6th Grade - Gateway 3

The instructional materials for Reveal Math Grade 6 meet the expectations that there is a clear distinction between problems and exercises in the materials.

In the instructional sections of each lesson, students complete examples and problems to learn new concepts through strategies such as guided instruction, step-by-step procedures, interactive slideshows, and problem solving.

Each lesson ends with independent practice, which include exercises that allow students to independently apply what they have learned. Some of the practice problems parallel the examples presented in the lesson, while others are labeled as Higher-Order Thinking Problems or Test Prep.

The instructional materials for Reveal Math Grade 6 meet the expectations that the design of assignments is intentional and not haphazard.

Modules include a Launch, which provides students an overview of the topics found in the module. A Vertical Alignment tab provides teachers information on Vertical Alignment between and within grade levels. Lessons are presented in a logical order that builds coherence throughout the grade. 

Each Lesson follows a consistent format that develops learning through building conceptual understanding, providing opportunity for practice of procedural skills, and providing application in real-world situations. Exercises intentionally encourage a progression of understanding and skills, and the format includes three main sections, each including multiple parts: 

• Launch: Warm Up (addresses prerequisite skills); Launch the Lesson (includes class discussions and short videos; Today’s Standards; and What Vocabulary Will You Learn?.
• Explore and Develop: Explore (provides Inquiry questions for the students to explore); Learn (guided instruction); Examples (scaffolded problems for students to work through); Apply (guided application problems); and Check (one problem follows each example to assess student understanding).
• Reflect and Practice: Exit Ticket; Practice Problems; Spiral Review Lesson; and Assessments (when applicable).

The instructional materials for Reveal Math Grade 6 meet the expectations for prompting students to show their mathematical thinking in a variety of  ways. Examples include:

• In Lesson 1-7, students record responses using their notebooks, paper, or other note-taking device.
• In Lesson 4-4, students verbally defend or critique the work of others in written form to show understanding when ordering rational numbers in various forms.
• In Module 6, students build models for a problem using bar diagrams and equations.
• In Lesson 7-3, students use a diagram and a coordinate plane to represent a linear equation.
• In Lesson 5-3, students use manipulatives (algebra tiles), in student pairs, to write algebraic expressions.
• In Lesson 9-3, students construct written responses to explain their thinking when finding surface area of triangular prisms.
• In Module 7, Performance Task, students evaluate data in a table and graph, generate equations, complete tables, and explain their reasoning related to the situation.
• In all lessons, students use a digital platform to conduct and present their work.

The instructional materials for Reveal Math Grade 6 meet expectations for having manipulatives that are faithful representations of the mathematical objects they represent and, when appropriate, are connected to written methods.

The series includes a variety of virtual manipulatives, although the materials rarely include physical manipulatives.

• Manipulatives and other mathematical representations are consistently aligned to the mathematical content in the standards.
• Virtual manipulatives, such as number lines, double number lines, bar diagrams, pie charts, algebra tiles, x-y tables, coordinate planes, and flashcards, are used for developing conceptual understanding.
• There are embedded links to programs such as Web Sketchpad and eTools.

The instructional materials for Reveal Math Grade 6 meet the expectations for providing teachers with quality questions for students. These questions support teachers in planning and providing effective learning experiences. 

• Questions are consistently provided throughout each lesson to help guide students’ mathematical development. The questions develop vocabulary of the  lesson, encourage mathematical discourse, develop conceptual understanding, promote justifications of thinking, and include differentiated questions to ask while students engage in the Interactive Presentation. Examples include: “If the triangles are similar, what do you know about the lengths of the sides?”and “What does it mean if your answer is not a whole number?”
• The Teacher Edition provides question prompts that are additional to what is in the student materials. 
• Explore sections include Inquiry Questions such as, “Why is writing an equation a useful way to represent and solve a real world problem?”

The instructional materials for Reveal Math Grade 6 meet the expectations for containing annotations and suggestions on presenting the content and using embedded technology for student learning.

The Teacher’s Edition contains annotations and suggestions in the margin notes at every phase of instruction, including students’ independent practice. In addition, teachers are provided with ample planning information at the Module and Lesson levels.

