4th Grade - Gateway 3

The materials reviewed for Reveal Math Grade 4 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.

Materials provide comprehensive guidance that will assist teachers in presenting the student and ancillary materials. Examples include:

• The Implementation Guide provides a program guide, which includes a program overview, the program components, unit features, instructional model, lesson walk-through, and a brief description of the different unit components, such as Math is…, focus, coherence, rigor, and language of math.  

• The Implementation Guide provides pacing for each unit; mapping out the lessons in each unit and how many days the unit will take.

• The Unit Planner contains an overview of the Lessons within the unit, Math Objective, Language Objective, Key Vocabulary, Materials to Gather, Rigor Focus, and Standard.

• The Unit Overview provides a description for teachers as to how the unit connects to Focus, Coherence, and Rigor. 

• Within each lesson, the Language of Math section, provides teachers with specific information about the vocabulary used in lessons and how to utilize vocabulary cards to enhance learning experiences. 

• In Unit 5, Numbers and Number Patterns, Unit Overview, Effective Teaching Practices, Facilitate Meaningful Math Discourse, “Student discourse is an interactive process of collaborative exploration, exchange of ideas, and building of shared understanding. The teacher is a facilitator and performs the following actions: 

  • Engages students as they explore and share ideas and strategies.

  • Observes what students are doing and saying and forms a plan for the whole-class discussion.

  • Creates an environment in which students take ownership.

  The student is leader, partner, problem-solver, and communicator, and performs the following actions:

  • Presents and explains ideas, strategies, and reasoning to peers.

  • Listens respectfully to peers and engages them in constructive argument.

  • Compares approaches and solutions with peers for shared understanding.”

• In Unit 7, Division Strategies with Multi-Digit Dividends and 1-Digit Divisors, Unit Overview, Math Practices and Processes, Reason Abstractly and Quantitatively, “During the course of a lesson, the teacher should encourage students to reason abstractly and quantitatively when approaching the mathematics. A goal in teaching is to enable students to make sense of the problems and mathematics by themselves. For example, students may reason abstractly when using an area model to find partial quotients.” 

Materials include sufficient and useful annotations and suggestions that are presented within the context of the specific learning objectives. The materials provide information about planning instruction, and give suggestions for presenting instructional strategies and content, as well as mathematical practices. Examples include:

• In Lesson 5-2, Understand Prime and Composite Numbers, Notice & Wonder, Teaching Tip, “Have students work in pairs to discuss objects in groups. Have them think of instances when they may have put real-life objects or manipulatives in equal groups, and what those representations may have looked like.”

• In Lesson 5-6, Analyze Features of a Pattern, Notice & Wonder, Teaching Tip, “Have student pairs take turns stating similarities and differences between the two sequences. Then compile a list of the similarities and differences from the class. This encourages participation on the part of all students as well as encouraging them to state an answer without consideration of whether it is the “correct answer.”

The materials reviewed for Reveal Math Grade 4 meet expectations for including standards correlation information that explains the role of the standards in the context of the overall series.

Correlation information is present for the mathematics standards addressed throughout the grade level. Examples of how individual units, lessons, or activities throughout the series are correlated to the CCSSM include:

• In the Digital Teacher Center, Program Overview: Learning & Support Resources, Implementation Guide, Correlations, identifies the standards included in each lesson. This guide also indicates whether the standards are considered major, supporting, or additional standards. 

• Each Unit Planner includes a pacing guide identifying the standards that will be addressed in each lesson.

• In Lesson 6-4, Multiply 2-Digit by 1-Digit Factors, the materials identify focus standard 4.NBT.5, multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers. The lesson also identifies MPs 1 and 4. 

• In Lesson 11-5, Solve Problems Involving Fractions and Mixed Numbers, the materials identify focus standard 4.NF.4c, solve word problems involving multiplication of a fraction by a whole number. The lesson also identifies MPs 1 and 8. 

