7th Grade - Gateway 3

The materials reviewed for Reveal Math 2025 Grade 7 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: Proportional Relationships, Lesson 3-6: Use Proportional Reasoning to Solve Multi-Step Ratio Problems, Develop, Session 2, Activity Based Exploration, Teacher Guidance states, “Facilitate Mathematical Discourse Facilitate a whole-class discussion of the students’ exploration findings. How did you approach the problem situation? What did you use to represent the relationships given in the problem situation? Discussion Supports: As students engage in discussing the answers to the questions, have them pay attention to each other’s understanding in order to increase their fluency in mathematical discussion about intervals, rate, proportions, and rations. Restate statements they mask as a question to seek clarification and to confirm comprehension, providing validation or correction when necessary. Encourage students to challenge each other's ideas when warranted, as well as to elaborate on their ideas and give examples. Elicit Evidence of Student Understanding states, “As students discuss the Concluding Question from the activity, listen for students’ understanding of proportional reasoning and how it can be used to solve multi-step problems. How did your initial conjecture about the solution change as you worked through the problem?” MPP: Have students share how their ideas about the problem changed throughout their exploration. Encourage students to highlight ways they need to change their thinking and strategies to solve the problem. Have students review their responses to the Concluding Question and make any adjustments based on the discussions with their partner and the class. Then encourage students to share their responses. How can you use proportional reasoning to solve a multistep ratio problem?”

• Unit 5: Sampling and Statistics, Lesson 5-4: Use Multiple Samples to Describe Accuracy, Explore, Session 1, Activity-Based Exploration, Using Multiple Samples, Teacher Guidance states, “Support Productive Struggle: As student-pairs explore the activity, check that all pairs understand the task and are completing their Activity Exploration Journal pages. If students need guidance or support, ask: How close to the mean of the sample-means are most of the sample means/ How do you think sample-size affects the variation among sample means? Why can we use the relationship between the sample means and the mean of the sample means to gauge error? Why is the mean of the sample means a very accurate estimate of the population mean? How many population values were used to calculate each sample mean? How many population values were used to calculate each sample mean? How many population values are represented in the mean of the sample means? Why is there less variation among 30 sample means than there is among 30 population values that form a sample?”

• Unit 8: Solve Problems Using Equations and Inequalities, Lesson 8-1: Solve Equations: px + q = r, Lesson Overview, Orchestrating Rich Mathematical Discourse states, “In this lesson, students explore solving equations of the form px + q = r. It is important that students have opportunities to discuss their reasoning when determining how to find a solution. These suggestions can help optimize the discussion about solving equations that can be constructed during either the Activity-Based or Guided Exploration. 1. Anticipate likely student responses. Activity-Based Exploration: As you plan for the lesson, think about the strategies your students are likely to use and misconceptions some students may have.. The visual provided in the digital option may help students grasp the need to apply properties of equality. The possible solution-steps that students choose from the hands-on activity may help them understand how to determine the correct operations to isolate the variable. Guided Exploration: As you plan for the lesson, review the questions in the teacher presentation and anticipate student responses to those questions. Consider how to explain to students why there are negative values when solving equations, but positive solutions. Think about how to respond to students’ questions about why they must perform the same operation to both sides of an equation.”

Materials include sufficient and useful annotations and suggestions that are presented within the context of the specific lessons in colored tags that are 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 state, “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 7 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: Solve Problems Involving Geometry, Unit Overview, Focus states, “A Deep Dive into Solving Problems Involving Geometry, Geometric reasoning is an integral part of mathematics instruction from Kindergarten through high school. Students are introduced to the properties of geometric figures through exploration with concrete objects. As they progress through the elementary grades, their observations are formalized into definitions of different figures. In Grades 6-8, students synthesize their understanding of properties of geometric figures with their knowledge of expressions and equations to derive and apply formulas for area, surface area and volume. Later, students will revisit formulas and properties, giving formal arguments to explain their validity.” 

