8th Grade - Gateway 3

The materials reviewed for Reveal Math 2025 Grade 8 provide strategies for informing all stakeholders, including students, parents, or caregivers about the program and suggestions for how they can help support student progress and achievement.

The instructional materials provide support for students and families. Examples include but are not limited to: 

• Dashboard, Reveal Math 2025, Table of Contents, Unit 1: Math Is…, Unit Resources, Family Letter states, “Dear Family, In this unit, Math Is..., students will think and talk about what it means to do math and to see themselves as a ‘doer of math’. They will be encouraged to notice and wonder about how math is used in everyday situations, talk about their mathematical ideas, and reflect on their experiences with mathematics. What Will Students Learn in This Unit? Math Is… All individuals are doers of math and use math in their daily lives in ways they may not realize. When we do math, we make sense of problems, quantities, and solutions. To solve problems, we develop a plan and adjust the plan as needed. Students will visualize problems using different tools and models. They use different tools, such as tables, to show relationships between quantities. When students do math, they can precisely and accurately communicate their reasoning to their classmates. Similarly, they listen to and question their classmates’ arguments and ask questions to determine whether arguments make sense. Identifying patterns and relationships can help us solve problems. We can also make generalizations based on repeated calculations. For example, if we identify a pattern in a table of values, we can make a rule for finding the next value in the table. Students will evaluate the reasonableness of their solutions and make any adjustments as needed. Students make up a community of math thinkers and doers. They will work together or on their own and show respect for their classmates and themselves. How You Can Provide Support 1. Ask your child to think about how they use math in everyday life. Money: Ask your child what math problems they can think of that involve money. For example, they may need to determine how much more money they need to save to buy a new bike. Games: Ask your child how they might use math in the games they play. For example, they may find by how many points they lead or trail in a game. 2. Encourage your child to have a positive attitude toward mathematics and learning. Talk about math in a positive way. Choosing positive words when talking about math at home can help your child develop positive feelings around learning math. Celebrate successes—both small and large.”

• Course Overview, Program Overview: Learning & Support Resources, Get Started with Reveal Math, Support for Students and Families, Reveal Math Family PowerPoint states, “This is a presentation that teachers can share with families to introduce Reveal Math”. Family Letter states, “This is a letter teachers can send home to inform families about the Reveal Math program.” There is a Spanish Family Letter located in the same spot. 

• Implementation Guide, Math Mindset Competencies (page 78) states, “Understanding Others involves the ability to understand, empathize, and feel compassion for others, especially for those from different backgrounds or cultures. It also involves understanding social norms for behavior and recognizing family, school, and community resources and supports.”

• Course Overview, Program Resources: Course Materials, Student Resources, Foldable Study Guide, “This support asset includes an interactive collection of videos on how to create Foldables.”

The materials reviewed for Reveal Math 2025 Grade 8 partially provide assessments which offer accommodations that allow students to demonstrate their knowledge and skills without changing the content of the assessment.

While few in nature, some suggestions for accommodations are included within the Grade 6-8 Implementation Guide. Examples include:

• Implementation Guide, Equity and Access to High Quality Math for All Learners (page 14) states, “The Reveal Math authors believe that all students must have access to high quality mathematics instruction. They identified six (6) areas that are important for ensuring equity and access to high quality mathematics. These six areas are presented visually in a circle to show that these six areas are interdependent. In each unit, one of the six areas are highlighted and unpacked. Go Deep with the Math, Use Effective Teaching Practices, Build Connections, Partner with Families and Communities, Set and Maintain High Expectations, Foster Strong Math Identity and Agency”

• Implementation Guide, Lesson Walk-Through, Assess & Differentiate (page 30) states, “Every session closes with an assessment. The first session ends with an Exit Ticket that can inform instruction for Session 2. The second session ends with a Lesson Quiz that can inform differentiation.”

• Implementation Guide, Targeted Intervention (page 66) states, “Reveal Math is committed to supporting all students to achieve high academic results. To that end, Reveal Math offers targeted intervention resources that provide additional instruction for students as needed.” Targeted Intervention at the Unit Level, “based on their performance on all Unit Readiness Diagnostics and Unit Assessments. The Item Analysis table lists the appropriate resource for the identified concept or skill gaps. Intervention resources can be found in the Teacher Center in both the Unit Overview and Unit Review and Assess sections.” Targeted Intervention at the Lesson Level states, “Teachers can easily assign a Take Another Look mini-lesson for students to complete during independent work time, or they can be used in a small group to review a skill or concept. Each mini-lesson consists of a three-part, gradual-release activity that reteaches a key skill or concept. One to three Take Another Look lessons are identified for every lesson. These align to the end-of-unit assessment intervention resources.”

• All digital pages have the option for the content to be read aloud using a small speaker button located on the right side of the page. On the digital pages the user is able to highlight and annotate the digital page. Students are able to change the font size on all digital pages. Digital assessments lose both of these functionalities.