Explanations of the role of the specific grade-level mathematics are present in the context of the series, and teacher materials provide information to allow for coherence across multiple course levels. This allows the teacher to make prior connections and teach for connections to future content. Examples include:

• The Unit Overview includes the section, Coherence, identifying What Students Have Learned, What Students Are Learning, What Students Will Learn. In Unit 2, Generalize Place-Value Structure, What Students Have Learned, “Students learned the place value of 3-digit numbers in different forms. (Grade 2), Students have had experiences comparing quantities and numbers that represent quantities since Kindergarten. Students compared two 3-digit numbers. (Grade 3), Students rounded whole numbers to the nearest ten and hundred. (Grade 3)” In What Students Are Learning, “Students generalize the base-ten place-value structure, and explain that a digit in one place represents ten times the value of the digit in the place to its right., Students represent multi-digit whole numbers using forms such as standard, expanded, and word forms., Students compare two multi-digit numbers using place value and round multi-digit numbers to an appropriate place for the given estimation need.” In What Students Will Learn, “Students expand their understanding of place value as they explore relationships between digits in decimal fractions. (Grade 5), Students represent decimals to thousandths in different forms. (Grade 5), Students apply their understanding of place value as they compare two decimals written in decimal notation, and round decimals to an appropriate place for the given estimation need. (Grade 5)”

• Each lesson begins by listing the standards covered within the lesson, indicates whether the standard is a major, supporting or additional standard and identifies the Standards for Mathematical Practice for the lesson. Each lesson overview contains a coherence section that provides connections to prior and future work. In Lesson 9-3, Add Fractions with Like Denominators, Coherence, Previous, “Students learned that fractions are numbers made up of equal parts of a whole (Grade 3)., Students composed and decomposed fractions (Unit 8).” Now, “Students model addition of fractions with common denominators, students add fractions with like denominators.” Next, “Students subtract fractions with like denominators (unit 9)., Students add and subtract fractions with unlike denominators (Grade 5).”

The materials reviewed for Reveal Math Grade 4 meet expectations for providing explanations of the instructional approaches of the program and identification of the research-based strategies.

The materials explain the instructional approaches of the program. Examples include:

• Digital Teacher Center, Program Overview: Learning & Support Resources, Teacher Welcome Letter Template specifies “Reveal Math, a balanced elementary math program, develops the problem solvers of tomorrow by incorporating both inquiry-focused and teacher-guided instructional strategies within each lesson.” 

• Teacher Guide, Volume 1, Welcome to Reveal Math, the overall organization of the math curriculum has five goals:

  • “The lesson model offers two instructional options for each lesson: a guided exploration that is teacher-guided and an activity-based exploration that has students exploring concepts through small group activities and drawing generalizations and understanding from the activities.

  • The lesson model incorporates an initial sense-making activity that builds students’ proficiency with problem solving. By focusing systematically on sense-making, students develop and refine not just their observation and questioning skills, but the foundation for mathematical modeling.

  • Both instructional options focus on fostering mathematical language and rich mathematical discourse by including probing questions and prompts.

  • The Math is… unit builds student agency for mathematics. Students consider their strengths in mathematics, the thinking habits of proficient “doers of mathematics,” and the classroom norms that are important to a productive learning environment.

  • The scope and sequence reflects the learning progressions recommended by leading mathematicians and mathematics educators. It emphasizes developing deep understanding of the grade-level concepts and fluency with skills, while also providing rich opportunities to apply concepts to solve problems.”

The Implementation Guide, located in the Digital Teacher Center, further explains the instructional approaches of specific components of the program. Examples include:

• Unit Features, Unit Planner, “Provides at-a-glance information to help teachers prepare for the unit. Includes pacing: content, language, and SEL objectives; key vocabulary including math and academic terms; materials to gather; rigor focus; and standard (s).”

• Unit Features, Readiness Diagnostic, “Offers teachers a unit diagnostic that can be administered in print or in digital. The digital assessment is auto-scored. Assesses prerequisite skills that students need to be successful with unit content. Item analysis lists DOK level, skill focus, and standard of each item. Item analysis also lists intervention lessons that teachers can assign to students or use in small group instruction.”

• Unit Features, Spark Student Curiosity Through Ignite! Activities, “Each unit opens with an Ignite! Activity, an interesting problem or puzzle that: Sparks students’ interest and curiosity, Provides only enough information to open up students’ thinking, and Motivates them to persevere through challenges involved in problem solving.”

