Reveal Math
2025

Reveal Math

Publisher
McGraw-Hill Education
Subject
Math
Grades
6-8
Report Release
03/12/2025
Review Tool Version
v1.5
Format
Core: Comprehensive

EdReports reviews determine if a program meets, partially meets, or does not meet expectations for alignment to college and career-ready standards. This rating reflects the overall series average.

Alignment (Gateway 1 & 2)
Meets Expectations

Materials must meet expectations for standards alignment in order to be reviewed for usability. This rating reflects the overall series average.

Usability (Gateway 3)
Meets Expectations
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About This Report

Report for 8th Grade

Alignment Summary

The materials reviewed for Reveal Math 2025, Grade 8 meet expectations for Alignment to the CCSSM. In Gateway 1, the materials meet expectations for focus and coherence. In Gateway 2, the materials meet expectations for rigor and meet expectations for practice-content connections.

8th Grade
Alignment (Gateway 1 & 2)
Meets Expectations
Gateway 3

Usability

26/27
0
17
24
27
Usability (Gateway 3)
Meets Expectations
Overview of Gateway 1

Focus & Coherence

The materials reviewed for Reveal Math 2025, Grade 8 meet expectations for focus and coherence. For focus, the materials assess grade-level content and provide all students extensive work with grade-level problems to meet the full intent of grade-level standards. For coherence, the materials are coherent and consistent with the CCSSM.

Criterion 1.1: Focus

06/06

Materials assess grade-level content and give all students extensive work with grade-level problems to meet the full intent of grade-level standards.

The materials reviewed for Reveal Math 2025, Grade 8 meet expectations for focus as they assess grade-level content and provide all students extensive work with grade-level problems to meet the full intent of grade-level standards.

Indicator 1A
02/02

Materials assess the grade-level content and, if applicable, content from earlier grades.

The materials reviewed for Reveal Math 2025 Grade 8 meet expectations for assessing grade-level content and, if applicable, content from earlier grades.

The materials provide a Course Diagnostic, Summative Assessments, Unit Readiness Diagnostics, Unit Performance Tasks for each Module, Unit Assessments (Forms A and B), Lesson Exit Tickets, Lesson Quizzes, and an End of Course Assessment. In addition, there are quarterly benchmark tests to show growth over the year. Examples of assessment items aligned to grade-level standards include:

  • Unit 2: Congruence and Similarity, Unit Assessment: Form A, Question 7, “Triangle QRS has vertices Q(2, 4), R(5, 4) and S(4, 1). Triangle TUV has vertices T(6, 4), U(9, 4) and V(8, 1). Determine if △QRS and △TUV are congruent. Explain your reasoning using transformations.” (8.G.2)

  • Unit 3: Linear Relationships and Equations, Performance Task: Tutoring Fees, “Mario tutors after school. He charges a flat fee of $8 to cover travel expenses, plus $11 per hour. Darin is also a tutor. The table below shows the proportional relationship between how much money he earns and how many hours he works.” Part A, “Graph the proportional relationship between the money Darrin earns and the time he works.” Students are given a graph with the x-axis labeled, “Time Worked (hr)” and the y-axis labeled, “Amount Earned ($)”. (8.EE.5)

  • Unit 4: Understand and Analyze Functions, Lesson 4-5: Model Linear Relationships with Functions, Lesson Quiz, Question 4, “Lisa currently has $50 in her savings account. She saves $15 per week for a school trip. 4. What is a function that models the number of weeks x Lisa must save to have y dollars in her savings account?” (8.F.4)

  • Unit 5: Patterns of Association, Lesson 5-1: Construct Scatter Plots, Exit Ticket, “Mr. Murphy’s math class collected data on each student’s height and arm span, in inches. Plot each ordered pair from the table in the scatter plot.” Students are given an x/y table. The x row is labeled, “x, arm span” and the y row is labeled, “y, height” students are given the ordered pairs, “(47,48), (49,51), (50,51), (46,46), (48,49), (51,52), (52,53), (50,52), and (52,52)” Students are given a graph labeled, “Arm Span vs. Height” with a given x-axis title of, “Arm Span (in.)” and the y-axis title of, “Height (in.).” (8.SP.1)

  • Unit 9: Irrational Numbers, Exponents, and Scientific Notation, Performance Task, “Lucina is analyzing a scientific photo of a portion of an asteroid belt where smaller asteroids are clustered around the largest asteroid, asteroid A. She measures the distances from asteroid A to the other marked asteroids, recorded in the table below.” Part A “Lucina starts by ordering the asteroids closest to farthest from asteroid A. Convert each measure to a decimal. Then, starting with A, write the asteroids in order from closest to farthest. Explain.” (8.NS.1)

Indicator 1B
04/04

Materials give all students extensive work with grade-level problems to meet the full intent of grade-level standards.