The materials reviewed for Reveal Math 2025 Grade 8 provide varied approaches to learning tasks over time and variety in how students are expected to demonstrate their learning with opportunities for students to monitor their learning.

Students engage with problem-solving in a variety of ways within a consistent lesson structure: Day 1: Launch, Explore, Wrap Up, Practice and Day 2: Launch, Develop, Summarize & Apply, Assess, Practice, Differentiate. According to the Implementation Guide, Instructional Model (page 20) states, “Reveal Math’s lesson model keeps sense-making and exploration at the heart of learning. Every lesson provides two instructional options to develop the math content and tailor the lesson to the needs and structure of the classroom.” Launch states, “Be Curious starts every session with the opportunity for students to be curious about math. Students focus on sense-making. Teachers foster students’ ideas through meaningful discussion.” Explore and Develop states, “Explore and Develop unpacks the lesson content through either an activity-based exploration or guided exploration. Students explore the lesson concepts and engage in meaningful discourse. Teachers utilize effective teaching practices to help students make meaningful connections.” Assess states, “The Exit Ticket is an assessment that students complete after Session 1. Teachers can use data from the Exit Ticket to inform instruction for Session 2. The Lesson Quiz is an assessment that students complete after Session 2. Teachers can use data from the Lesson Quiz to inform differentiation.” Practice and Reflect states, “Practice offers students opportunities to engage with math and reflect on their learning. Students practice lesson concepts by completing the Practice exercises independently. Teachers have students Reflect on the lesson content and their learning.” Differentiate states, “Differentiation helps support every student in their path to understanding. Students work on differentiated tasks to reinforce their understanding, build their proficiency, and/or extend their thinking.”

Examples of varied approaches across the consistent lesson structure include:

• Unit 2: Congruence and Similarity, Unit Opener, Am I Ready? states, “Have students work independently to complete the Am I Ready? exercises in either their Student Edition or Interactive Student Edition. The exercises review previously learned concepts that students will draw on in this unit. These include: Graphing Points on a Coordinate Plane (Exercises 1—5) Look for students who confuse the x- and y-coordinates. Along which axis do you plot the first coordinate? Along which axis do you plot the second coordinate? Which directions do positive and negative values represent for each coordinate? Adding and Subtracting Integers (Exercises 6—8) Look for students who use the wrong sign or operation. Guide them to use the context to determine the correct sign. Will tomorrow's temperature be less than or greater than today's temperature? Imagine a vertical number line. Are the diver and the climber on the same side of O on the number line or opposite sides? Multiplying Rational Numbers (Exercises 9—10) Check that students can explain why the sign of each product is negative. How do you know the product is negative? What signs must the factors have for a product to be positive?”

• Unit 3: Linear Relationships and Equations, Lesson 3-5: Describe Nonproportional Linear Relationships, Session 1, Activity-Based Exploration, Nonproportional Linear Relationships state, “Have students respond to the Introductory Question in their Activity Exploration Journal. How do the graphs of y = 3x and y = 3x + 2 differ? Group students in pairs to work on this activity. Today we will explore what it means for a linear equation to intercept the vertical axis at a point other than the origin. Digital: Students examine the effect of changing the values of m and b in the equation y = mx + b. Before students begin the activity, have them explore the Websketch^TM tools they will be using. Be sure they can adjust the sliders. Hands-On: Students examine the steps of the first pattern on the Pencil Patterns Teaching Resource and describe the relationship, in words, with their partner. Then, students graph the relationship on the 10 x 10 Grids Teaching Resource and discuss how they can describe the pattern using an equation. Students will repeat this process for each of the patterns shown. As student-pairs explore the activities, check that all pairs understand the task. If students need guidance or support, ask: What information do you need to write an equation for a linear relationship? What is the difference between a linear and proportional relationship? How can you connect mathematical ideas to representations? Help students in finding equations for nonproportional linear relationships by helping them understand what each part of the equations represents. Have students complete the Concluding Question in their Activity Exploration Journal. How can you write an equation that represents a linear relationship whose line intercepts the vertical axis at a point other than the origin?”