• Instructional Model, “Reveal Math’s lesson model keeps sense-making and exploration at the heart of learning. Every lesson provides two instructional options to develop the math content and tailor the lesson to the needs and structures of the classroom.” Each lesson follows the same structure of a “Launch, Explore & Develop, Practice & Reflect, Assess and Differentiate.” Each of these sections is further explained in the instruction manual.

• Number Routines, in each lesson there is a highlighted number routine for teachers to engage students with. These routines “are designed to build students’ proficiency with number and number sense. They promote an efficient and flexible application of strategies to solve unknown problems…”

The Implementation Guide, located in the Digital Teacher Center, discusses some of the research based features of the program. Examples include: 

• Implementation Guide, Effective Mathematical Teaching Practices, “Reveal Math’s instructional design integrates the Effective Mathematics Teaching Practices from the National Council of Teachers of Mathematics (NCTM). These research-based teaching practices were first presented and described in NCTM’s 2014 work Principles to Action: Ensuring Mathematical Success for All.”

• Implementation Guide, Social and Emotional Learning, “In addition to academic skills, schools are also a primary place for students to build social skills. When students learn to manage their emotions and behaviors and to interact productively with classmates, they are more likely to achieve academic success Research has shown that a focus on helping students develop social and emotional skills improves not just academic achievement, but students’ attitudes toward school and prosocial behaviors (Durlak et al., 2011)...”

• Implementation Guide, Support for English Learners, Lesson-level support, English Learner Scaffolds, each lesson has an “English Learner Scaffolds” section to support teachers with “scaffolded instruction to help students make meaning of math vocabulary, ideas, and concepts in context. The three levels of scaffolding within each lesson - Entering/Emerging, Developing/Expanding, and Bridging/Reaching are based on the 5 proficiency levels of the WIDA English Language Development Standards.”

• Implementation Guide, Math Language Routines, throughout the materials certain language routines are highlighted for teachers to encourage during a lesson, these routines were developed by a team of authors at Center for Assessment, Learning and Equity at Standard University and are “based on principles for the design of mathematics curricula that promote both content and language.” In the implementation guide, the material lists all eight Math Language routines and their purposes, “MLR1: Stronger and Clearer Each Time - Students revise and refine their ideas as well as their verbal or written outputs.”

• Implementation Guide, Math Probe - Formative Assessment, each unit contains a Math Probe written by Cheryl Tobey. Math Probes take time to discover what misconceptions might still exist for students. Designed to ACT, “The teacher support materials that accompany the Math Probes are designed around an ACT cycle - Analyze the Probe, Collect and Assess Student Work, and Take Action. The ACT cycle was originally developed during the creation of a set of math probes and teacher resources for a Mathematics and science Partnership Project.”

The materials reviewed for Reveal Math Grade 4 meet expectations for providing a comprehensive list of supplies needed to support instructional activities.

The Digital Teacher Center, Program Resources: Course Materials, Planning Resources, Materials List: Grade 4 specifies the comprehensive materials list. The document specifies classroom materials (e.g., markers, grid paper, dominoes, construction paper, etc.), materials from a manipulative kit (e.g., geoboards, base-ten blocks, transparent spinner, etc.), non-consumable teaching resources (e.g., number cards 1-10, place-value chart to millions, 10x10 grids, etc.), and consumable teaching resources (e.g., activity cards, problem solving tool, alphabet letters, etc.).

In the Teacher Edition, each Unit Planner page lists materials needed for each lesson in the unit, for example, Unit 10, Addition and Subtraction Strategies with Mixed Numbers, Materials to Gather:

• “Lesson 10-1 - fraction tiles, transparent spinner

• Lesson 10-2 - Blank Number Lines 2 Teaching Resource, fraction circles, fraction tiles, index cards, paper strips

• Lesson 10-3 - fraction circles, fraction tiles, number cubes, paper strips

• Lesson 10-4 - Blank Number Lines 2 Teaching Resource, fraction circles, fraction tiles, index cards, paper strips

• Lesson 10-5 - Blank Number Lines 2 Teaching Resource, fraction circles, fraction tiles, number cubes, paper strips

• Lesson 10-6 - index cards, Problem Solving Tool Teaching Resource.”

