build numbers on an abacus and see how the value changes when they add one bead. Educators ask, “What number would you get if we add one bead?” to get students thinking about place value and whether the change affects the ones or tens place. Students try out different placements, see how each one changes the number, and explain their reasoning. In class discussions, students compare both possible answers and justify why each is correct based on place value. These activities help students think flexibly, deepen their understanding of the base ten system, and explain their math reasoning using different strategies.

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 Math Journeys, lesson B2.7, “Addition: Making 10,” students work in pairs to talk and write about math. Pairs use shared manipulatives to move snap cubes across ten frames to build 8 + 5. Each pair writes the new equation, 10 + 3 = 13, on their Magic Pad to show their reasoning. The educator asks partners to explain how many cubes they moved and why, which prompts them to justify the making 10 strategy out loud. Educators spark peer discussion with questions like, “What happens when we move eggs from one carton to another?” and “What pattern do you notice when we make groups of ten?” In whole-group conversations, students explain how they moved counters, compare strategies, and share their thinking with the class.

Grade 1 students build math understanding by doing hands-on activities, writing, and discussing ideas with peers and educators. In lesson 14, “The Number 10 (Part 1),” students roll a ball to knock down 10 pins, count how many fall and how many stay standing, and model the results on ten frames. Students record both the fallen and standing pins to connect the activity to number relationships. This process helps students learn to compose and decompose numbers within 10. In the wrap-up students talk about their ten frame models and answer questions like, “How many pins did you knock down?” and “How many stayed upright?” Students compare strategies, explain their reasoning, and consider different outcomes. By doing, discussing, and writing about math, students deepen their understanding of number relationships, strengthen number sense, and build reasoning skills to communicate and justify their thinking.

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

In Math Journeys grade 1, lesson 7, “Addition: Making 10,” educators help students explain their thinking and justify their math strategies. In activity 1 educators ask students to describe what happens when they move eggs from one carton to another, which prompts them to share how the making 10 strategy works. Student pairs write the new equation, 10 + 3 = 13, and explain how moving two cubes changes the original expression, requiring students to make a mathematical argument. Educators also ask, “What pattern do you notice in how we make groups of 10?” When students work with the addition expression 9 + 6 using the ten frame widget, educators ask, “How many eggs do you need to move from the second ten frame to the first to fill it?” and “What new addition expression do you get by moving one egg from the second ten frame to the first?”

The materials help educators guide students to share and reflect on their problem-solving strategies. In lesson 15 students choose a number between 20 and 80, and the educator shows that number on an abacus. The educator asks students what new value they get if they add one more bead. Students explain, justify, and defend their reasoning based on whether they add the bead to the tens or ones column. Students analyze how the bead’s placement changes the number and use place value to support their answers. Students compare both outcomes to decide which number is greater. These activities give students chances to discuss how place value affects quantity and to communicate their reasoning out loud and in group discussions. By asking students to explain, justify, compare, and reflect, the materials build mathematical reasoning, critical thinking, and a deeper understanding of place value.

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

In Math Journeys grade 1, lesson 7, “Addition: Making 10,” educators use specific prompts to help students explain their thinking and recognize patterns in the making 10 strategy. Educators ask, “What happens when we move eggs from one carton to another?” and “What pattern do you notice when we make groups of 10?” When students use a procedure without naming the structure, educators restate their thinking using clear decomposition language. If students struggle to connect moving snap cubes to the equation, educators bring them back to the ten frame model to clarify the concept.

The materials give educators prompts and guidance to help students understand place value and address common misconceptions. In lesson 15, “Representing Numbers on the Abacus II,” educators ask questions like, “What happens to our number when we put a bead in the column on the right?” and “What happens when we put a bead in the column on the left?” These questions prompt students to explain how place value changes a number and connect hands-on work with number concepts. Educators remind students that a column cannot have more than nine beads because they must regroup 10 beads into the next column on the left. Throughout the lesson, educators use purposeful questions to clear up misunderstandings, strengthen students’ grasp of place value, reinforce reasoning, and use errors as chances for deeper learning and discussion.