Kindergarten - Gateway 3

The materials reviewed for Reveal Math Kindergarten 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 2, Numbers to 5, Unit Overview, Effective Teaching Practices, Elicit and Use Evidence of Student Thinking, “Use questioning and discussion to determine students’ understanding throughout the unit. Students’ conversations and responses will help determine the support that is needed. As you move through each lesson in the unit, spend time questioning students about the materials to assess their progress and understanding. 

  • Provide discussion opportunities among students and as a class to share ideas and to ask and answer questions. 

  • Pose questions to allow students to connect the current lessons to the previous lesson.  Asking how ideas are similar and different can give insight on student understanding.  

  • Allow students to justify their thinking in their own words. Language or vocabulary support can be provided as needed, but encourage students to express their thinking in their own words.” 

• In Unit 3, Unit Overview, Math Practice and Processes, Reason Abstractly and Quantitatively, “Comparable problem analysis: The concepts taught in this unit are similar to what was taught in the previous unit. Students can use prior knowledge as they solve similar problems in this unit.” 

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 as well as content and mathematical practices. Examples include:

• Lesson 3-1, Count 6 and 7, Explore & Develop, Bring it Together, Language of Math, “Add the vocabulary cards six and seven to the word wall. Ask six students to line up in the front of the room and count the group aloud. Then, repeat with seven students.” 

• Lesson 6-1, Represent and Solve Add to Problems, Number Routine, Counting Things, teachers are given guidance for incorporating number routines. “Build Fluency, students will build their visual discrimination and counting skills as they find an exact number of things. These prompts encourage students to talk about their reasoning: How many items are in each compartment? How do you know? Who counted these objects in a different way?” K.OA.1, represent addition and subtraction with objects, fingers, mental images, drawings, sounds (e.g., claps), acting out situations, verbal explanations, expressions, or equations.

• Lesson 10-2, Represent 16 and 17, Explore & Develop, Pose the Problem, teachers are provided guidance to generate student engagement and inquiry. “Read the problem to students. Edwin puts 16 bottles of bubbles on the shelves. How can he make a group with ten ones and some more ones?” Pose Purposeful Questions, “How many bottles of bubbles does Edwin have? How can he make a group with ten bottles?” K.NBT.1, compose and decompose numbers from 11 to 19 into ten ones and some further ones, e.g., by using objects or drawings, and record each composition or decomposition by a drawing or equation (e.g., 18 = 10 + 8); understand that these numbers are composed of ten ones and one, two, three, four, five, six, seven, eight, or nine ones.

The materials reviewed for Reveal Math Kindergarten 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 3-8, Compare Objects in Groups, the materials identify standard K.CC.6, identify whether the number of objects in one group is greater than, less than, or equal to the number of objects in another group, e.g., by using matching and counting strategies. The lesson also identifies MP2, reason abstractly and quantitatively. 

• In Lesson 7-2, Represent and Solve Take From Problems, the materials identify standard K.OA.1, represent addition and subtraction with objects, fingers, mental images, drawings, sounds (e.g., claps), acting out situations, verbal explanations, expressions, or equations. The lesson also identifies MP6, attend to precision. 

The teacher materials contain explanations of the role of the specific grade-level mathematics, including prior and future content connections. Examples include:

• The Unit Overview includes the section, Coherence, identifying What Students Have Learned, What Students Are Learning, What Students Will Learn. In Unit 4, Sort, Classify, and Count Objects, What Students Have Learned, “Students may be familiar with simple words that describe objects, notable color words, shape words, and size words (red, round, small). Students may know how to name numbers through ten or more. They may also have learned that each object in a group needs its own number when the group is being counted.” What Students Are Learning, “Students recognize attributes based on color, shape, and size and use these attributes to describe objects. Students create groups of objects based on the objects’ attributes. Students count to determine how many objects are in a group, understanding that the last number said represents the total number of objects, and sort groups according to the number of objects.” What Students Will Learn, “In Grade 1, students organize data into groups of up to three categories and ask and answer questions about the reasons for their groupings. In Unit 12, students expand on their understanding of counting to answer how many? questions about up to 20 objects arranged in a regular configuration, or up to 10 scattered objects. Given a number from 1-20, students learn to count out that many objects.”   

• 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. Each lesson overview contains a coherence section that provides connections to prior and future work. In Lesson 9-3, Decompose 11, 12, 13, Coherence, Previous, “Students decomposed numbers to 10 (Unit 8). Students composed 11, 12, and 13 into ten ones and some more ones (Unit 9).” Now, “Students apply their understanding of decomposing numbers to decompose 11, 12, and 13 into ten ones and some more ones.” Next, “Students make and decompose 14 and 15 (Unit 9). Students use place value to make numbers to 19 (Grade 1).”

The materials reviewed for Reveal Math Kindergarten 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.

  • 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, 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.” 

• 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 researched 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 Kindergarten 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 K, specifies the comprehensive materials list for the grade. The document specifies classroom materials (e.g., clay, index cards, tactile materials such as rice and sand, etc.), materials from a manipulative kit (e.g., pattern blocks, attribute blocks, connecting cubes, etc.), non-consumable teaching resources (e.g., ten frames, double ten frames, 2-part sorting mat, etc.), and consumable teaching resources (one more, equation symbol cards, number path).

In the Teacher Edition, each Unit Planner page lists materials needed for each lesson in the unit, for example, Unit 6, Understand Addition, Materials to Gather:

• “Lesson 6-1 - connecting cubes, counters

• Lesson 6-2 - connecting cubes, counters, Equation Symbol Cards Teaching Resource, Number Cards 0-10 Teaching Resource

• Lesson 6-3 - counters

• Lesson 6-4 - counters, Equation Symbol Cards Teaching Resource, Number Cards 0-10 Teaching Resource, number cube

• Lesson 6-5 - counters, number cube.”