• Unit 4: Solve Problems Involving Percentages, Lesson 4-1: Connect Percentages and Proportional Reasoning, Lesson Overview, Lesson Highlights and Key Takeaways states, ‘In this lesson, students connect percentages to proportions. They solve problems by representing a situation with a tape diagram and then writing a proportion to find the percent or part. A percent represents a part-to-whole ratio with the second term always 100. Proportional reasoning can be used to solve problems involving percentages.”

• Unit 7: Work with Linear Expressions, Unit Overview, Focus states, “A Deep Dive into Linear Expressions: Working with linear expressions requires not only understanding of expressions with variables, but also synthesis of mathematical concepts including operations with rational numbers and properties of operations. Linear expressions can be manipulated without context for the academic exercise of generating equivalent expressions, adding and subtracting expressions, and simplifying expressions. When the expression represents a problem situation, contextualizing the expression may reveal that some forms of the expression serve different purposes and provide different ways of seeing the problem. Working with linear expressions sets the foundation for algebraic reasoning concepts including solving linear equations and systems of linear equations, as well as building and transforming linear functions.”

• Unit 9: Probability, Lesson 9-4: Compare Probabilities of Simple Events, Lesson Overview, Lesson Highlights and Key Takeaways state, “In this lesson, students compare experimental and theoretical probabilities. Students are encouraged to look for and make use of structure to compare probabilities of simple events. The theoretical and experimental probability of an event are not always similar. The number of trials in an experiment may not result in all possible outcomes occurring. The experimental probability becomes closer to theoretical probability as the number of trials increases. Theoretical probability can be used when each outcome is equally likely, or when the relationship between outcomes can be quantified. Experimental probability is used when the outcomes are not equally likely or cannot be quantified, or when the theoretical probability is too complex to calculate.”

The materials reviewed for Reveal Math 2025 Grade 7 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 2: Solve Problems Involving Geometry, Unit Planner, Lesson 2-1, Solve Problems Involving Scale Drawings, Standard 7.G.1 is identified for this lesson.

• Unit 2: Solve Problems Involving Geometry, Lesson 2-5: Describe Cross Sections of Three-Dimensional Figures, Additional Standards 7.G.3 and 7.G.6 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 3: Proportional Relationships, Unit Overview, Math Background states, “Much of the learning progression for elementary years is designed to build the foundation for proportional thinking and reasoning. These concepts help to lay the foundation for proportional reasoning in K-5, skip counting (Grade 1), multiplication (Grade 3), scaled data displays (Grade 3), multiplicative comparison (Grade 4), multiplying as scaling up (Grade 5), Grade 6 students began their study of ratios and ratio reasoning. They developed an understanding of what ratios and rates are and what kinds of comparison a ratio can represent (part-to-part and part-to-whole). They used tables of equivalent ratios, bar diagrams, and double number lines to represent ratio relationships. Students are expected to apply ratio reasoning to solve problems.” 

• Unit 4: Solve Problems Involving Percentages, Lesson 4-3: Solve Percent Change Problems, Lesson Overview, Coherence, Previous states, “Students solved for percent, part, or whole in problems involving percentages. Students use the percent equation to solve problems.” Now states, “Students solve problems involving percent change. Students analyze change in terms of percent increase or percent decrease.” Next states, “Students understand connections between percent increase and markup and between percent decrease and markdown. Students solve markup and markdown problems.”

• Unit 7: Work with Linear Expressions, Lesson 7-5: Factor Linear Expressions, Math Background states, “Students' study of factoring linear expressions draws on concepts and skills students have gained in previous grades and units. Interpret Expressions Grade 5 students wrote and interpreted numerical expressions without evaluating them. This concept will help students as they interpret factored linear expressions. Greatest Common Factor Grade 6 students found the greatest common factor (GCF) of two whole numbers. This lays the foundation for factoring linear expressions. Identify Parts Grade 6 students identified parts of an expression using mathematical terms (sum, term, product, factor, quotient, coefficient). Students will need to be able to identify terms and coefficients of terms as they interpret factored linear expressions.”