The materials reviewed for Reveal Math 2025 Grade 8 meet expectations for giving all students extensive work with grade-level problems to meet the full intent of grade-level standards.

The instructional materials attend to the full intent of the grade-level standards by giving all students extensive work with grade-level problems. Each lesson consists of a Launch, Activity-Based and Guided Exploration, Summarize and Apply, and Practice Problems. The Launch is an opportunity for students to be curious about math and focus on sense-making. The Activity-Based and Guided Exploration allow students to explore the lesson concepts and engage in meaningful discourse. The Summarize and Apply allows the teacher to elicit evidence of student understanding, look for common misconceptions, and support productive struggle. Practice Problems, completed independently, provide opportunities for students to engage with the math, practice lesson concepts, and reflect on their learning. For example: 

  • Unit 3, Lesson 3-6: Solve Linear Equations, Explore, Session 1, Activity-Based Exploration, students solve one-variable linear equations. The problem reads, “Have students read and respond to the Introductory Question in their Activity Exploration Journal. If 3x+1=2x+53x+1=2x+5, how can you find the value of x? Group students in pairs to work on this activity.” In Lesson 3-7: Describe Solutions to Linear Equations, Session 2, Guided Exploration, Let’s Explore More, students explore patterns in equations that have no solutions compared to those with infinite solutions. Question a. “What do you notice about the structure of the equations with no solutions compared to those with infinitely many solutions?” In Unit 3, Unit Review, Item 15, students write a value that creates an equation that will have infinite solutions. The directions state, “Complete the equation with values that will result in an equation with infinitely many solutions (Lesson 7) .” These problems meet the full intent and give all students extensive work with 8.EE.7 (Solve linear equations in one variable.) 

  • Unit 4, Lesson 4-4: Explore Types of Functions, Practice, Exercises 6 and 7, students compare the graph of two equations and the parts of linear equations. The problem states, “6. How does the graph of the relationship between pounds of apples and cost relate to the equation that represents it? Explain? 7. How would the equation and graph for the cost y of picking x pound of apples change if the orchard increased the price per pound of apples to $2.25?” Lesson 4-6: Compare Functions, Session 2, Guided Exploration, Let’s Explore More, students compare linear functions. In Question a, “How do the two equations, A=s2A=s^2 and P=4sP=4^s, compare?” Unit Review, Item 10, students write an equation of a linear function given a real-world situation. The directions read, “The monthly cost for a magazine subscription is $8.99. Write an equation to determine the total cost, y, for m months. (Lesson 3).” These problems meet the full intent and give all students extensive work with 8.F.3 (Interpret the equation y=mx+by=mx+b as defining a linear function, whose graph is a straight line…) 

  • Unit 5, Lesson 5-5: Describe Patterns in Two-Way Tables, Session 1, Activity-Based Exploration, Patterns in Two-Way Tables, Hands-On, students gather and use data to create two-way frequency tables and answer questions. The directions read, “Conduct a survey with the two following questions: Would you rather only be able to shout or whisper? Would you rather have winter or summer forever? Record the results from each student and display the data for the class. Distribute the Would You Rather? Teaching Resource and ask students to use the data to complete table 1.” In Lesson 5-6: Interpret Two-Way Relative Frequency Tables, Session 1, Exit Ticket, Item 1, students complete a two-way table given a real-world scenario. The problem states, “The table on the left shows the results of a survey of middle school (MS) and high school (HS) students on whether they have a cell phone. Complete the relative frequency table on the right. Round to the nearest whole-number percent.” Assess to Inform Differentiation, Lesson Quiz, Item 2, students generalize bivariate categorical data using a relative frequency table. It states, “Use the relative frequency table in item 1 to complete the sentences. ___% of the students surveyed are 3 years old. The ___ received the greatest percentage of votes, while the ___ received the least percentage of votes.” These problems meet the full intent and give all students extensive work with 8.SP.4 (Understand that patterns of association can also be seen in bivariate categorical data by displaying frequencies and relative frequencies in a two-way table. Construct and interpret a two-way table summarizing data on two categorical variables collected from the same subjects.)