At the beginning of each lesson in the “Materials” section, a list of materials needed for each part of the lesson is provided: 

• In Lesson 2-4, Round Multi-Digit Numbers, Materials, “The materials may be for any part of the lesson: Activity Cards Teaching Resource, Blank Number Lines Teaching Resource, Place-Value Chart to Millions Teaching Resource.”

• In Lesson 4-3, Solve Comparison Problems Using Multiplication, Materials, “The materials may be for any part of the lesson: connecting cubes, counters, number cubes.”

• In Lesson 7-2, Estimate Quotients, Materials, “The materials may be for any part of the lesson: index cards, spinners labeled 2-9.”

The materials reviewed for Reveal Math Grade 4 meet expectations for including an assessment system that provides multiple opportunities throughout the grade, course, and/or series to determine students' learning and sufficient guidance to teachers for interpreting student performance and suggestions for follow-up.

Each unit, beginning with Unit 2, offers a Readiness Diagnostic that assesses the content of the unit and gives teachers a snapshot of the prerequisite skills the students already possess. Each unit also includes a Unit Assessment that evaluates students’ understanding of and fluency with concepts and skills from the unit. In the Teacher Edition, an Item Analysis lists each item’s DOK level, skill focus, content standard, and a Guided Support Intervention Lesson that teachers can assign or use for small groups or remediation. For example:

• In Unit 7, Division Strategies with Multi-Digit Dividends and 1-Digit Divisors, Unit Assessment (Form B), Item 13 lists “Interpret Remainders in Word Problems” as the Guided Support Intervention Lesson. This resource can be located in the Digital Teacher Center in the Targeted Intervention section of the Unit.

Unit Performance Tasks include a scoring rubric that evaluates student work for each section on a 2, 1, or 0 point scale. No follow-up guidance is provided for the Performance Task. For example:

• In Unit 2, Generalize Place-Value Structure, Performance Task Part B, Rubric (2 points), “2 Points: Students’ work shows proficiency with writing numbers through the millions in expanded form. Solution and explanation are accurate. 1 Point: Students’ work shows developing proficiency with writing numbers through the millions in expanded form. Solution shows one inaccurate number or explanation. 0 Points: Students’ work shows weak proficiency with writing numbers through the millions in expanded form. Solution and explanation are inaccurate.”

Math Probes analyze students’ misconceptions and are provided at least one time per Unit, beginning with Unit 2. In the Teacher Edition, “Authentic Student Work” samples are provided with correct student work and explanations. An “IF incorrect…, THEN the student likely…Sample Misconceptions” chart is provided to help teachers analyze student responses. A Take Action section gives teachers suggestions and resources for follow up or remediation as needed. There is a “Revisit the Probe” with discussion questions for students to review their initial answers after they are provided additional instruction, along with a Metacognitive Check for students to reflect on their own learning. For example:

• In Unit 11, Multiply Fractions by Whole Numbers, Math Probe Which is Greater?, Analyze The Probe, Targeted Concept, “Determine the product of a whole number and a fraction by reasoning about the magnitude of numbers.” For example, “Problem 2, Circle a or b to show which is greater. a. 3 x \frac{1}{2} OR b. 7 x \frac{1}{4}.” Targeted Misconceptions: “Some students have difficulty determining an estimated magnitude of a product when working with fractions. They may overgeneralize about the size of fractions in general or misjudge the magnitude of a particular fraction. Other students may multi[ly both the numerator and denominator when multiplying a fraction by a whole number.” Sample Student work is provided, along with “IF incorrect...THEN the student likely…” explanations of the sample misconception are provided.

