K-2nd Grade - Gateway 3

The materials reviewed for ClearMath Elementary Kindergarten through Grade 2 meet expectations for providing teacher guidance with useful annotations and suggestions for how to enact the student materials and ancillary materials, with specific attention to engaging students in order to guide their mathematical development.

The materials provide comprehensive teacher guidance for presenting both student and ancillary materials. For example:

• Each grade’s Teacher's Implementation Guide Overview introduces the instructional model and key components, equipping teachers with the context needed to use resources purposefully.

• The Module Overview outlines the mathematical focus and coherence across topics, previews learning goals, and highlights key concepts to support long-term planning.

• The Topic Overview provides more detailed guidance, including connections to prior and future learning, content expectations, pacing suggestions, supports for diverse learners, and a list of materials needed for instruction (e.g., manipulatives, games).

• The Lesson Overview identifies math, learning, and language goals and includes a pacing guide with a materials list.

• Within each activity, teachers receive guidance for setting the stage, facilitating the task, and leading closure, all linked to the student resource book.

• Ancillary supports such as Daily Math Routines, Cross-Curricular Activities, and Math in Action Centers are included. While the materials describe when these routines can occur throughout the day or during other subject areas, they do not specify how these supports should be incorporated into the designated 60-minute math block.

The materials provide sufficient annotations and suggestions connected to the specific learning objectives. For example:

• Purposeful questioning strategies are embedded throughout to promote mathematical discourse, elicit student thinking, and deepen understanding. Sample questions, prompts, and facilitation notes are highlighted with a speech bubble in the teacher’s guide.

• Each lesson includes guidance for supporting MLL learners in a blue-highlighted box. Differentiation strategies for students needing challenge, reinforcement, or whole-class supports are also highlighted in the topic overviews.

• An Instructional Strategies Handbook provides additional pedagogical moves for diverse learners. While the materials describe places where these strategies and routines may occur throughout the day or during other subject areas, they do not specify how these moves should be used within the designated 60-minute math block or how they connect to specific learning objectives to support student mastery of content.

The materials reviewed for ClearMath Elementary Kindergarten through Grade 2 meet expectations for containing explanations and examples of grade-level/course-level concepts and/or standards and how the concepts and/or standards align to other grade/course levels so that teachers can improve their own knowledge of the subject.

The materials provide adult-level explanations and examples of grade-level concepts so that teachers can improve their own knowledge of the subject. For example:

• The About the Math sections in Module, Topic, and Lesson Overviews provide explanations of mathematical concepts, the purpose behind them, and their connections across lessons.

• Grade 2, Module 4, Topic 9, Topic Overview, About the Math states: "Adding two 2-digit numbers helps students develop different strategies for solving problems. This moves students toward addition fluency, which includes number sense, accuracy, and efficiency. In this topic, students learn two key strategies: decomposition and compensation. Decomposition means breaking numbers into smaller parts to make adding more efficient. For example, students can split numbers based on place value and adjust them to create benchmark numbers. Compensation involves adjusting numbers to the nearest 10. After adding the adjusted addend, they compensate by subtracting the extra amount. This is especially helpful when one number ends in 8 or 9.” This is accompanied by examples of decomposition and compensation with 24 + 49 = ?. 

The materials provide adult-level explanations and examples of concepts beyond the current grade level so that teachers can expand their knowledge of the subject. For example:

• The Assessment Guide (Coach’s Playbook) identifies connections between prior and future work by listing instructional foci and progressions.

• Teacher Planning and Support Tools include slide decks covering major concepts across grades.

• In the Teacher Planning and Support Tools, Whole Number Addition and Subtraction, About the Math, the materials state: “Students work with adding and subtracting whole numbers throughout the elementary grades, starting with basic counting strategies and small sums and differences and progressing through more complex problems involving larger numbers and multiple steps.” This adult-level explanation highlights the progression of whole number operations across Kindergarten through Grade 5 and supports teachers in understanding how early counting strategies build toward fluency with multi-step problems involving larger numbers.

The materials reviewed for ClearMath Elementary Grade through Grade 2 meet expectations for including a year-long scope and sequence with standards correlation information.