  • Unit 6, Lesson 6-1: Understand Angle Relationships and Parallel Lines, Explore, Session 1, Activity-Based Exploration, students determine rules about the angles created when parallel lines are cut by a transversal. The materials read, “Digital: Students explore the angle relationships formed when parallel lines are crossed by a third line. Before students begin the first activity, have them explore the Websketch™ tools they will be using. Ensure that they can drag and rotate the angle and adjust the line position.” In Lesson 6-2: Understand Angle Relationships and Triangles, Session 1, Exit Ticket, Items 1 and 2, students find angle sums when parallel lines are cut by a transversal. “For items 1 and 2, use the image to complete the exercises. Lines m and n are parallel. 1. What is the sum of the measures of angles 3, 4, and 5? 2. How do the angles from item 1 relate to angles 1, 2, and 4? Explain.” The image shown is of parallel lines cut by 2 transversals. Unit Review, Item 8, “Lines a and b are parallel. 8. Which of the following pairs of angles are alternate interior angles? (Lesson 1) A. <2 and <4 B. <2 and <6 C. <1 and <5 D. <4 and <5 .” The image shown is of parallel lines cut by a transversal. These problems meet the full intent and give all students extensive work with 8.G.5 (Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles.) 

  • Unit 9, 9-1: Represent Rational Numbers in Decimal Form, Session 2, Guided Exploration, Repeating Decimals as Fractions, Let’s Explore More, students find and order irrational numbers. The materials state, Question A, “How is the process for writing repeating decimals as rational numbers similar to solving systems of equations?” In Lesson 9-2: Understand Irrational Numbers, Summarize & Apply, Apply: Garden Path, students find the approximate radius of a circular garden using a given formula. “The Radius of a circle can be approximated using the formula r=A3r=\sqrt{\frac{A}{3}}. Question: What is the approximate radius of a circular garden with an area of 378 square feet? Answer the question in the space below.” In Lesson 9-3: Compare and Order Rational and Irrational Numbers, Session 2, Guided Exploration, Order Rational and Irrational Numbers, Let’s Explore More, Question a, students compare and order rational numbers. “Between which two numbers from the example is 113\frac{11}{3}?” Students are given a number line that counts by tenths from 3 to 4. These problems meet the full intent and give all students extensive work with 8.NS.1 (Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion; for rational numbers show that the decimal expansion repeats eventually, and convert a decimal expansion which repeats eventually into a rational number.)

Criterion 1.2: Coherence

08/08

Each grade’s materials are coherent and consistent with the Standards.

The materials reviewed for Reveal Math 2025, Grade 8 meet expectations for coherence. The materials: address the major clusters of the grade, have supporting content connected to major work, and make connections between clusters and domains. The materials make explicit connections from grade-level work to knowledge from earlier grades and connections from grade-level work to future grades.

Indicator 1C
02/02

When implemented as designed, the majority of the materials address the major clusters of each grade.

The materials reviewed for Reveal Math 2025 Grade 8 meet expectations that, when implemented as designed, the majority of the materials address the major clusters of each grade.

Materials were analyzed from three different perspectives: units, lessons, and instructional days. The materials devote at least 65 percent of instructional time to the major work of the grade:

  • The approximate number of units devoted to major work, and supporting work connected to major work of the grade is 7 out of 10 units, approximately 70%.

  • The approximate number of lessons devoted to major work, and supporting work connected to major work of the grade, is 46 out of 64, approximately 72%.

  • The approximate number of instructional days devoted to major work, including assessments and supporting work connected to the major work is 117 days out of 173, approximately 68%. 

An instructional day analysis is most representative of the materials because it includes Lessons, Mathematical Modeling, Assessments, Probes, and Unit Openers devoted to major work, including supporting work connected to major work. As a result, approximately 68% of the instructional materials focus on major work of the grade.

Indicator 1D
02/02

Supporting content enhances focus and coherence simultaneously by engaging students in the major work of the grade.

The materials reviewed for Reveal Math 2025 Grade 8 meet expectations that supporting content enhances focus and coherence simultaneously by engaging students in the major work of the grade. 