• Unit 5: Patterns of Association, Lesson 5-1: Construct Scatter Plots, Session 1, Activity-Based Exploration, Construct Scatter Plots state, “Have students respond to the Introductory Question in their Activity Exploration Journal. How can you identify patterns and relationships between two variables? Group students in pairs to work on this activity. Today we will explore how patterns and relationships between two variables can be displayed. Digital: Students explore the relationship between temperature and lemonade sales by plotting and analyzing points on a graph. Before students begin the first activity, have them explore the Websketch^TM tools they will be using. Ensure that they can plot a point on the coordinate plane. As students carry out the activity, check that all understand the task. If students need guidance or support, ask: What relationship are you exploring? What patterns do you see in the graph? How can you tell if the temperature has an effect on lemonade sales? Hands-on: Students examine the data displayed on the Federal Minimum Wage Teaching Resource and make preliminary observations in their Activity Exploration Journal. Then, have students construct a graph on grid paper and plot the points shown in the table. Students should analyze the graph to verify their initial thoughts and use it to make new observations and descriptions. If students need guidance or support, ask: Which variables will you use to create your graph? How do you think the graph will appear? What information can you identify from the graph that may be difficult to see in the table? How can visualizing data help in analyzing the relationship between variables? Have students consider the advantages of graphing points on a coordinate plane to draw conclusions about the relationship between variables. Encourage them to understand that by using a scatter plot, they can more simply observe and identify clusters, outliers, and patterns. Have students complete the Concluding Question in their Activity Exploration Journal. How does graphing points on the coordinate plane show the relationship between the two variables?”

• Unit 9: Irrational Numbers, Exponents, and Scientific Notation, Lesson 9-5: Use Product and Quotient of Powers Properties, Session 2, Summarize & Apply, Powers Properties states, “How would you explain to a friend the relationship between the powers of the factors and the power of the product when multiplying expressions with the same exponential base? How would you explain to a friend the relationship between the power of the dividend, the power of the divisor, and the power of the quotient when dividing expressions with the same exponential base? How can you expand the factors of multiplication or division expressions that have exponential bases and integer exponents to illustrate why these properties are true?” Apply, Sound Intensity, “How can you express the number 1,000 as an exponential expression with a base of 10? What property can you use to simplify this division expression? How is the quotient related to the minimum intensity of sound that William is able to hear?”

The materials reviewed for Reveal Math 2025 Grade 8 provide opportunities for teachers to use a variety of grouping strategies.

The materials provide opportunities for teachers to use a variety of grouping strategies. Teacher Guidance includes suggestions for whole group, small group, pairs, and/or individual work. Examples include:

• Unit 4: Understand and Analyze Functions, Unit Opener, Preparing for the Explore and develop, Activity-Based Exploration (ABE) states, “Much of the content is new for students. 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, Lessons 4-1, 4-2, and 4-5 offer particularly strong opportunities for students to explore concepts related to functions. Consider whether students need practice working in pairs or small groups when planning for the ABE. While both partner work and group work involve collaboration, some students may struggle with one or the other grouping. Choose the groups or pairs so that students' math and mindset skills will complement each other and the groupings will promote collaboration.” Guided Exploration states, “The lessons that introduce and apply multiple representations could be opportunities for students to explore the concepts with more guidance. Lessons 4-3, 4-4, and 4-6 explore and apply tables, graphs, and equations, and could be an opportunity to implement the Guided Exploration if your students struggle with analyzing representations of functions. Consider whether students need practice presenting ideas to the entire class. The Guided Exploration provides opportunities to pause the instruction and have students speak to the group.”

• Unit 6: Angles, Triangles, and the Pythagorean Theorem, Ignite, The Clean Air Act states, “Students can work in pairs or groups of three to work on the Ignite questions. Support Productive Struggle What type of particles and gases pollute outdoor air? What are the sources of those particles and gases? What types of particles and gases pollute indoor air? What are the sources of those particles and gases? How might pollution from the air enter other systems on Earth? What experiences have you had with polluted air? How did it affect you? Facilitate Discourse As student-groups share their ideas about air pollution, ask other students to think about similarities and differences among the different answers. Focus on students' suggestions for dealing with air pollution.”

• Unit 7: Volume, Lesson 7-2: Solve Problems Involving Cylinders, Session 1, Guided Exploration, Which Storage Container states, “Have students think about the question independently. Then instruct students to take turns each sharing their ideas in small groups. Have groups work together to prepare an explanation. Encourage groups to think about how to use visuals to support their explanations. Facilitate a class discussion using the groups' responses.” Let’s Explore More states, “1. Groups: Divide the class into equal-sized groups of three or four. Give a number to each student in each group. 2. Assign the Task: Have students answer the Let's Explore More question, including formulating justifications or explanations. Encourage students to think about how to support their explanation with a visual 3. Heads Together: As students work on the question, they make sure that everyone in the group is prepared to provide an answer and explanation. 4. Report: Choose a student number at random. The students with this number are the reporters for their groups. The reporters share their answers and explanations with the entire class. Reporters either agree or provide their own answers and explanations.”

The materials reviewed for Reveal Math 2025 Grade 8 provide a balance of images or information about people, representing various demographic and physical characteristics.