• Unit 8: Solve Problems Using 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. Equations and inequalities can be used to model and solve real-world problems. An algebraic equation can be used to determine the single value that makes the scenario true. An algebraic inequality, in contrast, can be used to determine the set of values that makes the scenario true. In progressing from one-step equations and inequalities to two-step and multi-step equations and inequalities, models can represent situations with more variety and complexity. Reasoning with equalities and inequalities continues through high school mathematics, as students model with and solve increasingly complex equations and inequalities, as well as systems of equations and inequalities.”

The materials reviewed for Reveal Math 2025 Grade 7 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 5: Sampling and Statistics, Unit Overview, Effective Mathematics Teaching Practices, Establish Mathematics Goals to Focus Learning states, “In this unit, students build upon their knowledge of data analyses from prior grades and form the foundation for statistics and probability at the high school levels. As such, it is important to help students understand how the unit goals fit into the data analysis and statistics learning progression. As students learn about sampling and statistics, there are multiple opportunities to situate the goals within the learning progression: Assessment of visual overlap of two data sets relies on students’ knowledge of data representations learned in elementary grades and measures of center and variability learned in Grade 6. Making inferences about populations from sample statistics provides the basis for more extensive analysis in high school. Use the content objectives for each lesson to guide instructional decisions. Ask frequent questions to ensure students can satisfy the learning objectives before progressing to subsequent objectives. Use students’ response to inform instruction and determine what kinds of practice and review might be necessary. For example, in Lesson 5-2, if students struggle to determine whether inferences are valid, they may not have met the content objective of distinguishing between biased and unbiased samples.”

• Unit 8: Solve Problems Using Equations and Inequalities, Lesson 8-6: Write and Solve Two-Step Inequalities, Explore, Session 1, Activity-Based Exploration, Two-Step Inequalities, Support Productive Struggle states, “As student-pairs explore the activities, check that all pairs understand the task and are completing their Exploration Activity Journal pages. If students need guidance or support, ask: What steps can you take to isolate the variable? What does the open circle or dot denote about the value as a solution to the inequality? Hands-on: In this activity, the steps of writing and solving an inequality from a real-world scenario are divided into quadrants. Partners choose a scenario and use it to write a word problem that can be represented by a two-step inequality. Partner-teams then pass their page and use the word problem written by the preceding team to perform the task indicated in the first quadrant. At each pass, partners review the work of the preceding team, rotate the page, and perform the task in the next quadrant. It may be helpful to establish a time-limit for how long partners will work on each quadrant, and to use a timer to indicate when it is time to pass the scenario to the next partner-team.”

• Unit 9: Probability, Unit Opener, Preparing for Explore and Develop, “How Do I Choose? To decide which exploration to implement for the lesson in this unit, consider the following: Activity-Based Exploration (ABE) This unit introduces new concepts that are both conceptual and procedural. Students are often able to build deeper understanding with new concepts when they have opportunities to explore them. While all lessons have Activity-Based Explorations, Lesson 9-1, 9-2 and 9-4 offer particularly strong opportunities for students to explore probability. Students who made connections between the probability concepts during the Be Curious conversations in this unit could benefit from exploring the concepts on their own with the Activity-Based Explorations. Guided Exploration Students may require more guidance to explore some concepts involved in probability. Lesson 9-5 and 9-6 introduce the concepts of compound events and sample space. If your students did not demonstrate a solid foundation of theoretical probability of simple events in earlier lessons in this unit, these lessons could be opportunities to implement the Guided Exploration. Students who struggle to see the probability concepts in the Be Curious conversations in this unit could need extra support to make connections during the Explore and Develop and could benefit from the Guided Explorations.”

The materials reviewed for Reveal Math 2025 Grade 7 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 2: Solve Problems Involving Geometry, Unit Planner, Materials to Gather states, “Piet Mondrian Teaching Resource, ruler, graph paper, dry spaghetti noodles, tape, protractor, rods of varied lengths, Bridge Work Teaching Resource, modeling clay, blunt knife or dental floss, small gift boxes, colored paper, scissors, glue stick, Unfolding a Prism Teaching Resource, string or yarn, Area of a Circle Teaching Resource.”

