6th Grade - Gateway 3

The materials reviewed for Reveal Math 2025 Grade 6 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 found in a variety of sections within the Implementation Guide, including the Overview, Why, Achievement Descriptors Overview, and Lesson Structure. Examples include:

• Unit 3: Ratios and Rates, Lesson 3-4: Determine Equivalent Ratios Using Graphs, Lesson Overview, Lesson Pacing states, “Session 1, Lesson Instruction 45 min; Launch Notice & Wonder; Explore Choose Your Option Activity-Based Exploration Graphs of Equivalent Ratios or Guided Exploration Soccer Balls; Wrap Up AEJ Concluding Questions or Assess Exit Ticket.” 

• Unit 4: Understand and Use Percentages, Lesson 4-5: Determine the Whole Given the Part and Percent, Session 1, Guided Exploration, Teacher Guidance states, “Use the double number line to generate an equivalent ratio that represents the original price. Explain your reasoning. Students work with a partner to create a double number line to represent the problem situation. Student-pairs explain their reasoning for the way in which they create their double number lines with the class. Other student-pairs listen and ask clarifying questions. Use and Connect Mathematical Representations What two data points can you initially plot on the double number line? Which number line can you complete before performing an operation? How do you extend the upper number line to find the original price?”

• Unit 5: Solve Area, Surface Area, and Volume Problems, Lesson 5-2: Determine the Area of Triangles, Lesson Overview, Orchestrating Rich Mathematical Discourse states, “In this lesson, students investigate the relationships that can be found between triangles and parallelograms. Give students time to explore and discover. Use these suggestions to guide student discussion during either the Activity-Based or Guided Exploration. 2. Monitor students’ thinking Activity-Based Exploration: Monitor students’ responses as they work together on the activity. Encourage students to make connections with strategies that they use to compute the area of other figures. Record strategies and insights that you would like to discuss with the class during the Activity Debrief.” 

Materials include sufficient and useful annotations and suggestions that are presented within the context of the specific lessons in colored tags labeled: Effective Teaching Practices (ETP), Math Practices and Processes (MPP), Math Mindset (MM), Language of Mathematics (LOM), Math Language Development (MLD), Multilingual Learner Scaffolds (MLL), and Math Language Routines (MLR). The Implementation Guide states: 

• Implementation Guide, Professional Learning Resources (page 68) states, “Reveal Math teachers have access to a comprehensive set of online professional learning resources to support a successful initial implementation and continued learning throughout the year. These self-paced, digital resources are available on-demand, 24 hours a day, 7 days a week in the Teacher Center for each grade.” Reveal Math Quick Start states, “The Quick Start includes focused, concise videos and PDFs that guide teachers step-by-step through implementing the Reveal Math program.” Digital Walkthrough Videos, “Targeted videos guide teachers and students in how to navigate the Reveal Math digital platform and locate online resources.” Expert Insights Videos state, “At the start of each unit, teachers can view a 3-minute video of Reveal Math authors and experts sharing an overview of the concepts students will learn in the unit along with teaching tips and insights about how to implement the lesson.” Instructional Videos with Reveal Math Authors and Experts state, “Annie Fetter: Be Curious Sense-Making Routines, John SanGiovanni: Number Routines and Fluency, Raj Shah: Ignite! Activities, Cheryl Tobey: Math Probes” Model Lesson Videos state, “Classroom videos of Reveal Math lessons being taught to students show how to implement key elements of the Reveal Math instructional model.” Ready-to-Teach Workshops state, “Curated, video-based learning modules on instructional topics key to Reveal Math can be used by teachers for self-paced learning or by district and school leaders as ready-to-teach packages to facilitate on-site or remote professional learning workshops.”

The materials reviewed for Reveal Math 2025 Grade 6 meet expectations for containing adult-level explanations and examples of the more complex grade/course-level concepts and concepts beyond the current course so that teachers can improve their own knowledge of the subject.