The Teacher’s Implementation Guide Overview organizes grade-level content expectations by domain and module. These expectations are not labeled with CCSS codes but instead use publisher-created descriptions.

The Topic Planner shows the progression of lessons, including standards and learning goals for the topic. It also highlights the mathematical content of the lessons and prerequisite skills from earlier topics or grades. The Topic Planner also identifies when content expectations are addressed together in a single lesson or activity, noting opportunities for integrated learning across standards.

The Standards Overview documents found in the Mathematical Progressions and Connections book define the specific standards aligned at the lesson level across the whole course. The Standards Overview provides alignment to the standards by listing the lesson numbers where each standard is addressed. Page numbers are not included in this overview.

Each grade includes a Scope and Sequence document, which denotes an overview of the standards (learning goals) in the course with recommended pacing. In addition, the sequencing of modules, topics, and lessons is provided by grade level. The Scope and Sequence includes content standards but does not identify the Mathematical Practice Standards. The Habits of Mind, which reflect the MPs, are noted within lessons in the Teacher’s Implementation Guide, and a list of the MPs is provided in each Topic Overview.

Standards correlation information is consistent across the Scope and Sequence, Topic Planner, and Standards Overview documents, and no inaccuracies were noted.

The materials reviewed for ClearMath Elementary Kindergarten through Grade 2 meet expectations for explaining the program’s instructional approaches, including reference to research-based strategies, and explaining the role of the standards.

Materials explain the instructional approaches of the program. For example, the Instructional Strategies Handbook includes various instructional strategies and subcategories of strategies such as Application, Collaborative Problem Solving, Student-Generated Problems, Cumulative Review, Student Think Alouds, Think-Pair-Share, Notice and Wonder, Writing to Learn Math, Peer Analysis, Who’s Correct?, Worked Example, Guided Inquiry, Guided Play: Game, Guided Play: Puzzle, Guided Practice, Data Talk, Number Talk, Odd One Out, Would You Rather?, Multimodal Instruction, Visual Representations, Manipulatives, Number Line, Graphic Organizer, Mindset Reflection, Paired Practice, Gallery Walk, Peer Teaching, and Silent Teaching. The instructional approaches of the program are embedded within the lesson structure and pacing guide when they apply to an activity. Each strategy details the implementation phase and provides a Mathematical Language Routine (e.g., MLR 1: Stronger and Clearer Each Time, MLR 2: Collect and Display, MLR 3: Critique, Correct, and Clarify, MLR 4: Information Gap, MLR 5: Co-Craft Questions and Problems, MLR 6: Three Reads, MLR 7: Compare and Connect, MLR 8: Discussion Supports) to provide additional support for implementing the instructional strategy.

Materials include and reference research-based strategies. For example, each grade’s Instructional Strategies Handbook includes two sets of research-based strategies: 1) the Instructional Strategies come from the Learner Variability Navigator from Digital Promise, and 2) the Mathematical Language Routines come from Understanding Language/SCALE, based at Stanford University Graduate School of Education. Some of the Mathematical Language Routines (MLR 1, MLR 4, MLR 6, MLR 8) also cite specific research supporting them. Additionally, the Multilingual Learner Support Handbook “synthesizes the insights from the ELSF Guidelines, WIDA Proficiency Level Descriptors, and the comprehensive 2020 WIDA ELD Standards Framework.” The curriculum does not include or reference specific research that supports its overall design or component parts.

Materials include and reference the role of the standards in the program. For example, each grade’s Mathematical Progressions and Connections and Scope and Sequence explain the role of the standards. However, ClearMath Elementary “translates” the CCSS into “content expectations,” or “concise summaries of the main points within the larger standards.” It does not include the full text of the standards in the About the Math sections within the Module, Topic, and Lesson Overviews, nor does it refer to the standard code in each lesson.

The materials reviewed for ClearMath Elementary Kindergarten through Grade 2 meet expectations for providing a comprehensive list of supplies needed to support instructional activities.

