High School - Gateway 3

The instructional materials for Reveal Math Traditional 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 Reflect and Practice, which includes exercises that allow students to independently apply what they have learned. Practice exercises are found in the exit ticket, practice, spiral review, and activities.

The instructional materials for Reveal Math Traditional 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 courses. Lessons are presented in a logical order that builds coherence throughout the course. 

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 Traditional meet the expectations for prompting students to show their mathematical thinking in a variety of ways. Examples include:

• In Algebra 1, Module 2 Introduction, students are instructed to create a foldable to organize their notes.
• In Algebra 1, Module 8, Lesson 2, students fill in the blanks to answer missing steps of problems and construct responses to answer Think About It! Questions. 
• In Geometry, Module 4, Lesson 1, students use dynamic geometric software to explore reflections by manipulating coordinates. 
• In Geometry, Module 9, Lesson 5, students match trigonometric ratios to trigonometric expressions. 
• In Algebra 2, Module 3, Lesson 1, students use an interactive sketch to explore quadratic functions in the coordinate plane. 
• In Algebra 2, Module10, Lesson 4, students construct a relative frequency table and graph the probability distribution.

The instructional materials for Reveal Math Traditional 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 LearnSmart, Desmos, Web Sketchpad, ALEKS, and eTools.

The instructional materials for Reveal Math Traditional 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. 
• The Teacher Edition provides question prompts that are additional to what is in the student materials. 
• Explore sections include Inquiry Questions such as “How is graphing a linear inequality on the coordinate plane similar to and different from graphing on the number line?” (Algebra 1, Module 6, Lesson 5)

The instructional materials for Reveal Math Traditional 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 Traditional 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. 

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 Traditional 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 titled “Watch Out!” related to specific problems such as, “When determining the quantity to multiply by when rationalizing the denominator, make sure you raise the entire term under the radical to the power of n-x.” (Algebra 2, Module 6, Lesson 5).

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

• Check questions accompany one or more examples to assess student understanding. 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 Traditional meet the expectations for assessments clearly denoting which standards are being emphasized. 

Teachers can access metadata reports that indicate the standards that each assessment item addresses. These reports are found by accessing the Assessments menu, selecting the desired module Test Bank, and right clicking on the three dots to the right of the desired test and selecting Export Metadata. The metadata report will be located under My Downloads.

The instructional materials for Reveal Math Traditional meet the expectations that assessments include aligned rubrics and scoring guidelines that provide sufficient guidance to teachers for interpreting student performance and suggestions for follow-up.

• In the Checks, completed after each Example in the lessons, teachers can reference the performance results and are guided to assign differentiated practice as needed for remediation. 
• A chart is provided for teachers on the End of Module Review pages. Related standards and lessons for each question are referenced and can be used to determine areas of strength/weakness.
• Each module contains a Performance Task, which includes a scoring rubric. The rubric provides the expectations for student responses to the task and a suggested scoring guide based on student responses. The Performance Task and Rubric are located on each module’s landing page under Review and Assess.
• The online Printable Module Tests contain answer keys and are located on each module’s landing page under Review and Assess: On-Level Assessments (Form A) and Differentiated Assessments (Forms B and C).

The instructional materials for Reveal Math Traditional 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 include 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 Traditional 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, and Remediation and Extension Tasks.
• 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 Traditional 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 Traditional 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 instructional materials for Reveal Math Traditional meet the expectations for providing opportunities for advanced students to investigate mathematics content at greater depth. There are multiple opportunities to address the needs of advanced learners. Extensions are included that present students with opportunities for problem solving, and examples include:

• In Algebra 1, Module 2, Lesson 5, Extension, students work with absolute value equations with variables on both sides of the equal sign, whereas during the preceding lesson, students worked with absolute value equations with variables on only one side of the equal side. 
• In Geometry, Module 6, Lesson 2, Extension, students extend their learning of angle bisectors from the lesson to create an inscribed circle within a triangle. 
• In Algebra 2, Module 3, Lesson 7, Extension, students extend their learning of graphing a quadratic inequality from the lesson to graphing a set of quadratic inequalities.