Annotations and suggestions at the Module level include:

• Module Goal
• Focus (standards addressed)
• Be Sure to Cover (prerequisites required)
• Coherence (vertical alignment)
• Rigor (how rigor is specifically addressed in the module)
• Suggested Pacing
• Analyze the Probe (what the probe measures, targeted misconceptions, when to assign the probe, actions that should be taken after the probe)
• Essential Questions (suggestions for students’ graphic organizers)
• What Will You Learn? (students self ratings before and after)
• Dinah Zike Foldables (instructions for foldables)
• Launch the Module (notes on what the Launch video addresses)
• Pause and Reflect
• What Vocabulary Will You Learn?
• Are You Ready? (prerequisite information)
• Mindset Matters (notes on risk taking, regular reflection, “Not Yet” Doesn’t Mean “Never”, etc.)

Annotations and suggestions at the Lesson level include:

• Content standards and Mathematical Practices
• Essential Question
• Lesson Activities
• Differentiate (including Resources and Language Development Support)
• Vertical Alignment (containing Previous, Now, and Next learning)
• Rigor
• Mathematical Background
• What if my students don’t have devices?

 Cues to reference online resources include:

• Additional teaching notes 
• Videos on how to teach the Mathematical Practices
• Assistance with the Talk About It! questions to promote discourse
• Performance reports of the checks
• Extra examples

The instructional materials for Reveal Math Grade 6 meet the expectations for providing strategies for gathering information about students’ prior knowledge within and across grade levels. There are multiple opportunities to gather information about prior knowledge and prepare for the content addressed in the Module. 

In the beginning of the school year, Diagnostic and Placement Tests can be assigned to determine whether a student has mastered prerequisite concepts for the current course. 

At the beginning of each Module, Be Sure to Cover lists prerequisite skills required for the module. The Module Pretest can be used to diagnose student readiness for the module, and Are You Ready? has a few exercises over necessary prerequisite concepts. The Teacher Edition contains an extensive list of prerequisite concepts.

At the beginning of each Lesson, Warm-Up exercises address prerequisite skills for the lesson.

The instructional materials for Reveal Math Grade 6 meet the expectations for providing strategies for teachers to identify and address common student errors and misconceptions.

• Formative Assessment Math Probes by Cheryl Tobey provide an analysis of targeted misconceptions. “This formative assessment asset helps the teacher to target common misconceptions students may have about the mathematics covered in this module. The Teacher’s Guide provides a key as well as a description of common misconceptions, and how they might be addressed.” There is one per Module which can be completed more than once to ensure that misconceptions have been addressed.
• Each lesson notes anticipated misconceptions, and teachers are provided ideas to help students address them.
• Within Independent Practice, there are Common Misconception pointers related to specific problems such as, “Students may mistakenly order integers based on absolute value rather than numerical value or vice versa.” and “Some students may not identify like terms correctly when one of the coefficients is 1 or -1 since the number 1 is not written explicitly.”

The instructional materials for Reveal Math Grade 6 meet the expectations for providing opportunities for ongoing review and practice, with feedback, for students in learning both concepts and skills.

• After each example in a lesson, there is a Check to assess understanding of that component of the lesson. These are done online so teachers can access performance reports. If students do not “pass”, teachers can assign relevant practice.
• Exit Tickets are provided in every lesson.
• Put It All Together, mid-module, formative assessments provide opportunities to assess student understanding of multiple lessons.
• Classroom discourse has students discuss their thinking and provides another formative assessment opportunity for teachers to identify what students have learned and respond with appropriate prompts and clarifications.
• Test Practice pages are provided at the end of each module to help students review module content and prepare for online assessments. Many of the exercises mirror the questions students will see on the online assessments.
• Each lesson contains additional digital practice allowing students to complete several problems, getting immediate feedback about what is correct.
• Some lessons include a digital Spiral Review containing content from multiple lessons. The resource notes specify the exact concepts on the Spiral Review.

The instructional materials for Reveal Math Grade 6 meet the expectations for providing strategies to help teachers sequence or scaffold lessons so that the content is accessible to all learners.