Examples of how the materials connect supporting standards to the major work of the grade include:

  • Unit 5: Patterns of Association, Lesson 5-3: Analyze Linear Associations in Bivariate Data, Explore, Session 1, Guided Exploration, Let’s Explore More, Problems a and b, connects the supporting work of 8.SP.2 (Know that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, informally fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line.) to the major work of 8.F.4 (Construct a function to model a linear relationship between two quantities. Students determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. They interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values.) as students “determine how the line of fit is used to model relationships between two quantitative variables.” For example, “a. How does drawing the line of fit confirm the possible association you can see in the scatter plot? b. How would any outliers affect a line of fit?”

  • Unit 7: Volume, Lesson 7-5: Solve Problems Involving Volume, Session 2, Practice, Problems 7 and 8, connects the supporting work of 8.G.9 (Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems.) to the major work of 8.EE.2 (Use square root and cube root symbols to represent solutions to equations of the form x2=px^2=p and x3=px^3=p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that 2\sqrt{2} is irrational.) as students, “use the formulas for the volumes of cones, cylinders, and spheres to solve real-world and mathematical problems.” For example, “A cylinder with a height of 6 inches has a volume of approximately 1,205.76 cubic inches. A cone with a radius of 3 inches is removed from its center. 7. What is the radius of the cylinder? 8. What is the volume of the cylinder after the cone is removed?” There is a picture of the cylinder with a cone on the inside with the given measurements labeled. 

  • Unit 9: Irrational Numbers, Exponents, and Scientific Notation, Lesson 9-1: Represent Rational Numbers in Decimal Form, Explore, Session 1, Guided Exploration, Let’s Explore More, Problems a and b, connect the supporting work of 8.NS.1 (Know that numbers that are not rational are called irrational. Students understand informally that every number has a decimal expansion; for rational numbers show that the decimal expansion repeats eventually, and convert a decimal expansion which repeats eventually into a rational number.) to the major work of 8.EE.2 (Use square root and cube root symbols to represent solutions to equations of the form x2=px^2=p and x3=px^3=p, where p is a positive rational number. They evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that 2 is irrational.) as students “convert fractions into decimals so that they learn that every number has a decimal expansion; for rational numbers show that the decimal expansion repeats eventually” For example, “a. What does mean? b. is possible?”

Indicator 1E
02/02

Materials include problems and activities that serve to connect two or more clusters in a domain or two or more domains in a grade.

The materials reviewed for Reveal Math 2025 Grade 8 meet expectations for including problems and activities that serve to connect two or more clusters in a domain or two or more domains in a grade.

Materials are coherent and consistent with the Standards. Examples of connections between major work to major work and/or supporting work to supporting work throughout the materials, when appropriate include:

  • Unit 3: Linear Relationships and Equations, Lesson 3-4: Describe Proportional Linear Relationships, Session 2, Guided Exploration, Rocket Fuel, connects the major work of 8.EE.A (Work with radicals and integer exponents) to the major work of 8.F.A (Define, evaluate, and compare functions), as students explore how to derive the equation of a line from a table of values using a rocket-fuel scenario, “Liquid oxygen is one type of fuel used in rockets. Engineers take into consideration the weight of the liquid oxygen when planning a rocket launch. How could you determine the weight of liquid oxygen for any number of gallons?” Let’s Explore More states, “a. Why is it important to know that a relationship is proportional? b. When is an equation more beneficial than a table or graph? c. A gallon of liquid hydrogen weighs 0.5908 pound. What is the equation that can be used to determine how much 25,000 gallons of liquid hydrogen would weigh?”

  • Unit 4: Understand and Analyze Functions, Lesson 4-5: Model Linear Relationships with Functions, Explore, Session 1, Guided Exploration, connects the major work of 8.F.A (Define, evaluate, and compare functions.) to the major work of 8.F.B (Use function to model relationships between quantities.) as students construct a function to model a linear relationship between two quantities and then use the function to Interpret the equation. The materials read, “Another Way, Use the table of values to write an equation of the function.” Let’s Explore More, “Question a. Will the population of the town be exactly 4,100 people in 5 years? Why or why not?”

  • Unit 6: Angles, triangles, and the Pythagorean Theorem, Lesson 6-4: Understand the Pythagorean Theorem, Launch, Session 1, Be Curious: Notice and Wonder, connects the major work of 8.G.A (Understand congruence and similarity using physical models, transparencies, or geometry software) to the major work of 8.G.B (Apply the Pythagorean Theorem to find the distance between two points in a coordinate system) as students think about the relationship between the sides of the triangle and the areas of the squares. The materials state, “What do you notice about the squares? How can you classify the triangle formed by the squares? Pause and Reflect Students think about the relationship between the sides of the triangle and the areas of the squares. How are the sides of the triangles and the areas of the squares related?” The previous lesson focused on square roots and Lesson 6-4 uses that information to explain a proof of the Pythagorean Theorem.