Exit Tickets are provided at the end of each lesson and evaluate students’ understanding of the lesson concepts and provide data to inform differentiation. Each includes a Metacognitive Check allowing students to reflect on their understanding of lesson concepts on a scale of 1 to 3, with 3 being the highest confidence, and beginning in Unit 2, include an Exit Skill Tracker that lists each item’s DOK, skill, and standard. The Exit Ticket Recommendations chart provides information regarding which differentiation activity to assign based on the student’s score. For example, “If students score…Then have students do” which provides teachers information on what Differentiation activities to use such as Reinforce Understanding, Build Proficiency or Extend Thinking. For example:

• In Lesson 14-3, Draw and Measure Angles, Exit Ticket, Item 1, “What is the measure of the angle? Use a protractor to measure the angle.” Exit Ticket Recommendations: “If students score 2 of 2, Then have students do Additional Practice or any of the B (Build Proficiency) or E (Extend Thinking) activities. If students score 1 of 2, Then have students Take Another Look or any of the B activities. If students score 0 of 2, Then have students do Small Group Intervention or any of the R (Reinforce Understanding) activities.”

The materials reviewed for Reveal Math Grade 4 meet expectations that assessments include opportunities for students to demonstrate the full intent of grade-level standards and practices across the series. 

Reveal Math offers a variety of opportunities for students to demonstrate the full intent of grade-level standards and mathematical practices. While content standards and DOK levels are consistently identified for teachers in the Teacher Edition, and content standards are labeled for students in digital assessments, the standards for mathematical practice are not identified for teachers or students. It was noted that although assessment items do not clearly label the MPs, students are provided opportunities to engage with the mathematical practices.

Unit Readiness Diagnostics are given at the beginning of each unit, beginning with Unit 2. Formative assessments include Work Together, Exit Tickets, and Math Probes. Summative assessments include Unit Assessment Forms A and B, and Unit Performance Tasks at the end of a unit. Benchmark Assessments are administered after multiple units, and an End of the Year (Summative) Assessment is given at the end of the school year. Examples include:

• In Unit 4, Multiplication as Comparison, Performance Task, Ticket Sales, supports the full intent of 4.OA.2 (Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number…), and MP4 (Model with mathematics) as students model a situation with an appropriate representation and use an appropriate strategy. “Part C, The theater sold a combined total of 36 tickets to its drama and historical performances. The theater sold 5 times as many drama tickets as spy show tickets. How many drama tickets were sold? How many tickets to the historical performance were sold? Show your work by writing equations with a symbol for the unknown.”

• In Unit 11, Multiply Fractions by Whole Numbers, Unit Assessment Form B, Item 11 supports the full intent of 4.NF.4b (Understand a multiple of a/b as a multiple of 1/b, and use this understanding to multiply a fraction by a whole number), and MP5 (Use appropriate tools strategically) as students choose an appropriate tool or strategy to solve the problem. “Michelle picks 2\frac{5}{6} quarts of blackberries on Monday. On Tuesday, she picks 4 times as many blackberries as on Monday. How many quarts of blackberries did she pick on Tuesday?

• In Lesson 13-1, Relate Metric Units, Assess, Exit Ticket, Item 5, supports the full intent 4.MD.1 (Know relative sizes of measurement units within one system of units...), and MP7 (Look for and make use of structure) as students look for patterns to make generalizations and solve problems. “Choose whether each measurement statement is True or False. 24 kilograms = 2,400 grams; 35 kilometers = 35,000 meters; 49 meters = 49,000 centimeters, 52 liters = 52,000 milliliters.”

• Summative Assessment, Item Analysis, Item 5 supports the full intent of 4.OA.3 (Solve multistep word problems posed with whole numbers having whole-number answers using the four operations), and MP2 (Reason abstractly and quantitatively) as students consider the units involved and represent the problem situation symbolically. “Carlos has 264 stickers in his collection divided equally among 6 books. He trades Zoe 2 full books of stickers in exchange for 61 of her stickers. How many total stickers does Carlos have now? A. 176 stickers, B. 237 stickers, C. 325 stickers, D. 413 stickers.”

The materials reviewed for Reveal Math Grade 4 meet expectations for providing strategies and supports for students in special populations to support their regular and active participation in learning grade-level mathematics.

There are multiple locations of supports for students in special populations at the unit and lesson level. These supports are specifically aligned to lessons and standards, making them engaging in a variety of ways. They also scaffold up to the learning instead of simplifying or lowering expectations.

The Implementation Guide, Support for English Learners, identifies three features at the Unit level:

• “The Math Language Development feature offers insights into one of the four areas of language competence - reading, writing, listening, and speaking - strategies to build students’ proficiency with language.”