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

• Lesson 1-3, Math Is In My World, Material, “The materials may be for any part of the lesson, Shape Cards Teaching Resource.” In Explore & Develop, Activity-Based Exploration, “Materials: Shape Cards teaching resource.” 

• Lesson 10-3, Decompose 16 and 17, Materials, “The materials may be for any part of the lesson, Connecting cubes, Number Bond 3 Teaching Resource. In Explore & Develop, Activity-Based Exploration, “Materials: connecting cubes (17 per group), Number Bond 3 Teaching Resource (2 per group).”

The materials reviewed for Reveal Math Kindergarten meet expectations for including an assessment system that provides multiple opportunities throughout the grade 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 4, Sort, Classify, and Count Objects, Unit Assessment (Form A), Item 1 lists “Alike and Different Objects” 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 5, 2 Dimensional Shapes, Unit Review, Performance Task, Rubric (4 Points), Part A-2 points, “2 Points: Students' work shows proficiency with identifying a circle and describing its position relative to objects in a picture. 1 Point: Students work shows developing proficiency with identifying a circle and describing its position relative to other objects. The student either correctly identifies the circle OR describes its position. 0 Points: Students work shows weak proficiency with identifying a circle and describing its position relative to other objects. The student does not correctly identify the circle OR describe its position.” 

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 8, Addition and Subtraction Strategies, Math Probe, Analyze the Probe, “Students interpret a number bond to determine the missing addend when breaking apart a number.” Students use number bonds and connecting cubes to decompose 5, 6, and 7. Guidance is provided in an “If incorrect...Then” chart as to common misconceptions students have leading to an incorrect answer. Exercise 2 shows a number bond with 6 at the top and 2 connecting cubes in one of the bottom parts. “IF incorrect (student answers 2 for the remaining part) THEN the student likely incorrectly reasons that the number of connecting cubes shown in the given part is the same as the missing part.” Sample Misconceptions, “Teacher: Circle the correct number for the number bond. [Student circles 2.] How did you decide it was 2? Student: I saw 2 cubes [Student points to the 2 cubes shown in the number bond and writes 2 in the number bond.] Teacher: What about this 6? Student: That number should be 4.” Take Action, “Revisit breaking apart activities and the use of number bond models. Provide experiences for students to create number bonds for the same whole.” Revisit the Probe, “Are there any answers that you would like to change? Explain why you would like to change them. Are there any questions you still have about any of the items on this probe?” Reflect on Your Learning provides students with a “thumbs up, thumbs sideways, thumbs down” to circle to show their understanding.

Exit Tickets are provided at the end of each lesson and intended to determine the 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 8-5, Exit Ticket, “If students score 2 out of 2, Then have students do Additional Practice or any of the B or E activities.” The Build Proficiency (B) activities include Practice It! Game Station, Make 8 and 9 Task Cards Workstation, and Interactive Additional Practice. The Extend Thinking (E) activities include Use It! Application Station, Make a Shaker workstation, and Websketch Exploration.

The materials reviewed for Reveal Math Kindergarten 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 9, Numbers 11-15, Performance Task, supports the full development of K.CC.3 (Write numbers from 0 to 20), K.NBT.1 (Compose and decompose numbers from 11 to 19 into ten ones and some further ones) and MP4 (Model with mathematics) as students demonstrate their understanding of writing and representing numbers up to 15. Stimulus, “Listen carefully. Arjun sets up a game with Penny. They are getting ready to play the game. Part A. Arjun did not finish writing the numbers on the game board. Write the missing numbers on the game board. Part B. Penny moves her marker to the number after 13. Write the number Penny moves to. Draw to show this number as 10 ones and some more ones.”

• In Lesson 12-4, Count From Any Number to 100, Assess, Exit Ticket, supports the full intent of K.CC.2 (Count forward beginning from a given number within the known sequence) and MP6 (Attend to precision). Exercise 1, “How many blocks? Count each set of blocks. Write the number that comes next.” Students are shown 5 tens and 4 ones and 5 tens and 5 ones in base ten blocks.

• In Unit 13, Analyze, Compare and Compose Shapes, Performance Task, assesses K.G.5 (Model shapes in the world by building shapes from components) and supports the full development of MP4 (Model with mathematics) as students name and draw shapes based on attributes. Part A, “Ada and Oscar each draw a shape. Ada’s shape has 4 sides. It has 2 short sides and 2 long sides. It also has 4 corners. What is Ada’s shape? Draw Ada’s shape. Oscar’s shape also has 4 sides. It has 4 corners. Oscar’s shape has 4 sides that are the same length. What is Oscar’s shape? Draw Oscar’s shape.” 

• Benchmark Assessment 3, Item Analysis, Item 3, is aligned to DOK 2 and develops the full intent of K.MB.3 (Classify objects into given categories), K.G.2 (Correctly name shapes regardless of their orientations or overall size), and MP2 (Reason abstractly and quantitatively) as students identify everyday items that are shaped like circles and triangles. “Which object is a circle or a triangle? Circle the object that is shaped like a circle. Draw an x on the object that is shaped like a triangle.” Students see a triangular sign, a whole pizza cut into 10 triangular slices, and 2 square shaped interlocking pieces.

The materials reviewed for Reveal Math Kindergarten 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, and therefore are 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 Kindergarten 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 Kindergarten 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 Kindergarten 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.