In the Teacher's Implementation Guide, comprehensive materials lists are provided at the Topic and Lesson level. For example, in Grade 1, the materials list outlines the resources needed for instruction; each grade includes a similar structure.

• In Grade 1, Topic 1 Overview under Preparing Topic-Level Materials, the Downloadable Resources section states, “To print, copy, and prepare Downloadable Resources for the topic, refer to the Downloadable Resources Digital Book.” The Manipulatives Kit section lists: “Large quantity manipulatives and recommendations for organization: Attribute blocks (15–20 per student in Center), Blank number cubes (labeled with 3 different colors, 1 per Center pair), Farm animal counters (18 per pair), Number cubes (1 per pair), Pattern blocks (20 blocks per pair), Two-color counters (1 per pair).” The Other Materials section lists: “Blank paper (1 piece per student), Books (15 per class), Crayons (1 per student), Cups (1 per pair), Sealable baggies (1 per pair), Tape (1 per student in Center).” A key is included that uses stars to indicate materials used multiple times within the topic and bullets to show materials used in only one lesson.

• At the lesson level, materials lists also include icons indicating whether the resource is in the Student Resource Book, a downloadable resource, a manipulative, or an additional tool.

The materials reviewed for ClearMath Elementary Kindergarten through Grade 2 meet expectations for providing consistent opportunities to determine student learning throughout the school year. The assessment system provides sufficient teacher guidance for evaluating student performance and determining instructional next steps.

A comprehensive system of varied assessments designed to help teachers monitor student progress consistently throughout the year is included in these materials. Assessments are embedded at the lesson, topic, module, and course levels and are designed to capture growth over time and inform instructional decisions. For example:

• Assessments include: Beginning-of-Year Assessments, Middle-of-Year Assessments, End-of-Year Assessments, Snapshot Assessments, End-of-Topic Assessments, End-of-Module Assessments, Performance Tasks, and ReadyCheck Pre-Assessments (Grades 1–5 only).

• Assessment opportunities are also consistently embedded throughout lessons and topics, not just at the end, ensuring teachers can monitor and support student learning continuously. These embedded assessments enable in-the-moment instructional adjustments, fostering student reflection and engagement with their learning.

• Ongoing Assessments appear throughout the Lesson Facilitation Notes, offering teachers real-time prompts designed to elicit student thinking and assess understanding as activities unfold.

• Reflect Activities, such as Reflect and Summarize, My Just Right Problem, and Mindset Reflections, appear at the end of each lesson. These tasks prompt students to explain their reasoning and apply what they’ve learned, providing formative assessment data that guides next steps for Re-Engagement Lesson planning.

Materials provide teachers with rubrics, scoring guidelines, and open-ended feedback tools that support consistent and effective assessment of student learning. These tools help teachers evaluate not only accuracy but also reasoning, strategy use, and conceptual understanding. The Assessment Guide includes a blueprint for each assessment, providing scoring guidance and alignment with standards. Performance Tasks at the end of each topic include rubrics that outline criteria for evaluating student responses across multiple dimensions, such as reasoning, problem-solving, and communication. These rubrics are paired with sample student responses and notes to guide teachers in interpretation and scoring. For example:

• Grade 1, Assessment Guide, Topic 5, Performance Task, provides a rubric to score the Performance Task and identifies three criteria covered in the task: “Applies properties of operations, adds within 10, and subtracts within 10.” Each criterion is scored with 0 points, 1 point, or 2 points. The guide also includes suggestions for using the Performance Task as an assessment for learning. “Create a portfolio for each student that includes their performance tasks from across the grade. This will help teachers, students, and caregivers observe progress across the year. Conduct a Gallery Walk of sample student responses.”