Student materials include images as clip art. These images represent different races and portray people from many ethnicities in a positive, respectful manner, with no demographic bias for who achieves success based on the problem contexts and grade-level mathematics. Examples include: 

• Unit 1: Math Is…, Unit Opener, What Do I Already Know?, Math History Minute states, “In 1949, Dorothy Johnson Vaughn (1910—2008) was promoted to lead the West Area Computing Unit for the National Advisory Committee for Aeronautics, later known as NASA. The unit was entirely composed Of African-American female mathematicians. They performed complex calculations and analyzed data for aerospace engineers. Their efforts were essential to the success of the early space program in the United States.”

• Unit 5: Patterns of Association, Lesson 5-1: Construct Scatterplots, Session 2, Guided Exploration, Science Experiment states, “Rafael is doing a science experiment to determine how the amount of sunlight affects the growth of sunflower plants. His hypothesis is that the more sunlight a plant is exposed to, the greater the plant growth. How can you determine whether Rafael's hypothesis is valid?”

• Unit 6: Angles, Triangles, and the Pythagorean Theorem, Unit Review, Performance Task states, “For each part A through C, answer the question and include justifications. Amir is working with a company that is designing a new apartment building. His job is to make sure that the air quality levels are acceptable at the apartment. Part A: Air filters are installed for each apartment in the building. Each filter is rated for an area of 1,000 square feet. If each apartment is going to have a square floor plan, what is the maximum side length of an apartment with this filter? Round to the nearest tenth of a foot. Part B: Amir is running a diagnostic test to determine if an air filter is properly installed. The location Of his diagnostic tool and the filter form a right triangle. The tool is 9 feet from the location on the wall where the air filter is located. The filter is 8 feet above the diagnostic tool. How far is the diagnostic tool from the air filter? Round to the nearest tenth of a foot. Part C: For air quality reasons, the apartment building cannot be built within 5 miles Of a factory. The map shows the location Of the factory and the proposed location of the apartment building on a coordinate plane. Each unit on the coordinate plane represents 1 mile. Is this an acceptable location for the apartment building? Explain.”

• Unit 10: Math Is…, Unit Opener, What Do I Already know?, Math History Minute states,  “Maryam Mirzakhani (1977—2017) only became interested in mathematics when she was in her last year of high school. In 2014, she became the first woman and the first Iranian honored with the Fields Medal for her work on hyperbolic geometry. Hyperbolic geometry is used to explore concepts of space and time. The Fields Medal is the highest scientific award for mathematicians and is only presented every four years.”

The materials reviewed for Reveal Math 2025 Grade 8 partially provide guidance to encourage teachers to draw upon student home language to facilitate learning.

Reveal Math 2025 provides student materials in Spanish and includes a Multilingual eGlossary in 14 languages. There is some guidance for teachers to draw upon student home language; however it is not consistent. Examples include: 

• Teacher Edition, Volume 2, Course 3, Glossary states, “The Multicultural eGlossary contains words and definitions in the following 14 languages: Arabic, Bengali, Brazilian Portuguese, English, French, Haitian Creole, Hmong, Korean, Mandarin, Russian, Spanish, Tagalog, Urdu, Vietnamese.” For example, “English: association (Lesson 5-2) A relationship between a set of data with two variables. Español: asociación Es la relación que hay en un conjunto de datos con dos variables.

• Unit 3: Linear Relationships and Equations, Lesson 3-4: Describe Proportional Linear Relationships, Session 1, Guided Exploration, Weight on the Moon, Multilingual Learner Scaffolds state, “Entering/Emerging Help students understand the conditional mood of the initial question by focusing on the meaning of each clause individually. Preteach key academic language, such as check, simplify, determine, and gravity. Point out Spanish cognates, such as simplify/simp/ificar and determine/determinar.”

• Unit 8: Systems of Linear Equations, Lesson 8-4: use Substitution to Solve Systems of Equations, Session 2, Activity-Based Exploration, Multilingual Learner Scaffolds state,“Entering/Emerging As students complete the MLR, allow them to explain the strategies they used to solve the puzzles in their home language, though they should use English to report out. Give them a graphic organizer, such as a Venn Diagram or a T-Chart, to help them compare and contrast. Provide sentence frames, such as I did... because I think…”