  • Unit 7: Volume, Lesson 7-4: Solve Problems Involving Spheres, Session 2, Summarize & Apply, Apply Rate of Inflation, Question 2, connects the supporting work of 8.NS.A (Know that there are numbers that are not rational, and approximate them by rational numbers, with the supporting work of 8.G.9 (Solve real-world and mathematical problems involving volume of cylinders, cones, and spheres.) as students use rational approximations of irrational numbers while finding the volume of a sphere. Question 2 states, “What is the pump rate of pump 2? Round to the nearest cubic foot per minute.” Prior to the question, students are given the following information, “Pump 2 inflated a beach ball with a diameter of 4 feet in about 5 minutes.”

Indicator 1F
02/02

Content from future grades is identified and related to grade-level work, and materials relate grade-level concepts explicitly to prior knowledge from earlier grades.

The materials reviewed for Reveal Math 2025 Grade 8 meet expectations that content from future grades is identified and related to grade-level work, and materials relate grade-level concepts explicitly to prior knowledge from earlier grades.

Within Unit and Lesson Overviews, a Coherence section provides information about ”What Students Have Learned, What Students Are Learning, and What Students Will Learn Next.” Each lesson contains a Math Background section that identifies the concepts and skills students have learned in previous grades and units that build towards current content.

Content from future grades is identified and related to grade-level work. For example:

  • Unit 2: Congruence and Similarity, Unit Overview, Coherence, What Students Will Learn Next, connects the current grade-level work as, “Students explain why two figures are congruent using rigid motions,” to future work where “Students use properties of rigid motions to prove theorems. (High School)”

  • Unit 8: Systems of Linear Equations, Unit Overview, Coherence, What Students Will Learn Next, connects the current grade-level work as, “Students use substitution or elimination to solve a system of two linear equations,” to future work where “Students solve a system consisting of a linear equation and a quadratic equation. (High School).”

  • Unit 9: Irrational Numbers, Exponents, and Scientific Notation, Unit Overview, Coherence, What Students Will Learn Next, connects the current grade-level work, “Students generate equivalent expressions using zero and negative exponents and properties of powers.” to future work where “Students use properties of rational and irrational numbers. (High School)”

Materials relate grade-level concepts explicitly to prior knowledge from earlier grades. For example:

  • Unit 5: Patterns of Association, Unit Overview, Coherence, connects the current grade-level work, “Students draw lines of fit in a scatter plot of bivariate data, assess the closeness of fit of the associations in the data, and use a line of fit or its equation to make predictions.” to prior work where “Students graphed equations for proportional relationships. (Grade 7)”

  • Unit 6: Angles, Triangles, and the Pythagorean Theorem, Unit Overview, Coherence, connects the current grade-level work, “Students explore the relationships between the interior and exterior angles of a triangle.” to prior work where “Students used facts about supplementary, complementary, vertical, and adjacent angles to find an unknown angle. (Grade 7)”

  • Unit 7: Volume, Unit Overview, Coherence, connects the current grade-level work, “Students use the volume formula to find the volume of cones.” to prior work where “Students used a formula to find the area of a circle. (Grade 7)”

Indicator 1G
Read

In order to foster coherence between grades, materials can be completed within a regular school year with little to no modification.

The materials reviewed for Reveal Math 2025 Grade 8 foster coherence between grades and can be completed within a regular school year with little to no modification.

The Teacher Edition and Implementation Guide provide pacing that fits within a typical 180 day school year. The pacing guide is based on daily classes of 45 minutes. As designed, the instructional materials can be completed in 173 days. For example: 

  • 128 days of content-focused lessons 

  • 10 days of Unit Opener with Ignite

  • 20 days of Mathematical Modeling 

  • 4 days of Math Probes

  • 8 days of Unit Assessments

  • 3 days of Benchmark Assessments 

Grade 8 consists of ten units. Each Unit is broken down into Lessons which include additional resources for differentiation, additional time, and additional practice activities. Each lesson consists of two session pacing options: Session 1 and Session 2. Session 1 includes Number Routines, Launch, Explore (Activity-Based Exploration and Guided Exploration), Assess to Inform Instruction, and Practice. Session 2 includes Number Routines, Launch, Develop (Activity-Bases Exploration and Guided Practice), Summarize and Apply, Assess to Inform Differentiation, and Practice. 