Materials consistently contain adult-level explanations, examples of the more complex grade/ course-level concepts, and concepts beyond the course within Unit Overviews and/or Lesson Overviews. Each Unit Overview has a Focus section that reviews the math background needed for the unit and a deep dive into the major theme of the unit. Teachers are provided with a coherence section that reviews the material that math students have learned, are learning, and will learn next. In the Lesson Overviews, teachers are provided with lesson highlights and key takeaways as well as the math background needed for the lesson. Example include:

• Unit 2: Understanding the World Around Us Through Statistics, Lesson 2-2: Represent and Describe Data in a Histogram, Lesson Overview, Lesson Highlights and Key Takeaways states, “In this lesson, students explore constructing and interpreting histograms based on data presented in frequency tables. They compare using a dot plot to using a histogram and they explore how changing data would change a histogram. Students are encouraged to use structure to approach the task. Histograms are a tool to display quantitative (numerical) data. The data displayed in a histogram can be described by its shape.”

• Unit 4: Understand and Use Percentages, Unit Overview, Focus states, “A Deep Dive into Understanding Percentages The concept of percentages is an integral part of our daily lives. We use percentages to represent battery life for electronics and completion of downloads or uploads; as rates of return in investments or tax rates; and as academic grades. Students likely have considerable experience in using percentages as a relative quantity (100% is all, 80% is most, 40% is some) but have not yet decontextualized percentages as mathematical quantities. Percentages represent relationships as ratios whose second term is 100. In fact, the word percent is derived from the Latin for “to hundred. A percentage is a proportional relationship in which the percent is the ratio of one quantity to 100 of the other quantity. Understanding and using percentages are foundational skills for statistics and probability, which students will study in Grades 7 and 8 and throughout high school.”

• Unit 6: Numerical and Algebraic Expressions, Lesson 6-1: Division Expressions with Fractions and Whole Numbers, Lesson Overview, Lesson Highlights and Key Takeaways states, “In this lesson, students explore how to use models to represent the division of a whole number by a fraction and a fraction by a whole number. Students relate multiplication expressions to division of fractions by whole numbers. Quotients of whole numbers divided by fractions can be found by using representations, such as tape diagrams. Quotients of fractions divided by whole numbers can be found by using representations and equations.”

• Unit 9: Relationships Between Two Variables, Unit Overview, Focus states, “A Deep Dive into Two-Variable Relationships Our understanding of cause and effect begins at an early age through experimentation with objects around us. Cause and effect can be modeled with a two-variable relationship; changing one variable causes an effect in the other variable. The variable that we control is the independent variable, and the variable that is subjected to the consequences of our changes is the dependent variable. Quantitative two-variable relationships exist in many facets of our lives: the total cost of x units of something, the amount of money we have left after spending x dollars, the distance we travel in x hours. Representing and analyzing quantitative relationships between variables are foundational skills for middle- and high-school mathematics, starting with concepts of linear functions and extending to quadratic, exponential, and trigonometric functions, geometric modeling, and statistics.

The materials reviewed for Reveal Math 2025 Grade 6 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 throughout the grade level. A Unit Planner is provided at the beginning of each unit, identifying each lessons’ alignment to math, language, and math mindset objectives; key vocabulary; materials to gather; rigor focus; and content standard. At the lesson level, content standards are identified as major, supporting, or additional; and Math Practices and Processes are also provided. Examples include:

• Unit 3: Unit Planner, Ratios and Rates, Lesson 3-1, Understand Ratios, Standards: 6.RP.A.1 and 6.RP.A.3 are identified for this lesson.

• Unit 3: Ratios and Rates, Lesson 3-2, Understand Rates and Unit Rates, Major standards 6.RP.A.2, 6.RP.A.3, and 6.RP.A.3.b; and Math Practices and Processes, MPP: Reason abstractly and quantitatively are identified for this lesson. 

Explanations of the role of the specific grade-level mathematics are present in the context of the series. Each Unit Overview provides a Math Background and a Deep Dive into the concept. At the lesson level, sections about Coherence and Math Background are also provided. Examples include: 

• Unit 2: Understanding the World Around Us Through Statistics, Unit Overview, Math Background states, “The learning progression of the elementary years includes categorical data (classifying objects, crafting data representations, answering questions based on graphs) and measurement (generating measurement data, representing data on line plots, answering questions about data). The data analysis performed in Grade 6 also builds upon number and operations skills (multi-digit division, decimal notation) developed in Grades 4 and 5. Grade 6 students develop a deeper understanding of variability, using measures of center and measures of spread to describe and compare data distributions. They use dot plots, histograms, and box plots to represent and analyze data distributions.”