• Unit 10: Math Is…, Spanish Unit Resources, Carta para la familia [Family Letter] states, “Querida familia: En esta unidad, Matemáticas es..., los estudiantes relacionarån las matemåticas con lugares, objetos y situaciones cotidianas. Advertir su relación con la vida diaria muestra que matemáticas es más que una materia escolar. ¿Qué aprenderán los estudiantes en esta unidad? Matemáticas es... Los estudiantes ampliarán las destrezas matemáticas y de razonamiento desarrolladas en el curso para relacionar las matemáticas con objetos y situaciones familiares, y explorarán cómo se aplican en profesiones, pasatiempos, arte, tecnología y más. Las matemáticas son bellas e ilimitadas. Los estudiantes analizarán los diseños presentes en la naturaleza, el arte y la arquitectura, por ejemplo, los fractales en los copos de nieve. Los patrones y las relaciones ayudan a ver el sentido de los problemas y pensar soluciones lógicas. Los estudiantes analizarán cómo los patrones ayudan a visualizar estrategias para ganar y soluciones a los rompecabezas, como el cubo de Rubik. Los estudiantes pensarån como las matemáticas ayudan a innovar y dar soluciones creativas a los problemas diarios, como tecnología para una mejor comunicación. “[Dear Family, In this unit, Math Is..., students will connect mathematics to everyday places, objects, and situations. Recognizing connections between everyday life and mathematics reinforces that math is more than just a school subject. What Will Students Learn in This Unit? Math Is... Students will extend the mathematical and reasoning skills they have developed throughout the course to connect math to everyday objects and situations. They will explore how math appears in professions, hobbies, art, technology, and more. Math is beautiful and boundless. Students will analyze designs found in nature, art, and architecture. For example, they will examine fractals in snowflakes. Patterns and relationships can help make sense of problems and to think logically about solutions. Students will examine how patterns can help them visualize winning strategies for games and solutions to puzzles, such as a Rubik's cube. Students will think about ways in which math is used to innovate and produce creative solutions to everyday problems, such as technology for more efficient communication.]”

The materials reviewed for Reveal Math 2025 Grade 8 provide guidance to encourage teachers to draw upon student cultural and social backgrounds to facilitate learning.

While Spanish materials are accessible within lessons and within the Family Support Materials, there are few specific examples of drawing upon student cultural and social backgrounds. Examples include:

• Multilingual eGlossary, Korean, Volume, provides the definition of the vocabulary word used in the curriculum in Korean such as the definition for the word volume, “입체가 차지한 공간을 채우기 위해 필요한 세제곱 단위의 수이다. [The number of cubic units needed to fill the space occupied by a solid.]

• Unit 1: Math I…, Lesson 1-6: Math is Ours, Launch, Session 1, Be Curious: Notice and Wonder states, “Purpose Students make conjectures about a picture of volunteers working in a garden. What do you notice? What do you wonder? Teaching Tip Students may have varied amounts of experience seeing or working in gardens depending on where they live. Discuss as a class how gardens may be different and the same in rural, suburban, and urban areas. Pose Purposeful Questions Where was the picture taken? What are the volunteers doing? Why is volunteer service important? Pause & Reflect Students think about the connection between math class and volunteer service. How might the volunteers use math in their work?” There is a picture of 4 volunteers, one being former President Obama.

• Unit 4: Understand and Analyze Functions, Lesson 4-1: Describe Qualitative Relationships, Session 2, Guided Exploration, Gas Tank Levels state, “Ebony drove from home to the gas station, filled up her car's gas tank, then drove several hours to her destination. What would a qualitative graph that shows the relationship between the gas tank level and time look like? The situation has three intervals, so a qualitative graph will also have three intervals.” There is a picture of a person of color filling up their car at a gas station. Multilingual Learner Scaffolds, “Entering/Emerging Preteach unfamiliar words and phrases, such as gas tank level, and academic language, such as situation (referencing the Spanish cognate situación). Point out that the idiomatic phrase filled up has the same meaning as filled.”

• Unit 10: Math Is…, Lesson 10-1: Math is Everywhere, Launch, Session 1, Be Curious: Notice & Wonder states, “Purpose Students discuss what they notice and wonder about the photo of a town. What do you notice? What do you wonder?” Teaching Tip, “Ask students if they have been somewhere similar to the photo. Does it look familiar to them? How is it the same or different from places they have been?” Pose Purposeful Questions, “What data can you collect from the photo? How does math fit into the analysis of this image? What features of the building can you compare in the photo? Pause & Reflect Students share their thinking about the photo. How can the features in the picture be described using math? Before beginning the sense-making routine, have students discuss the Math is Mindset prompt. How can you show that you understand someone else's ideas? Understanding Others, “How can students show understanding when listening to others? Make a list of ways that students can show someone that they are listening and understanding what others are saying. For this session, provide students opportunities to communicate their math ideas to their peers.” Students are shown a picture of a town with brick lined streets, it looks like the mainstreet of a town with a church steeple at the end of the street.

The materials reviewed for Reveal Math 2025 Grade 8 partially provides supports for different reading levels to ensure accessibility for students.