Additional Resources that are not counted in the program days include:

  • End-of-Year-Assessment

  • Unit Reviews 

  • Fluency Practices

  • Performance Tasks 

  • Readiness Diagnostic Assessments

Overview of Gateway 2

Rigor & the Mathematical Practices

The materials reviewed for Reveal Math 2025, Grade 8 meet expectations for rigor and balance and practice-content connections. The materials help students develop procedural skills, fluency, and application. The materials also make meaningful connections between the Standards for Mathematical Content and the Standards for Mathematical Practice (MPs).

Criterion 2.1: Rigor and Balance

08/08

Materials reflect the balances in the Standards and help students meet the Standards’ rigorous expectations, by giving appropriate attention to: developing students’ conceptual understanding; procedural skill and fluency; and engaging applications.

The materials reviewed for Reveal Math 2025, Grade 8 meet expectations for rigor. The materials develop conceptual understanding of key mathematical concepts, give attention throughout the year to procedural skill and fluency, and spend sufficient time working with engaging applications of mathematics. There is a balance of the three aspects of rigor within the grade.

Indicator 2A
02/02

Materials develop conceptual understanding of key mathematical concepts, especially where called for in specific content standards or cluster headings.

The materials reviewed for Reveal Math 2025 Grade 8 meet expectations for developing conceptual understanding of key mathematical concepts, especially where called for in specific content standards or cluster headings.

Materials provide opportunities for students to develop conceptual understanding throughout the grade level. Unit Overviews outline the three parts of rigor–conceptual understanding, procedural skill & fluency, and application. The Be Curious activities, which occur during the Launch, focus on sense making with different routines, such as the Notice and WonderTM. During the Explore & Develop (Activity-Based and Guided Exploration), instruction links the sense-making activity to conceptual understanding, ensuring students understand the “why” behind operations and other important mathematical skills. Additionally, the eToolkit provides eTools to help students develop a conceptual understanding of math concepts.” Examples include:

  • Unit 2, Unit Overview: Congruence and Similarity, Lesson 2-2: Explore Reflections, Rigor, Conceptual Understanding, “Students verify experimentally the properties of reflections. Students describe the effects of reflections on two-dimensional figures using coordinates.” (8.G.3)

  • Unit 4: Understand and Analyze Functions, Lesson 4-1: Describe Qualitative Relationships, Session 1, Practice, Items 1 - 3, students build conceptual understanding of the relationship between two quantities as they interpret and describe a graph. The materials state, “1. How can you describe the relationship between the volume of water in the reservoir and time? 2. Integral A represents a period of rainy weather. How can you interpret interval B? 3. How can you explain the different slopes that are visible during intervals A and C?” Students are given a graph labeled Time on the x-axis and Volume of Water on the y-axis. The graph has 3 line segments labeled A, B, and C. (8.F.5)

  • Unit 6: Angles, Triangles, and the Pythagorean Theorem, Lesson 6-3: Understand and Use Square Roots, Session 1, Guided Exploration, Let’s Explore More, students build conceptual understanding as they explore squares, square roots, and different ways to represent solutions. The materials state, “a. What is the relationship between squares and square roots? b. What other squares less than 125 are there? Express their factors as square roots. c. What are the different ways you can represent the solution to the equation x2=121x^2= 121?” (8.EE.2)

  • Unit 8: Systems of Linear Equations, Lesson 8-4: Use Substitution to Solve Systems of Equations, Session 1, Launch, Be Curious: Notice & Wonder, students build conceptual understanding of solving systems. The materials ask, “What do you notice? What do you wonder? What do you think the different shapes represent? How might the figures in the columns and rows be related to the numbers at the end of each column and row? What strategies might you use to find the value of each figure?” Students are given a 4x4 chart, each box has either a triangle, circle, or star in it. At the end of each row and column is a number. (8.EE.8)