• Unit 5: Solve Area, Surface Area, and Volume Problems, Lesson 5-5: Determine the Volume of Rectangular Prisms, Coherence, Previous states, “Students determined volume using unit cubes. Students determined areas of polygons and composite figures.” Now states, “Students determine volumes of rectangular prisms by using unit cubes. Students determine volumes of rectangular prisms by using a formula.” Next states, “Students explore faces and surface areas of three-dimensional figures. Students solve problems involving volume, area, and surface area.”

• Unit 7: Integers, Rational Numbers, and the Coordinate Plane, Lesson 7-4: Compare and Order Integers and Rational Numbers, Math Background states, “Students’ study of comparing and ordering rational numbers draws on concepts and skills students have gained in previous grades and units. Use Number Lines Grade 3 students used number lines to plot and compare fractions. Compare Decimals Grade 5 students compared decimal numbers to the thousandths place. Understand Rational Numbers Earlier in Grade 6, students plotted rational numbers on the number line.” 

• Unit 8: Equations and Inequalities, Unit Overview, A Deep Dive into Equations and Inequalities states, “The concept of equality is an integral part of mathematics instruction that begins in kindergarten when students decompose numbers and understand that two parts are equal to the whole. The concept of inequality follows from equality; if two quantities are not equal, then one must be greater than the other…”

The materials reviewed for Reveal Math 2025 Grade 6 meet expectations for providing explanations of the instructional approaches of the program and identification of the research-based strategies.

The Grade 6-8 Implementation Guide includes a variety of references to both the instructional approaches and research-based strategies. Each Unit Overview and Lesson Overview includes explanations of instructional approaches and teacher directions throughout the lesson. Examples include but are not limited to:

• Implementation Guide, Lesson Walk-Through, Explore & Develop (page 26) states, “For the main instruction, the teacher can choose between two equivalent approaches to instruction, both of which provide the same level of access to rigorous content. For each session, there is a full page of teacher support to implement either instructional option.” Unit Walk-Through, Mathematical Modeling (page 34) states, “As part of the STEM focus, each unit ends with a Mathematical Modeling project that offers students the opportunity to apply the math concepts they have learned. Each unit contains two options from which students can choose, promoting engagement and student agency. These STEM-focused projects also encourage students to make decisions about how to approach the project, what mathematics to use, and how to present their project findings.”

• Unit 1: Math Is…, Unit Overview, Effective Teaching Practices, “Ambitious Teaching In 2014, the National Council for Teachers of Mathematics released Principles to Actions: Ensuring Mathematical Success for All, a publication designed to support teachers in implementing “ambitious teaching,” an approach to teaching that views students as able to engage productively in the problem-solving process and encourages and values students’ thinking and ideas. To implement “ambitious teaching,” the authors of Principles to Actions offer eight teaching practices. These research-based practices are grounded in the goals of helping students develop sense-making, thinking, and reasoning skills. Each unit will highlight one of the eight teaching practices, providing an overview of what the practice means and how it helps to contribute to students’ success in learning mathematics.”

• Unit 2: Understanding the World Around Us Through Statistics, Unit Overview, Effective Mathematics Teaching Practices, Elicit and Use Evidence of Student Thinking states, “As students progress through the unit, ask them to explain their reasoning. Understanding the reasoning for their answers whether they are correct or incorrect—allows for targeted instruction to reinforce and expand or enhance their understanding or address misconceptions and misunderstandings in a timely way. As students learn about statistics, there are multiple possibilities for errors in execution. Students may have misconceptions about the difference between the median and the mean and when it is appropriate to use each measure; the difference between measures of variation and measures of center and what each represents; how box plots represent a data set. Ask frequent questions, especially those that require reasoning. Use students' responses to inform instruction and determine what kinds of practice and review might be necessary. For example, as students are introduced to each data display, monitor closely their responses and thinking to ensure they understand how each display represents data and how they can accurately analyze the data. In Lesson 2-9, if students struggle to calculate the mean absolute deviation, work through additional examples with small data sets that have single-digit deviations from the mean to ensure students understand the concepts and steps involved.” 