• Unit 4: Solve Problems Involving Percentages, Unit Planner, Materials to Gather states, “Baskets or waste cans for waste can basketball, calculators, Percent of Shots Taken Teaching Resource, Restaurant Menu Teaching Resource, Changes in Internet Usage Teaching Resource, Tape Diagram Teaching Resource, Markup and Markdown Teaching Resource, Interest Earned Teaching Resource, Percent Error Teaching Resource, scissors.”

• Unit 6: Solve Problems Involving Operations with Integers and Rational Numbers, Lesson 6-6: Divide Integers and Rational Numbers, Lesson Overviews, Materials states, “The materials may be for any part of the lesson, Blank Number Line Teaching Resource, algebra tiles.”

• Unit 8: Solve Problems Using Equations and Inequalities, Lesson 8-3: Solve Equations p(x+q)=r, Lesson Overview, Materials states,“The materials may be for any part of the lesson, Solution Steps Teaching Resource, poster board, scissors, tape.”

The materials reviewed for Reveal Math 2025 Grade 7 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, “Amir wants to enlarge a scale drawing by 15%. By what number should he multiply each dimension. A. 15 B. 1.5 C. 1.15 D. 0.15.” In the Item Analysis, the question is aligned to 7.G.1 "Use a scale drawing" and MP7, Look for and make use of structure, for students.

• Unit 5: Sampling and Statistics, Unit Assessment, Form A, Item 1 states, “A survey of 120 athletes finds that 48 are in favor of reducing the length of their sports season by 2 weeks. What conclusion can you make from the results of the survey? About ___% of athletes are in favor of reducing the length of their sports season by 2 weeks.”  In the Item Analysis, the question is aligned to 7.SP.1 "Populations, Samples, and Statistics" and MP2, Reason abstractly and quantitatively. 

• Unit 6: Solve Problems Involving Operations with Integers and Rational Numbers, Math Probe, Operations with Rational Numbers, Question 1 states, “Without calculating, determine the best choice for an estimate for each expression. 1. \left(-5\frac{13}{20}\right)\left(-\frac{4}{7}\right)” Analyze the Probe states, “Review the probe prior to assigning it to your students. In this probe, students will determine the best choice for an estimate for each expression without calculating. Targeted Concept Estimating a product or quotient involves reasoning about the values and signs of rational numbers and the effect of multiplication and division. Targeted Misconceptions- Students may apply incorrect estimation strategies. Students may apply an overgeneralization of "multiplication always results in a bigger answer." Students may overgeneralize rules for calculating with integers.” The question is aligned to 7.NS.2.

• Unit 9: Probability, Performance Task, Winning Gift Cards states, “Zion is the manager of a bicycle store. To encourage customers to come to the store, Zion decides to let one customer play a game each day to win a $500 gift card to the store. Each day Zion writes a number from 1 to 20 on a piece of paper. If the customer correctly guesses the number, they win the gift card. Part A. What is the theoretical probability that a customer wins the gift card on any particular day? Explain how to find the answer. Part B. Describe the chance that a customer wins the gift card on any particular day as impossible, unlikely, equally likely, likely, or certain. Explain your reasoning. Part C. Design a spinner with equal parts a customer could use to simulate the probability that they will win the gift card on any particular day. Spin the spinner 40 times and record the results in a table. What is the probability that a customer will win the gift card on any particular day? Explain your reasoning. Part D. How does the experimental probability (or the simulated probability) that a customer will win the gift card on any particular day compared to the theoretical probability? Is the experimental probability (or simulated probability) a good predictor that a customer will win the gift card on any particular day? Explain your reasoning. Part E. What is the probability that a customer will win the gift card two days in a row?” The teacher’s guide states “Students draw on their understanding of dependent and independent variables. Use the rubric shown to evaluate students’ work. Standards: 7.SP.5, 7.SP.7, 7.SP.7a, 7.SP.8, 7.SP.8a, 7.SP.8b, 7.SP.8c”