• The English Language Learner feature provides an overview of the lesson-level support.”  

• The Math Language Routines feature consists of a listing of the Math Language Routines found in each lesson of the unit.” 

The Implementation Guide, Support for English Learners, also identifies three features at the Lesson level:

• Language Objectives: “In addition to a content objective, each lesson has a language objective that identifies a linguistic focus for the lesson for English Learners. The language objective also identifies the Math Language Routines for the Lesson.”

• English Learner Scaffolds: “English Learner Scaffolds provide teachers with scaffolded instruction to help students make meaning of math vocabulary, ideas, and concepts in context. The three levels of scaffolding within each lesson - Entering/Emerging, Developing/Expanding, and Bridging/Reaching are based on the 5 proficiency levels of the WIDA English Language Development Standards. With these three levels, teachers can scaffold instruction to the appropriate level of language proficiency for their students.”  

• Math Language Routines: “Each lesson has at least one Math Language Routine specifically designed to engage English Learners in math and language.”  

The Implementation Guide, Differentiation Resources, provides a variety of small group activities and resources to support differentiation to sufficiently engage students in grade level mathematics. Examples include: 

• Reinforce Understanding: “These teacher-facilitated small group activities are designed to revisit lesson concepts for students who may need additional instruction.”  

• Build Proficiency: “Students can work in pairs or small groups on the print-based Game Station activities, written by Dr. Nicki Newton, or they can opt to play a game in the Digital Station that helps build fluency.”  

• Extend Thinking: “The Application Station tasks offer non-routine problems for students to work on in pairs or small groups.”   

The Implementation Guide, Differentiation Resources, provides a variety of independent activities and resources to support differentiation to sufficiently engage students in grade level mathematics. Examples include:

• Reinforce Understanding: “Students in need of additional instruction on the lesson concepts can complete either the Take Another Look mini-lessons, which are digital activities, or the print-based Reinforce Understanding activity master.”

• Build Proficiency: “Additional Practice and Spiral Review assignments can be completed in either print or digital environment. The digital assignments include learning aids that students can access as they work through the assignment. The digital assignments are also auto-scored to give students immediate feedback on their work.”  

• Extend Thinking: “The STEM Adventures and Websketch activities powered by Geometer’s Sketchpad offer students opportunities to solve non-routine problems in a digital environment. The print-based Extend Thinking activity master offers an enrichment or extension activity.”  

The Teacher Edition and Implementation Guide provide overarching guidance for teachers on how to use the supports provided within the program. Examples include:

• Teacher Edition, Volume 1, Lesson Model: Differentiate, for every lesson, there are multiple options for teachers to choose to support student learning. Based on data from Exit Tickets, students can reinforce lesson skills with “Reinforce Understanding” opportunities, practice their learning with “Build Proficiency” opportunities, or extend and apply their learning with “Extend Thinking” opportunities. Within each of these opportunities, there are options of workstations, online activities and independent practice for teachers to elect to use. 

• Implementation Guide, Targeted Intervention, “Targeted intervention resources are available to assign students based on their performance on all Unit Readiness Diagnostics and Unit Assessments. The Item Analysis table lists the appropriate resources for the identified concept or skill gaps. Intervention resources can be found in the Teacher Center in both the Unit Overview and Unit Review and Assess sections.”  The Item Analysis can be found in the Teacher Edition. Intervention resources include Guided Support, “Guided Support provides a teacher-facilitated small group mini-lesson that uses concrete modeling and discussion to build conceptual understanding” and Skills Support, “Skills Support are skills-based practice sheets that offer targeted practice of previously taught items.”  Both of these can be located in the Digital Teacher Center.

The materials reviewed for Reveal Math Grade 4 meet expectations for providing extensions and/or opportunities for students to engage with grade-level mathematics at higher levels of complexity.

Each unit opens with an “Ignite!” activity that poses an interesting problem or puzzle to activate prior knowledge and spark students’ curiosity around the mathematics for the unit. In the Digital Teacher Center, “What are Ignite! Activities?” video, contributing author Raj Shah, Ph.D., explains, “An Ignite! Activity is an opportunity to build the culture of your classroom around problem-solving, exploration, discovery and curiosity.” The activity gives teachers, “the opportunity to see what the students can do on their own, without having to pre-teach them anything.” This provides an opportunity for advanced students to bring prior knowledge and their own abilities to make insightful observations. 