• Unit 3: Ratios and Rates, Unit Opener, Preparing for Explore and Develop, “How Do I Choose? To decide which exploration to implement for the lessons in this unit, consider the following: Activity-Based Exploration (ABE) is designed for optimal student engagement and deep understanding and is grounded in research-based teaching practices. In this unit, the ABE activities in Lesson 3-1, 3-2, and 3-5 offer unique learning opportunities. Students are introduced to ratios for the first time in Lesson 3-1 and to rates in Lesson 3-2. The ABEs for these two lessons offer students opportunities to dig into the relationships between the parts and the whole that are foundational to these concepts. In Lesson 3-5, students compare ratio relationships. The ABE allows students to build understanding of how to compare ratio relationships. Consider the grouping of students when planning for the ABE. Because students are expected to work productively on their own, plan groups of students to provide the richest learning opportunities for everyone in the group.”

• Unit 9: Relationships Between Two Variables, Lesson 9-1: Explore Relationships Between Two Variables, Session 1, Activity-Based Exploration, Support Productive Struggle states, “As student-pairs explore the activities, check that all pairs understand the task. If students need guidance or support, ask: What relationships do you notice that could be described as dependent? What does it mean to be dependent? Independent? Hands-On: Student-groups build a ramp using the materials listed above or using materials of your choice. One student rolls the toy car down the ramp while another records the distance it travels. They change the angle of the ramp and make predictions about distance traveled. If students need guidance or support, ask: What relationships do you notice that could be described as dependent? What do you notice about the relationship between height and length of the ramp in your data?”

The materials reviewed for Reveal Math 2025 Grade 6 meet expectations for providing a comprehensive list of supplies needed to support instructional activities.

Each Unit Planner, under Materials to Gather, provides a list of materials needed for each lesson. Additionally, each Lesson Overview provides a materials section on the first page. Examples include: 

• Unit 5: Solve Area, Surface Area, and Volume Problems, Lesson 5-6: Represent Three-Dimensional Figures in Two Dimensions, Lesson Overview, Materials states, “The materials may be for any part of the lesson. grid paper, Nets Teaching Resource, ruler, scissors, tape.”

• Unit 7: Integers, Rational Numbers, and the Coordinate Plane, Unit Planner, Materials to Gather: Blank Open Number Lines Teaching Resource, Counting Numbers and Their Opposites Cards Teaching Resource, ruler or string, Blank Open Number Lines 2 Teaching Resource, Four Lines Playing Board Teaching Resources, Rational Number Cards Teaching Resource, Coordinate Plane 2 Teaching Resource (optional), Town Map Teaching Resource, colored pencils.” 

• Unit 8: Equations and Inequalities, Unit Planner, Materials to Gather: calculator, balance, nickels, paper clips, Blank Open Number Lines Teaching Resource, Inequalities Table Teaching Resource, colored pencils or markers.

• Unit 10: Math Is…, Lesson 10-3: Math is Playful, Lesson Overview, Materials states, “The materials may be for any part of the lesson. counters or chips.”

The materials reviewed for Reveal Math 2025 Grade 6 meet expectations for having assessment information included in the materials to indicate which standards are assessed.

The materials consistently and accurately identify grade-level content standards for formal assessments in the Item Analysis within each assessment answer key. Examples include:

• Benchmark Assessment 1, Item 2 states, “Rodrigo asks his classmates a statistical question. Which could be the question that Rodrigo asks his classmates? A. What state do you live in? B. How many pets do you have? C. What is the name of the principal? D. How many laps are equal to a mile?” In the Item Analysis, the question is aligned to 6.SP.1 "Understand statistical questions" and MP2, Reason abstractly and quantitatively.