The materials reviewed for Reveal Math 2025 Grade 7 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 2: Solve Problems Involving Geometry, Performance Task, Part C states, “A circular fountain on the scale drawing has a diameter of 1 inch. What is the actual circumference of the fountain? How much space will the fountain cover? Use. 3.14 for \pi. The teacher guidance includes the right answer, 125.6 ft; 1,256 ft^{2} and states, “Content Standards: 7.G.1, 7.G.6, 7.G.4, Practice Standards: MPP Make sense, MPP Modeling.” The rubric states, “3 points: Student work reflects a strong understanding of scale and proficiency with applying scale and properties of circles to solve problems. 2 points: Student work reflects a developing understanding of scale and developing proficiency with applying scale and properties of circles to solve problems. 1 point: Student work reflects a weak understanding of scale and weak proficiency with applying scale and properties of circles to solve problems. 0 points Student work reflects a lack of understanding of scale and a lack of ability to apply scale to properties of circles concepts to solve problems.”

• Unit 3: Proportional Relationships, Unit Assessment, From A, Item 3 states, “Jana ran the first 3\frac{1}{2} miles of a 5-mile race in \frac{1}{3} hour. What was her average rate, in miles per hour, for this first part of the race? Explain how you solved the problem.” Item Analysis states, “Item 3, DOK 2, Lesson 3-1, Compute Unit Rates-Complex Fractions, Standard 7.RP.A.1” 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.

• Unit 7: Work with Linear Expressions, Math Probe, Item 1, “3m+4+5m and 12m, Are they equivalent?” A sample of correct student work is included in the teacher guide, “Review the probe prior to assigning it to your students. In this probe, students will determine if each pair of expressions is equivalent. Targeted Concept: Expressions can look different but still be equivalent. Strategies such as combining like terms, factoring, and distribution can be used to determine whether expressions are equivalent. Targeted Misconceptions: Students may fail to recognize the Distributive Property or apply the property incorrectly. Students may factor incorrectly or factor only part of an algebraic expression. Students may lack understanding of “like terms.”

• Unit 10: Math Is…Unit Opener, Am I Ready?, Exercise 7 states, “DeShawn bought 5 tickets to a basketball game for himself and his friends. While at the game, he bought a bag of popcorn for $6. If he spent $41 in all, how much did each ticket cost?” The Teacher Guidance states, “Working with Equations and Inequalities (Exercise 7) Check that students can explain each problem. How can you write an equation/inequality to represent the situation? How many steps will you need to solve the equation/inequality? What operation will you perform first to solve the problem?”

The materials reviewed for Reveal Math 2025 Grade 7 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. These 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 4, Solve Problems Involving Percentages, Lesson 4-4: Solve Markup and Markdown Problems, Practice, Question 12, students use proportional relationships to solve multi step problems. The question states, “Error Analysis: A classmate says that if you markdown an item that regularly sells for $56 by 25% the new price is $14. Do you agree? Explain.” (7.RP.3 and MP3)

• Unit 5: Sampling and Statistics, Performance Task, Part C, students infer information about a population by examining a sample of the population. “The research group also takes a survey of 400 registered voters in Hillview's school district. They are asked if they support passing the school levy. The 400 registered voters for the survey are randomly generated from a list of library card owners. The results are shown in the table. Based on the results of the survey, what is a possible inference that can be made? Explain.” (7.SP.1 and MP2)

• Benchmark 3, Item 13, students are assessed by solving a real-world problem with rational numbers. The problem states, “Kiah cuts 3\frac{3}{4} feet from a piece of fabric with a length of 7\frac{7}{8} feet. With the fabric she has left, Kiah makes 11 decorations of equal size. How many inches of fabric does each decoration use?” (7.NS.3 and MP7)