Materials provide teachers with clear, actionable guidance on how to respond to assessment results. These supports are embedded throughout the program to ensure teachers can meet the diverse needs of students following any assessment. The Assessment Guide offers guidance after each assessment, including targeted instruction recommendations. These supports help teachers decide next steps based on data and ensure all students stay on track toward grade-level goals. For example:

• Grade 2, Assessment Guide, Topic 4, End-of-Topic Assessment Blueprint, Targeted Instruction Recommendations by CCSS, provides teachers with targeted recommendations for instructional work for students who have not mastered the standard on the assessment. “Facilitate a small group activity. Create a measurement scavenger hunt. Provide a list of random lengths in inches, feet, centimeters, and meters. Students must locate an object that is approximately each length and write the name or draw a picture of the object beside the measurement. Utilize these activities from the CLEAR Learning Center: Fastest Path, Find That Length! Play these games in MATHia Adventure: Laser Cutter, Mind the Gap.”

The materials reviewed for ClearMath Elementary Kindergarten through Grade 2 meet expectations for providing strategies and support for students in special populations to work with grade-level content and meet or exceed grade-level standards, which support their regular and active participation in learning.

Materials provide strategies, supports, and resources for students in special populations to ensure their regular and active participation in grade-level mathematical tasks and problem-solving activities. The materials embed research-based strategies throughout the instructional materials to support students in special populations, including students with disabilities and those with unfinished learning, so they can access, engage with, and succeed in grade-level mathematics. Within the Teacher’s Implementation Guide Overview, the Intentional Design for Accessible Learning section supports teachers in adjusting instruction to promote independence and engage students in mathematical reasoning. Examples within the program include: 

• The materials align with Universal Design for Learning (UDL) principles by offering multiple means of engagement, representation, and expression. The instructional materials support diverse learning needs through consistent structures that are designed to develop executive functioning skills and support mathematical practices. Across each course, instructional guidance encourages asset-based inclusive practices that allow all students, especially those in special populations, to engage with grade-level mathematics in ways that promote independence, agency, and reasoning.

• Instructional Strategies Handbook: “Instructional strategies provide teachers with pedagogical moves they can use to support the varied needs of all learners in their classroom. These strategies are research-based to support student learning.”

• Teacher’s Implementation Guide Overview, Understanding the Teaching Cadence: “Each Concept Lesson concludes with a Reflect activity that provides you with data to inform how to group students into one or more of the possible Re-Engagement Explore Centers. Stretch Center provides students with an opportunity to extend the work of the concept lessons.” The center provides a challenging option for students who are above grade level.

The materials reviewed for ClearMath Elementary Kindergarten through Grade 2 meet expectations for regularly providing extensions and/or opportunities for advanced students to engage with grade-level/course-level mathematics at greater depth.

ClearMath Elementary does not offer optional enrichment lessons for advanced students. The program offers a comprehensive set of options for teachers to support all students.

The instructional materials include tasks that ask students to analyze problems, justify their thinking, and make generalizations, with opportunities for engagement in grade-level content. These examples are not limited to advanced learners but demonstrate opportunities for teachers to provide access to all students that promote this type of reasoning. The instructional materials extend learning beyond procedural fluency through investigations, multi-step problem-solving tasks, and discussions that require reasoning, justification, and abstraction. These opportunities are embedded within core instruction so that all students, including those ready for greater challenge, are supported in exploring mathematical ideas at increasing levels of depth and sophistication. These tasks invite students to model with mathematics, connect ideas across topics, and explore patterns, structure, and mathematical relationships at their level of readiness. The instructional materials include supports for teachers to extend instruction and increase cognitive demand for all students through challenge activities embedded directly within lesson materials.

The materials reviewed for ClearMath Elementary Kindergarten through Grade 2 meet expectations for providing manipulatives, both virtual and physical, that are accurate representations of the mathematical objects they represent and, when appropriate, are connected to written methods.

ClearMath Elementary K-5 integrates both physical and virtual manipulatives to support students’ conceptual understanding and strengthen connections to written mathematical representations. Manipulatives are embedded across lessons, providing opportunities for students to explore, communicate, and make sense of mathematical ideas. Each course includes a Manipulatives Kit and additional resources, which are outlined in the Teacher’s Implementation Guide under Student Tools for Learning. These resources include items from the Manipulatives Kit, the Student Resource Book, printable cutouts, and downloadable materials. For example, the Grade 1 Kit contains a range of tools (e.g., base-ten blocks, counters, geometric shapes) that are accurately represented and connected to written methods.