• Unit 4: Understand and Use Percentages, Unit Assessment, Form A, Item 7 states, “Jordan completes \frac{5}{8} of his homework assignment. What percent of his homework does he complete?” In the Item Analysis, the question is aligned to 6.RP.3c "Ratios with Unknown Parts" and MP6, Attend to precision.

• Unit 5: Solve Area, Surface Area, and Volume Problems, Performance Task states, “Zoe and Adam are making posters for an event, Zoe’s poster is in the shape of a trapezoid and Adam’s poster is in a shape of a triangle. Some materials for the event are stored in different-shaped containers including a rectangular prism, triangular prism, and square pyramid. Part A The dimensions of Zoe’s poster are shown. What is the area of Zoe’s poster?” Teacher’s Guide, “Students draw on their understanding of area, volume, and surface area. Use the rubric shown to evaluate students’ work. Standards: 6.G.A.1, 6.G.A.2, 6.G.A.4.”  

• Unit 7: Integers, Rational Numbers, and the Coordinate Plane, Math Probe, Compare Rational Numbers, Question 1 states, “For each item, determine whether the sign that replaces the ? should be >, <, or =. 1. -7.5 ? -7 Circle one: > < =” Analyze the Probe, “Review the probe prior to assigning it to your students. In this probe, students determine the correct inequality or equal sign to complete each statement. Targeted Concept The magnitude of two negative quantities can be compared by reasoning about the distances from zero based on their positions on a number line or by expressing both in decimal or fraction form. Targeted Misconceptions Students may ignore the negative number signs and apply positive number comparisons. Students may incorrectly interpret the relative position of numbers on a number line.” The question is aligned to 6.NS.7.

The materials reviewed for Reveal Math 2025 Grade 6 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.

The assessment system provides multiple opportunities to determine students' learning, and sufficient guidance for teachers to interpret student performance is reinforced by the provided answers and sample student work. The system continuously updates with real-time data from sources like NWEA MAP, Reveal, and ALEKS, offering insights into student proficiency. Teachers receive automated, data-driven recommendations and access to scaffolded digital mini-lessons, AI-powered learning paths, and small group lesson options for intervention, reinforcement, or acceleration. While teachers can refer back to specific lessons and utilize real-time data insights, they are also provided with suggested practice and lessons based on the standards students missed from assessments to support student progress. Examples include:

• Unit 3: Ratios and Rates, Readiness Diagnostic states,“Administer the Readiness Diagnostic to determine your students’ readiness for this unit. Use the Intervention Lessons recommended in the table to provide targeted intervention to students who need it. These lessons are available in the Digital Teacher Center and are assignable.” Item 2 states, “There are 1,323 students at Rockland High School. If there are 49 classes at one time, approximately how many high school students are in each class?”

• Unit 7: Integers, Rational Numbers, and the Coordinate Plane, Performance Task, Part A states, “A parallelogram is going to be plotted on a coordinate plane. Part A: One of the vertices of a parallelogram is (-7,6). Which coordinate has the greater absolute value?” An exemplar answer is included, “-7; The absolute value of -7 is 7 and the absolute value of 6 is 6. |-7|>6." Teacher guidance includes a rubric for Part A, “2 POINTS Work reflects proficiency. Student correctly identifies the coordinate and explains. 1 POINT Work reflects developing proficiency. Student correctly identifies the coordinate but fails to explain. 0 POINTS Work reflects weak proficiency. Student’s answer and explanation are incorrect.”

• Unit 8: Equations and Inequalities, Math Probe, Item 1 states, “Six friends went out to eat and split the $66 bill evenly. How much money, in dollars p, did each friend pay?” A sample of correct student work is included in the teacher guide states, “Review the probe prior to assigning it to your students. In this probe, students select all of the equations that can represent the given situation and explain their choice. Targeted Concept: Understand the mathematical meaning of words used to describe relationships among quantities and know that different mathematical equations can be used to represent the same mathematical relationships. Targeted Misconceptions: Students may incorrectly determine the operation needed to solve the equation. Students may believe there is only one correct equation for solving a problem.”