• Unit 8: Solve Problems Using Equations and Inequalities, Unit Review, Mathematical Modeling, students solve multi-step problems posed with positive and negative rational numbers through a constructed response. The materials state, “Project Two: You are part of a team that is designing new hiking trails in a regional park. There is a section of the trail that rises 20 feet along a horizontal distance of 80 feet and is too steep for most hikers to safely climb. Your team has to come up with the four possible solutions shown in the table. Propose a design for the section of the trail. Justify your design choice and show that your plan meets the specifications for the solution you propose.” (7.EE.3 and MP4)

The materials reviewed for Reveal Math 2025 Grade 7 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 3: Proportional Relationships, Lesson 3-2: Use Tables to Determine Proportionality, Differentiate, Extend Thinking, students extend their thinking of 7.RP.2, recognize and represent proportional relationships between quantities. The materials state, “For exercises 1-8, the number of units and the total cost of the units is given in Column A and Column B. Determine whether the columns are proportional or nonproportional. Question 9: You own a gift shop. You want to stock some coffee mugs. Would you choose to order based on the scenario in problem 7 or problem 8? Explain your answer.”

• Unit 5: Sampling and Statistics, Lesson 5-1: Relationships Between Populations, Samples, and Statistics, Differentiate, STEM Adventures, students apply and extend their learning of 7.SPP.1, understand that statistics can be used to gain information about a population by examining a sample of the population. The materials state, ”In this STEM Adventure, students explore the benefits and potential drawbacks of using pesticides to protect our crops. Apply your understanding of statistics to investigate.”

• Unit 6: Solve Problems with Operations with Integers and Rational Numbers, Lesson 6-3: Understand Additive Inverses, Differentiate, Extend Thinking, STEM Adventures, students apply and extend their learning of 7.NS.1, apply and extend previous understanding of addition and subtraction to add and subtract rational numbers. The materials state, “In this STEM Adventure, students gather and synthesize data on drought resistant plants. They learn about drought and its effect on food production and how plants adapt to be drought resistant.”

• Unit 9: Probability, Lesson 9-4: Compare Probabilities of Simple Events, Differentiate, Extend Thinking, students extend their learning of 7.SP.6, approximate the probability of a chance vent by collecting data on the chance process that produces it and observing its long-run relative frequency, and predict the approximate relative frequency given the probability. “For exercises 1-3, each cube has six faces and has been rolled 100 times. The outcomes are recorded in the table. Complete each table. What are the possible colors of the unseen faces of the cube? Explain. Remember the theoretical probability of the cube landing on any given face is \frac{1}{6} or approximately 0.167.” Students are given three tables with the colors green, blue, and red listed with the frequency and they are expected to find the experimental probability.”

The materials reviewed for Reveal Math 2025 Grade 7 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, “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: “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, Multilingual Learner Scaffolds, Entering/Emerging states, “Reference the Spanish cognates sujeto, verbo, and objeto as needed. Allow students to "draft" sentences orally and receive feedback before writing them. For the final part of the activity, provide a word bank with math terms.” Developing/Expanding states, “Help students practice the revision stage of the writing process by having them trade sentences with a partner. Tell them to add information to the drafts, or clarify them, in ways that stay true to the original meaning and structure.” Bridging/Reaching states, “Challenge students to explore sentence construction by combining subjects to form compound subjects, verbs to form compound predicates, and simple sentences to form compound sentences. Remind them that they can also invert subject-verb order by writing questions.”

• Unit 5: Sampling and Statistics, Lesson 5-1: Relationships Between Populations, Samples, and Statistics, Lesson Overview, Language Objectives states, “Students will understand and use commas in sentences. To optimize output, students will participate in MLR: Collect and Display, MLR: Critique, Correct, and Clarity, and MLR: Discussion Supports: Think Aloud.