In materials reviewed for Reveal Math 2025, there are no specific strategies provided to engage students in reading. There are, however, details about the language of math. In the Grade 6-8 Implementation Guide (page 48) states, “Throughout Reveal Math, teachers will find language supports embedded to help students build a shared language and communicate effectively about math. The Language of Math feature highlights math terms that students will use during the unit. New terms are highlighted in yellow. Terms that have a math meaning different from everyday meaning are also explained.” Math Language Routines state, “Math Language Routines engage students in thinking and talking about mathematics. This feature provides a listing of the Math Language Routines found in the lessons of the unit.” Examples include:

• Unit 5: Patterns of Association, Unit Overview, Math Language Development, Language Development - Academic Language states, “These mini-lessons focus on the academic terms listed in the Unit 5 planner.” Morphology states, “Throughout this unit students will encounter words that are variations of other words, with the only difference being changes that reflect a shift in part of speech. Students may not know, however, that there are consistent patterns to such changes, and that they can use a knowledge of these patterns to decode meanings and learn new words. Introduce the word morphology by asking students if they have ever heard the colloquial verb morph in pop culture or technology. Explain that the meaning is the same here, and is related to a change or the process of changing. In short, you can explain the principle of morphology by referencing the word itself. The suffix -logy changes morph into a noun meaning the study of changes. Morphological would then be the adjective built from it, and morphologically the adverb built from it. Illustrate this process by having students brainstorm words, and families of words, that undergo these same changes in spelling and part of speech. For example, high-frequency words with the -ical adjectival ending include magical, medical, and musical. To help students apply such principles to acquiring and using math vocabulary, you can use key terms from this unit. The noun category gives rise to the adjective categorical. The noun association can help students understand the verb associate as well as the adjective in the well-known math term associative property. Work with students both to define these words and to use them in context in sentences.”

• Unit 7: Volume, Lesson 7-4: Solve Problems Involving Spheres, Session 1, Guided Exploration, Spherical Bird Feeder states, “MLR Co-Craft Questions and Problems: Co-Craft Problems 1. Create: Pair students and have them co-create a problem where they find the volume of a sphere given the volume. 2. Solve: Have both students in each pair work together to solve their problem using the formula they found from Let's Explore More problem b. 3. Exchange: Have student-pairs trade their problem with another pair and solve. Then have the student-pairs form a group of four to check solutions and correct any mistakes.”

• Unit 8: Systems of Linear Equations, Lesson 8-5: Use Elimination to Solve Systems of Equations, Session 1, Guided Exploration, Restaurant Owner states,“MLR Stronger and Clearer Each Time: Successive Pair Shares 1. Think Time: Provide students with the following statement: What form, properties, or structure of a system of equations suggests that elimination is a good strategy to use? Have students record their thinking. 2. Structured Pairing: Have students explain their responses to at least two different partners. Each time, the student speaking focuses on explaining their reasoning clearly and precisely. The student listening asks clarifying questions to help their partner to be clearer and more precise in their communication. 3. Post-Write: Students revisit and clarify or revise their responses to the question.”

The materials reviewed for Reveal Math 2025 Grade 8 integrate technology such as interactive tools, virtual manipulatives/objects, and/or dynamic mathematics software in ways that engage students in the grade-level/series standards, when applicable.

Teachers and students have access to a robust digital experience. The 6-8 Implementation Guide, Teacher Digital Experience (page 10) states, “Teachers have access to an intuitive and easy-to-use platform from which they can plan and implement engaging instruction. The teacher experience includes: Daily interactive lesson presentations, Engaging, rich differentiation resources, Auto-scored practice and assessment items, Customizable assessments and item banks, Teacher and administrator data and reporting, Professional development workshops and videos, Unit and lesson files that can be downloaded with one click, Ability to add resources, including presentations, website links, and more…” Student Digital Experience states, “Students have access to a robust set of engaging digital tools and interactive learning aids, including: Interactive Student Edition, Daily interactive practice with embedded learning aids, Online assessments with interactive item types, Digital games designed for purposeful practice, Instructional mini-lessons to reinforce understanding, Rich exploratory STEM Adventures, Videos and eTools.” Examples include: 

• Program Resources: Digital Game Center, Chip Flip: Irrational Numbers, Exponents, and Scientific Notation, Description states, “This interactive game provides practice working with irrational numbers, exponents, and scientific notation.” Instructions state,“Select a chip to flip it and reveal a mathematical term, image or definition. Match equivalent terms or images with their definitions to complete the circuit board.”

• Unit 4: Understand and Analyze Functions, Lesson 4-2: Explore Functions, Session 2, Differentiate, teachers can assign tasks that build proficiency for students. Digital Game Center, Build Fluency states, “The Digital Game Center offers students anytime access to all the digital games for Reveal Math 6-8. These games are designed to help students build proficiency with key middle school concepts and skills. Among the skills practiced are operations with rational numbers and integers, ratio and proportional reasoning, and foundational linearity. Teachers may opt to assign games to students through the Digital Teacher Center.” Build Proficiency states, “Interactive Additional Practice Assign students either the print or digital assignment to practice lesson concepts. The digital assignment includes algorithmic exercises. Spiral Review: Assign students either the print or digital version to review these concepts and skills. Properties of Translations (1 of 2)” 