• Unit 9: Relationships Between Two Variables, Unit Assessment, Form A, Item 14 states, “The owner of a coffee shop is donating a portion of the day’s proceeds to charity. For each cup of coffee sold, he will donate $0.50. Part A Write an equation to represent the relationship between the number of cups of coffee sold c and the money d, in dollars, donated to charity.” Item Analysis, “Item 14A DOK 2, Lesson 9-3, Equations of Two-Variable Relationships, Standard 6.EE.C.9” The Item Analysis and Plus+ Personalized Learning identify specific personalized practice and teacher-led mini-lessons to address prerequisites, reinforce learning, support on-lesson instruction, or provide extensions.

The materials reviewed for Reveal Math 2025 Grade 6 meet expectations for providing assessments that include opportunities for students to demonstrate the full intent of grade-level/course-level standards and practices across the series.

According to the Implementation Guide, “Reveal Math offers a comprehensive set of assessment tools designed to be used in one of three ways: as a diagnostic tool to determine students’ readiness to learn and diagnose gaps in their readiness; as a formative assessment tool to inform instruction, and as a summative assessment tool to evaluate students’ learning of taught concepts and skills.” The assessment system includes but is not limited to: Course Diagnostic, Unit Diagnostic, Lesson Quiz, Exit Ticket, Math Probe, Unit Assessment, Performance Task, Benchmark Assessment, and End of the Year Assessment. These assessments use a variety of question types, such as constructed response, multiple select, multiple choice, single answer, and multi-part. The assessments consistently list grade-level content standards for each item. While Mathematical Practices are not explicitly identified on assessments, they are regularly assessed. Students have opportunities to demonstrate the full intent of the standards using a variety of modalities (e.g., oral responses, writing, modeling, etc.). Examples include:

• Unit 2: Understanding the World Around Us Using Statistics, Lesson 2-3: Describe Data Using the Median, Session 2, Assess to Inform Differentiation, Lesson Quiz, Items 2 and 3 state, students calculate the median and explain their answer. “The list below shows the number of laps that Katie has swum each morning for the last 8 days. 12, 8, 6, 10, 8, 6, 16, 10” Item 2, “What is the median number of laps that Katie has swum?” Item 3 states, “How would the median change if Katie were to swim 15 laps tomorrow? Explain your answer.” (6.SP.3 and MP8)

• Unit 6: Numerical and Algebraic Expressions, Performance Task, Part A, students write and model an algebraic expression, and describe what each variable represents. The task states, “Ron buys 4 pounds of bananas, 2 pounds of mangos, and 6 pounds of papaya. He has a coupon for $10 off his purchase. Part A: Write an algebraic expression that represents the money Ron spends. Describe what each variable represents.” (6.EE.2 and MP4)

• Benchmark 2, Item 12, students compare ratios and determine which size provides the best buy. “The table shows the costs of four different size spaghetti boxes. Which size provides the best buy? A. 8 ounces B. 16 ounces C. 32 ounces D. 48 ounces” Students are provided a table labeled Spaghetti Costs. The left column is labeled, “Size (oz)” with the numbers 8, 16, 32, and 48 provided. The right column is labeled, Cost ($)” with the prices $0.64, $1.12, $1.92, and $3.36 (6.RP.3 and MP7)

• Unit 9: Relationships Between Two Variables, Unit Review, Mathematical Modeling, students are assessed through a constructed response by choosing one of two projects on melting glaciers. The materials state, “Scientists use a variety of models to explain and predict how glaciers change. The mass of a glacier increases as snow and ice accumulate, and decreases as snow and ice melt and run off. Choose one of the projects to complete. Project One Melting glaciers and rising sea levels have accelerated in recent decades. The rising sea level can threaten infrastructure, such as bridges, roads, and water supplies, and create stress on coastal ecosystems. Figure 1 below shows the average cumulative mass lost by a set of “reference” glaciers since 1956– that is, how much mass has been lost, in total, since 1956. Figure 2 below shows the cumulative changes in sea level for the world’s oceans since 1880– that is, how much sea level has changed, in total, since 1880. You are working with local officials in a coastal area to plan for potential impacts of climate change. Provide an analysis of the data that you could share with local officials. In your analysis, include a prediction of potential future impacts and recommendations for how local officials should respond.” (6.EE.9 and MP4)

The materials reviewed for Reveal Math 2025 Grade 6 meet expectations for providing extensions and/or opportunities for students to engage with grade-level/course-level mathematics at higher levels of complexity.