The Teacher Edition, Unit Resources At-A-Glance page includes a Workstations table which, “offers rich and varied resources that teachers can use to differentiate and enrich students’ instructional experiences with the unit content. The table presents an overview of the resources available for the unit with recommendations for when to use.” This table includes Games Station, Digital Station, and Application Station. 

Within each lesson, there are opportunities for students to engage in extension activities and questions of a higher level of complexity. The Practice & Reflect, On My Own section of the lesson provides an Item Analysis table showing the aspect of rigor and DOK level of each item. The Exit Ticket at the end of each lesson provides differentiation that includes extension through a variety of activities.

Additionally, there are no instances of advanced students doing more assignments than their classmates.

The materials reviewed for Reveal Math Grade 4 meet expectations for providing strategies and supports for students who read, write, and/or speak in a language other than English to regularly participate in learning grade-level mathematics.

The materials provide strategies for all students to foster their regular and active participation in learning mathematics, as well as, specific supports for English Learners. 

In the Implementation Guide, Support for English Learners, Unit-level support, “At the unit level are three features that provide support for teachers as they prepare to teach English Learners. The Math Language Development feature offers insights into one of the four areas of language competence - reading, writing, listening, and speaking - and strategies to build students’ proficiency with language. The English Language Learner feature provides an overview of lesson-level support. The Math Language Routines feature consists of a listing of the Math Language Routines found in each lesson of the unit.” The Unit Overview also includes a Language of Math section highlighting key vocabulary from the unit. These sections provide an overview of the strategies present within the unit ,and give guidance as to possible misconceptions or challenges that EL students may face with language demands. Included within the Unit Review is a Vocabulary Review that includes an Item Analysis for each item as well as what lesson/s the term was found in.  

At the lesson level, there are supports to engage ELs in grade-level content and develop knowledge of the subject matter. These involve oral language development and reading and writing activities. The Teacher Edition and Implementation Guide outline these features. Examples include:

• Language Objective, “In addition to a content objective, each lesson has a language objective that identifies a linguistic focus of the lesson for English Learners. The language objective also identifies the Math Language Routine of the lesson.”

• Math Language Routine, “Each lesson has at least one Math Language Routine specifically designed to engage English Learners in math and language.” Math Language Routines (MLR), listed and described in the Implementation Guide include: Stronger and Clearer Each Time, Collect and Display, Critique, Correct, and Clarify, Information Gap, Co-Craft Questions and Problems, Three Reads, Compare and Connect, Discussion Supports.

• English Learner Scaffolds, “English Learner Scaffolds provide teachers with scaffolded instruction to help students make meaning of math vocabulary, ideas, and concepts in context. The three levels of scaffolding within each lesson - Entering/Emerging, developing/Expanding, and Bridging/Reaching are based on the 5 proficiency levels of the WIDA English Language development Standards. With these three levels, teachers can scaffold instruction to the appropriate level of language proficiency of their students.”

• Language of Math, ”The Language of Math feature promotes the development of key vocabulary terms that support how we talk about and think about math in the context of the lesson content.”

• Number Routines such as “Would You Rather?” or “Math Pictures” and Sense-Making Routines such as “Notice and Wonder” or “Which Doesn’t Belong?” provide opportunities to develop and strengthen number sense and problem solving through discussion or written responses.

Most materials are available in Spanish such as the Student Edition, Student Practice Book (print), Student eBook, Math Replay Videos, eGlossary, and Family Letter (digital).

The materials reviewed for Reveal Math Grade 4 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.

Physical manipulatives needed for each unit and lesson can be found in the Teacher Edition, Unit Planner, at the beginning of each unit under “Materials to Gather”. Each lesson also identifies needed materials in the “Materials” section on the first page of each lesson.

Virtual manipulatives can be found online under “e-Toolkit”. Manipulatives are used throughout the program to help students develop a concept or explain their thinking. They are used to develop conceptual understanding and connect concrete representations to a written method.