• Unit 5: Patterns of Association, Lesson 5-4: Use Linear Models to Solve Problems, Session, Activity-Based Exploration, Using Linear Models to Solve Problems, Implement Tasks That Promote Reasoning and Problem Solving states, “Students explore how to write an equation representing a line of fit using the slope and Y-intercept.” Materials state, “Digital: Activity Exploration Journal, 1 per student” Directions state, “Have students respond to the Introductory Question in their Activity Exploration Journal. How can you use a line of fit to make a prediction? Group students into pairs to work on this activity. Today we will explore how to use a line of fit from a scatter plot to make a prediction. Digital: Students develop an equation for a line of fit and use it to predict ice cream sales on a day when the temperature is 900. Before students begin the first activity, explain that the Websketch^TM shows data for ice cream sales at different outdoor temperatures. Encourage students to explore the tools they will be using to analyze the line of fit.”

• Unit 6: Angles, Triangles, and the Pythagorean Theorem, Lesson 6-5: Understand the Converse of the Pythagorean Theorem, Number Routines, Five Breaks, Go Online states, “Five Breaks provides opportunity for Students to hone their skills with number decomposition and flexible thinking about numbers. A number is given, and students identify five different ways to break it apart. Then small groups of students compare their decompositions and share with the other groups.” Build Fluency states, “Students build fluency with number decomposition and flexibility with numbers as they decompose a given number in at least five different ways. These prompts encourage students to talk about their estimates: What patterns do you notice in your decompositions? What would happen if you ___ to one of your parts? Which examples are the most unique in our class? Which decompositions were easy to think about? Why?”

The materials reviewed for Reveal Math 2025 Grade 8 include or reference digital technology, but do not provide opportunities for teachers and/or students to collaborate with each other when applicable.

Although there are a number of interactive tools throughout the teacher and student digital experience, Reveal Math 2025 lacks the opportunities for teachers and/or students to collaborate with each other within the program. Implementation Guide, Digital Experience, Student Center (page 70) and Teacher Center (page 72) state, “The Student Dashboard is designed with our learners in mind—allowing them to access all learning tools with ease. Students can access specific lessons. Students can review previously completed work and their scores on assignments. Students open to their To-Do list and click on assignments. Students can access their Interactive Student Edition, eToolkit, and Glossary” eToolkit is crossed off with a red horizontal bar. Interactive Student Edition, “The Interactive Student Edition allows students to interact with the Student Edition as they would in print. Embedded tools allow students to type or draw as they work out problems and respond to questions. Students can access the eToolkit at any time and use virtual manipulatives to represent and solve problems.” Digital Practice states, “Assigned Spiral Review provides a dynamic experience, complete with learning aids integrated into items at point-of-use, that support students engaged in independent practice.” Teacher Center states, “Teachers can access digital classroom resources and tools through the Teacher Center. Browse the Course Navigation Menu to go directly to a unit or lesson. Shortcuts to the Interactive Student Edition and eBooks of the Teacher Edition and Spanish Student Edition are available on the dashboard.” Unit and Lesson Resource Pages state, “Unit and lesson resources are organized into landing pages for point-of-use access. Teachers can easily plan and prepare to teach units and lessons using the simple layout organization that aligns with their print Teacher’s Edition. Assign activities or assessments to a group, individual, or whole class.”

The materials reviewed for Reveal Math 2025 Grade 8 have a visual design (whether in print or digital) that supports students in engaging thoughtfully with the subject, and is neither distracting nor chaotic.

There is a consistent design across units, topics, and lessons that support student understanding of mathematics. For example:

• Every Unit follows a similar layout: Unit Planner, Unit Overview, Unit Routines, Readiness Diagnostic, Unit Opener: Explore Through STEM, Unit Opener: Ignite!, a series of lessons for the Unit, Unit Review, Performance Task, Fluency Practice, and then Unit Assessment. Every Lesson follows a similar layout: Lesson overview that is comprised of: Learning Targets, Standards, Vocabulary, Materials, Focus, Coherence, Rigor, Lesson Highlights and Key takeaways, Math background, Lesson pacing, 2 Number Routines, Orchestrating Rich Mathematical Discourse, Session 1 Launch, Session 1 Activity-Based Exploration, Session 1 Guided Exploration, Exit ticket, Practice, Session 2 Launch, Session 2 Activity-Based Exploration, Session 2 Guided Exploration, Summarize & Apply, Lesson Quiz, Practice, and then a set of 3 Differentiate Activities. 

• Unit 1: Math Is…, Lesson 1-2: Math is Exploring and Thinking, Summarize & Apply, Math is Exploring and Thinking, Apply: Stuffed-crust Pizza states, “A pizza parlor sells three different shapes of pizza. Each of the three pizzas have stuffed crusts. Question 1: If you wanted the most stuffed crust, which pizza would you order? Question 2: If you wanted the most pizza, which pizza would you order? Choose one of the questions. Then answer in the space below. Be sure to justify your answers.” The task includes an image of 3 pizzas. The first pizza is square with the dimensions of 5 inches. The second pizza is rectangular with the dimensions of 8 inch by 3.5 inches. The final pizza is round and has a diameter of 7 inches. 