Advanced students have opportunities to think differently about learning with extension activities and are not required to do more assignments than their classmates. The Implementation Guide, Professional Learning Resources (page 65) states, “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.” Specific recommendations are routinely part of the Differentiate and STEM sections of lessons and Units, as noted in the following examples: 

• Unit 2: Understanding the World Around Us Through Statistics, Lesson 2-4: Understand and Describe Data in a Box Plot, Differentiate, Extend Thinking, students extend their thinking of 6.SP.4, display numerical data in plots on a number line, including dot plots, histograms, and box plots. The materials state, “For exercises 1-6, use the initial data set to complete each problem. 2, 1, 5, 4, 6, 3, 8, 9, 2, 4, 3, 5, 2, 6, 3, 2, 9, 12, 8, 7, 4 1. Use the data to draw a box plot. 2. Add 3 to each piece of data and draw a new box plot. How does the box plot change? 3. Subtract 1 from each piece of data and draw a new box plot. How does it change? 4. Double each piece of data and draw a new box plot. How does the box plot change? 5. Half each piece of data and draw a box plot for the new data. How does this change the box plot?”

• Unit 3: Ratios and Rates, Lesson 3-7: Ratio Reasoning: Convert Measurements Between Systems, Differentiate, STEM Adventures, students apply and extend their learning of 6.RP.3.d, use ratio reasoning to convert measurement units, manipulate and transform units appropriately when multiplying or dividing quantities. The materials state, “In this STEM Adventure, students learn about fish farms, overfishing, and efforts to sustain fish populations. Then they use rates and ratios to make fish feed, analyze population data, and model how fishing rates affect fish populations. 

• Unit 6: Numerical and Algebraic Expressions, Lesson 6-4: Write and Evaluate Numerical Expressions with Exponents, students apply and extend their learning of 6.EE.1, write and evaluate numerical expressions involving whole-number exponents. The materials state, “In this STEM Adventure, students learn what practices help make agriculture sustainable. Then they use their knowledge of numerical and algebraic expressions to help solve problems as they farm and produce food in a sustainable way. Finally, they help a food truck calculate their profits. 

• Unit 8: Equations and Inequalities, Lesson 8-1: Understand Equations and Their Solutions, Differentiate, Extend Thinking, students extend their learning of 6.EE.6, use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number. The materials state, “For exercises 1-8, substitute the values into the equation to determine which one is the solution to the equation. Show your work. Use your answers to finish the joke’s punchline. If there is no solution, leave a blank. 1. 48 + x = 100 A. 52 B. 62 C. 72.”

The materials reviewed for Reveal Math 2025 Grade 6 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.

Within the Implementation Guide, Support for Multilingual Learners, Unit-Level support (page 50) states, “At the unit level are three features that provide support for teachers as they prepare to teach English Learners. The Designated Language Support 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.” Lesson-level support, Language Objectives state, “In addition to a content objective, each lesson has a language objective that identifies a linguistic focus of the lesson for English Learners.” Multilingual Learner Scaffolds state, “Multilingual Learner Scaffolds provide teachers with scaffolded supports to help students participate fully in the instruction. 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.” Support for active participation in grade-level mathematics is consistently included within lessons. Examples include: 

• Unit 1: Math Is…, Unit Overview, Math Language Development states, “Language Development – Academic Language Effective sentences in this unit, students will explain their thinking on how they use and interact with math in their lives and in academic settings. To communicate their ideas effectively, students will need to be able to speak and write clear, grammatically correct sentences. Tell students that effective sentences follow basic rules. Some of these conventions may be different from those that students are accustomed to in their home language.”