• Each module introductory page includes Be Sure to Cover which identifies prerequisite skills students need for the module content.
• Each module and lesson includes tabs for pacing and vertical alignment. Vertical Alignment makes connections to both prior and future knowledge and skills to assist with sequencing instruction.
• The Warm Up at the beginning of each lesson “helps the teacher determine whether students are proficient in the prerequisite skills needed for this lesson.” 
• Each Module includes a Pretest that can be used to “diagnose students' understanding of the prerequisite skills required for this module.”
• Teachers Notes are embedded alongside the lessons and student tasks that provide prompts that scaffold instruction.
• Discussion questions are embedded in the Examples and Apply tasks.

The instructional materials for Reveal Math Grade 6 meet the expectations for providing teachers with strategies for meeting the needs of a range of learners.

• The opening page to each lesson contains Differentiate that lists learning resources available for use. These are identified and color-coded in the Teacher Edition as Approaching Level (AL), On Level (OL), and Beyond Level (BL). They include collaboration strategies, Remediation and Extension Tasks, and Arrive Math which is an intervention program integrated into Reveal Math.
• Questions for Mathematical Discourse in the Teacher Edition margin are also identified and color-coded as AL, OL, or BL. 
• After each problem during the instruction portion of the lesson, there is a computer-based Check to gauge student understanding. The Teacher’s Guide provides direction on using the data to assign practice problems and other exercises.
• Each lesson has Additional Examples that help students reinforce their understanding of the concept. It includes an extra problem for the teacher to use, as well as questions to help elicit meaningful responses.
• Supporting All Learners, an online resource, includes a Language Development Handbook which provides graphic organizers, note taking using sentence frames, and vocabulary worksheets. 
• Digital Differentiate activities include auto-scored Lesson Practice problems, Collaboration Strategy activities related to the math concepts/vocabulary, prerequisite skill Review activities, and a Personal Tutor.

The instructional materials for Reveal Math Grade 6 meet the expectations for embedding tasks with multiple entry-points that can be solved using a variety of solution strategies or representations.

• Talk About It! and Write About It! prompts often encourage students to describe their approaches to problems and to think about other possible approaches. 
• Each lesson presents an Inquiry question for students to explore, often with a digital resource such as Web Sketchpad. 
• Apply tasks include a variety of entry-points and a variety of solution strategies. 
• Common prompts for Apply problems involve different approaches to the tasks or strategies that students could use.

The instructional materials for Reveal Math Grade 6 meet the expectations for suggesting support, accommodations, and modifications for English Language Learners and other special populations.

In the Teacher’s Edition, ELL icons introduce various supports specifically related to students’ native languages such as a Spanish Interactive Student Edition, Digital Spanish Personal Tutors, or a Multilingual eGlossary. Additional supports for ELLs and other special populations include:

• Math-Language Building Activities
• Language Scaffolds
• Think About It! and Talk About It! prompts that assist in deepening understanding 
• Audio options
• Graphic organizers
• Web Sketchpad, Desmos, eTools
• A Language Development handbook found online in Program Resources. 
• Language Objectives for almost every lesson
• What Vocabulary Will You Learn? at the beginning of each lesson. The Teacher Edition provides a prompt for ELL students: “As you proceed through the chapter, introduce each vocabulary term using the following routine. Ask the students to say each term aloud after you say it. Define...Example…Ask...” 
• Each module has a Foldable Study Organizer containing key concepts/vocabulary which students create.

The Arrive Math Booster is a Tier 2 intervention program which provides digital mini-lessons for students who need a different presentation of the content addressed in the lesson.

The instructional materials for Reveal Math Grade 6 meet the expectations for providing a balanced portrayal of various demographic and personal characteristics.

• Multinational names are used in the examples and practice. Cartoon characters presented in the textbook represent students of both genders and various ethnicities.
• The diversity of names throughout the problems are used in ways that do not stereotype characters by gender, race, or ethnicity.
• When multiple characters are involved in a scenario, they are often doing similar tasks or jobs in ways not expressing gender, race, or ethnic bias, and there is no pattern in one character using more/fewer sophisticated strategies. 
• When people are shown, there is a balance of demographic and personal characteristics.