• Unit 2: Congruence and Similarity, Lesson 2-7: Use Angle-Angle Similarity, Session 1, Guided Exploration, Roof Trusses states, “A contractor will use king post trusses to build the roof on a shed. The king post truss consists of triangles of different sizes as shown in the sketch. How can the contractor determine whether the triangle with vertices ABC is similar to the triangle with vertices FAB? Two triangles are similar if there exists a sequence of transformations that maps two angles in one triangle onto two angles in the other triangle.” The task includes an image of a king post truss labeled ABC. Angle B is 45 degrees, angle A is split into two 45 degree angles. Bisecting the line BA is the point D which is split into two 45 degree angles. Bisecting the line CA is the point E which is split into two 45 degree angles. Bisecting the line BC is the point F which is split into four angles.

• Unit 9: Irrational Numbers, Exponents, and Scientific Notation, Lesson 9-4: Explore Patterns of Exponents, Session 2, Guided Exploration, Rules of Exponents states, “A student is using a calculator to explore negative and zero exponents. How do the values on the calculators compare?” The task includes an image of 2 calculators. One calculator screen reads, 5⁰ and the second calculator screen reads, 5^-3.

• Unit 10: Math Is…, Lesson 10-2: Math is Beauty, Session 1, Launch, Be Curious: Notice & Wonder, Purpose states, “Students discuss what they notice and wonder about the picture of shells. What do you notice? What do you wonder?” Teaching Tip states, “Make sure that students are aware of what the image contains. Discuss with them where you would find shells like the ones shown and ask if any students have seen them before.” Pose Purposeful Questions state, “Do you see any patterns in the shells? Are all of the shells the same? Do the shells have symmetry? Pause & Reflect: Students share their thinking on the shells. Have you ever seen a shell like this in nature?” The task includes an image of about 10 Snail shells in a pile.

The materials reviewed for Reveal Math 2025 Grade 8 provide teacher guidance for the use of embedded technology to support and enhance student learning, when applicable.

The materials provide technology guidance for teachers, and an additional format for student engagement and enhancement of grade-level mathematics content. Examples include:

• Implementation Guide, Fluency (page 58) states, “We know fluency is not developed after one lesson, so Reveal Math provides ample opportunities for students to practice concepts. The Game Station provides opportunities to build on concepts from the lessons, while Spiral Review provides a rotating review of previously learned concepts and skills.” Digital Station states, “The Digital Station includes games that offer an engaging environment to help students build computational fluency. The Digital Station is part of the Differentiated Support for each lesson.” Spiral Review states, “Spiral Review, available as a print-based or digital assignment, provides practice with mixed standard coverage for major clusters within the grade level to build fluency.”

• Implementation Guide, Differentiation Resources, Digital (page 64), Reinforce Understanding states, “These teacher-facilitated small group activities are designed to revisit lesson concepts for students who may need additional instruction.” Build Proficiency states, “Students can work in pairs or small groups on the print-based Game Station activities, written by Dr. Nicki Newton, or they can opt to play a game in the Digital Station that helps build fluency.” Extend Thinking states, “The Application Station tasks offer non-routine problems for students to work on in pairs or small groups.” Independent Activities, Reinforce Understanding state, “Students in need of additional instruction on the lesson concepts can complete either the Take Another Look mini-lessons, which are digital activities, or the print-based Reinforce Understanding activity master.” Build Proficiency states, “Additional Practice and Spiral Review assignments can be completed in either a print or digital environment. The digital assignments include learning aids that students can access as they work through the assignment. The digital assignments are also auto-scored to give students immediate feedback on their work.” Extend Thinking states, “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.”

• Implementation Guide, Digital Experience (page 70), Student Center states, “The Student Dashboard is designed with our learners in mind—allowing them to access all learning tools with ease.” Interactive Student Edition states, “The Interactive Student Edition allows students to interact with the Student Edition as they would in print.” Digital Practice states, “Assigned Spiral Review provides a dynamic experience, complete with learning aids integrated into items at point-of-use, that support students engaged in independent practice.” Digital Games states, “Digital Games encourage proficiency through a fun and engaging practice environment.”

• Implementation Guide, Digital Experience (page 72), TeacherCenter states, “Teachers can access digital classroom resources and tools through the Teacher Center.” Unit and Lesson Resource Pages state, “Unit and lesson resources are organized into landing pages for point-of-use access. Teachers can easily plan and prepare to teach units and lessons using the simple layout organization that aligns with their print Teacher’s Edition.”