• Unit 2: Understanding the World Around Us Through Statistics, Unit Overview, Multilingual Learner Scaffolds state, “Entering/Emerging Have students find examples of formulas. Point out that formulas are like examples without words. Tell students that there will be many times when they can respond to a question by showing a formula or a sequence of equations. Have students collect and discuss examples of formulas and other text features. Create a display and begin labeling displays with words and phrases. Developing/Expanding Bring students’ attention to the highlighted terms throughout the unit. Tell students that the highlighting indicates that a term is important. Have students make flash cards or word lists using the highlighted terms. Bridging/Reaching: Have students use the headings on the pages to predict the general topic of the lessons.” 

• Unit 5: Solve Area, Surface Area, and Volume Problems, Lesson 5-3: Determine the Area of Trapezoids, Lesson Overview, Language Objectives state, “Students define terms in speech and writing. To optimize output, students will participate in MLR: Compare and Connect, MLR: Stronger and Clearer Each Time, and MLR: Critique, Correct, and Clarify.”

• Unit 6: Numerical and Algebraic Expressions, Lesson 6-6: Identify Equivalent Algebraic Expressions, Session 1, Activity-Based Exploration, Multilingual Learner Scaffolds state, “Entering/Emerging Allow students to use symbols, circling, and underlining to visually represent their responses. As students complete the activity, ask them to respond to the question What happens here? If students provide correct but incomplete answers, restate their thinking in a complete sentence that incorporates the word or phrase they used. Developing/Expanding As students work, circulate, and listen to the words they use to discuss how the expressions are simplified. Provide assistance and encourage the use of academic vocabulary such as rearrange, group, original, simplify, and redistribute. Clarify meaning of unfamiliar words. Bridging/Reaching Have students test their responses to the Concluding Questions by generating an example. Tell students to include this information in their responses.

The materials reviewed for Reveal Math 2025 Grade 6 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.

Each lesson includes a list of materials needed for teachers and students. Examples include:

• Unit 2: Understanding the World Around Us Through Statistics, Lesson 2-10: Choose Appropriate Measures, Session 1, Activity-Based Exploration states, “Digital: Using Websketch^TM, students explore measures of center of data sets. Hands-On: Students create a dot plot using the Blank Open Number Lines, Teaching Resource for the data shown in the Average Salary Teaching Resource and answer questions about measures of center.”

• Unit 5: Solve Area, Surface Area, and Volume Problems, Lesson 5-1: Determine the Area of Parallelograms and Rhombuses, Session 1, Activity-Based Exploration states, “Digital: Students explore finding the area of parallelograms using two different methods. Before students begin the activity, have them explore the Websketch^TM tools they will be using. Ensure that they understand how to use the Height, Measure, and Calculate tools. Explain that they will look at the parallelogram from different perspectives as they determine the area of the parallelogram. Hands-On: Students determine which figure on the Area of Quadrilaterals Teaching Resource has the greatest area. Students can cut the paper and move the pieces around to form squares or rectangles if needed.”

•  Unit 6: Numerical and Algebraic Expressions, Lesson 6-7: Find Factors and Multiples, Session 1, Activity-Based Exploration states, “Hands-On: Activity 1: Place the pencils and pens where all students can see them. Present the scenario: You are helping out in the school store. You are tasked with selling a combo pack of writing utensils as a back-to-school item. Each combo pack needs to have an equal number of pencils and an equal number of pens. Activity 2: Students find the common multiples of the weeks with a painting class and weeks with a pottery class using the Community Center Classes Teaching Resource. Student-pairs work together to answer the question in their Activity Exploration Journals.”

• Unit 10: Math Is…, Lesson 10-3: Math Is Playful, Session 1, Activity-Based Exploration states, “Group students in pairs or small groups to work on this activity. Today we will make statements about how we can win games. Digital: Using Websketch^TM, students read and follow the rules to play the game of Nim several times with a partner. Hands-On: Have students arrange the counters or chips in three rows: one row of three, one row of four, and one row of five. Tell students they will play a game in pairs. They will take turns removing chips. On each student’s turn, they can remove any number of chips, as long as those chips come from the same row. The winner of the game is the player who takes the last chip. Have students play the game several times, paying attention to strategies they can implement to win and whether the player who goes first has an advantage.”