• Unit 6: Solve Problems Involving Operations with Integers and Rational Numbers, Lesson 6-5: Multiply Integers and Rational Numbers, Explore, Session 1, Activity-Based Exploration, Multilingual Learner Scaffolds states, “Entering/Emerging Review relevant vocabulary, particularly the math term signs, which students may know in other contexts. Consider rephrasing the Concluding Questions to make them less abstract: What can you say about…?; What do you always know about…? Developing/Expanding To support students responding to the Concluding Questions, point out that they are virtually the same in their structure and wording. Explain that is madeans students can use one response as a model or framework for the other. Bridging/Reaching Extend learning, encourage metacognition, and enrich math discourse by having students orally explain their reasoning for their responses to the Concluding Questions. Encourage them to use examples, transition and sequence words, and precise academic language.”

• Unit 10: Math Is…, Unit Overview, Math Language Development, Reading Comprehension Strategies, states, As a math educator, you know that content can be accessed by those who “read to learn”--but this does mean that “learning to read” has already been mastered. This is why reviewing comprehension strategies in the context of math, and using the student edition as a model text, can greatly benefit students. Here are some basic approaches with which some students may be familiar. Self-monitoring. Tell students to keep track, and in a sense take ownership, of their level of comprehension regarding any given passage. Sometimes it works simply to keep reading, allowing background knowledge and context clues to work together. Readers also should have a sense of when to stop and apply a formal strategy or ask for help. Previewing the text–Explain that this is a strategy that almost all readers employ. It is partly the reason why text is organized the way it is and why it often features heads, subheads, boldface, and graphics: they provide a quick way to identify the topics in a general way. Using context clues. This is an effective strategy for all kinds of unfamiliar vocabulary including academic and specialized domain terms. Coach students to focus on the part of speech of the unknown words and to look to neighboring sentences for hints to its meanings. Read symbols and graphics. Remind students to examine accompanying figures, illustrations, diagrams, or charts for clarification of the same information conveyed in less detail in the main text.”

The materials reviewed for Reveal Math 2025 Grade7 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: Solve Problems Involving Geometry, Lesson 2-3: Analyze Attributes of Geometric Figures, Explore, Session 1, Activity-Based Exploration, How Many Quadrilaterals states, “Hands-On: Have students select 4 rods and measure the length of each it may be helpful to use sets of straws or stir-sticks as rods; with 4 whole rods, 4 half-rods, and 4 quarter-rods. This will ensure that students are able to explore both quadrilaterals they are familiar with and irregular quadrilaterals, and that they can encounter segments that do not form a quadrilateral. Students should use the lengths to determine how many quadrilaterals they can take. Have students repeat this process, recording their findings in the Activity Exploration Journal.”

• Unit 5: Sampling and Statistics, Lesson 5-1: Relationships Between Populations, Samples, and Statistics, Explore, Session 1, Activity-Based Exploration, Populations and Samples state, “Hands-On: Students work in groups of 3 or 4. Provide each group with a mini building set, and each student with a copy of the Parameters and Statistics Teaching Resource and access to a large tub of building bricks. For the two proportion sections of the Teaching Resources, have each group select an attribute to investigate, such as a certain color or shape, and use their selection to define the parameter.”

• Unit 7: Work with Linear Expressions, Lesson 7-3: Add Linear Expressions, Explore, Session 1, Activity-Based Exploration, Add Linear Expressions states, “Hands-On: Give each group a set of algebra tiles. Have them think of two linear expressions that they can represent with the algebra tiles. Then have them write an expression representing the sum of their two expressions. Make sure students understand that by writing each linear expression inside of parentheses, they are showing addition of 2 linear expressions, as opposed to addition of 4 terms, but that the use of parentheses does not affect the sum.”

• Unit 8: Solve Problems Using Equations and Inequalities, Lesson 8-5: Write and Solve One-Step Multiplication and Division Inequalities, Explore, Session 1, Activity-Based Exploration, Solve Multiplication and Division Inequalities states,“Digital: Before students begin the activity, have them explore the Websketch^TM tools they will be using. Ensure that they can change the values of the numbers and adjust the markers to change the values.”