  • Unit 9: Irrational Numbers, Exponents, and Scientific Notation, Lesson 9-4: Explore Patterns of Exponents, Session 1, Guided Exploration, Let’s Explore More, students explore the properties of integer exponents through the metric system. The materials ask, “How can you compare units in the metric system?” then “a. What does it mean when a power has an exponent of zero? b. What is the value of 10510^{-5} written as a fraction and as a decimal? c. What is the difference between 10310^3 and 10310^{-3}? d. how 818^{-1} do 828^{-2} and relate?” (8.EE.1)

Materials provide opportunities for students to independently demonstrate conceptual understanding throughout the grade level. Examples include:

  • Unit 2: Congruence and Similarity, Lesson 2-3: Explore Rotations, Session 1, Guided Exploration, students explore the properties of rotations by moving furniture in a room. The materials state, “a. Where would the love seat be placed if it were rotated 360° clockwise about the center of rotation? b. A classmate concludes that if the love seat was rotated 270° counterclockwise it will be in the same location as a 90° clockwise rotation. Is your classmate correct? Explain your thinking.” (8.G.1)

  • Unit 4: Understand and Analyze Functions, Lesson 4-1, Describe Qualitative Relationships, Session 1, Launch, Be Curious: Notice & Wonder, students share their thinking about information shown on the treadmill screen while building towards describing qualitative relationships. The materials state, “What question can you ask? What information does the screen show? What does the height of each section in the graph represent? Why does the height of the graph change? What happens when the graph is going up or down?” Pause & Reflect states, “Students think about how the quantities shown on the treadmill are related.” (8.F.5)

  • Unit 5: Patterns of Association, Lesson 5-3: Analyze Linear Associations in Bivariate Data, Session 1, Activity-Based Exploration, students construct a line of fit for bivariate data and determine the closeness of the association. The materials state, “Digital: Students explore how shifting points on a scatterplot affects the line of fit. Before students begin the first activity, have them explore the WebsketchTM tools they will be using. They ensure that they can move a point on the coordinate plane.” then the materials state, “Hands-On: Students individually construct a straight line that best describes the data for graphs A-D on the Scatter Plots Teaching Resource. Then, students then compare their lines, debating who has the better line and why.” (8.SP.2)

  • Unit 7: Volume, Lesson 7-2: Solve Problems Involving Cylinders, Session 1, Activity-Based Exploration, students demonstrate conceptual understanding as they find the volume of a cylinder is like finding the volume of a prism. The materials state, “Digital: Students explore how a cylinder’s height and base affect its volume. Before students begin the first activity, have them explore the WebsketchTM tools they will be using. They ensure that they understand how to use the calculation widget with the given values for the area of the base and for the height.” The problem states, Practice, Item 1, “How would you explain to a classmate how to find the volume of a cylinder?” (8.G.9)

  • Unit 8: Systems of Linear Equations, Lesson 8-3: Determine the Number of Solutions, Session 1, Practice, Item 7, students demonstrate understanding of identifying the number of solutions to a system of equations. The materials state, “7. Which of these describes a system of equations that has no solutions? A. They have the same y-intercept. B. They are perpendicular. C. They have the same slope and different y-intercepts. D. They have the same x-intercept and different y-intercepts.” (8.EE.8)

Indicator 2B
02/02

Materials give attention throughout the year to individual standards that set an expectation for procedural skill and fluency.

The materials reviewed for Reveal Math 2025 Grade 8 meet expectations for giving attention throughout the year to individual standards that set an expectation of procedural skill and fluency.

Materials provide opportunities for students to develop procedural skill and fluency throughout the grade level. Reveal Math provides students with multiple opportunities to revisit concepts and develop these areas of fluency within each unit. Implementation Guide (page 58) “Number Routines provide students with daily opportunities to develop number sense, deepening their understanding of number relationships. In addition, every unit reviews a computational strategy previously learned to revisit concepts and strategies adding to students’ flexibility when choosing methods.” Examples include:

  • Unit 3: Linear Relationships and Equations, Lesson 3-6: Solve Linear Equations, Session 2, Guided Exploration, students explore the concept of the Distributive Property through a problem involving costs for an end-of-year party. The problem states, “The students in eighth grade are planning an end-of-year party for 45 classmates. They have a budget of $1500 for the party. The party room costs $170.25. Each guest will get a $6 gift. How much can the students spend per guest on food? Step 1, Make sense of the quantities. The budget is $1500. The party room is $170.25. Each of the 45 guests receive a $6 party favor. You need to determine how much the class can spend per guest on food. 1500=170.25+45(x+6)1500=170.25+45(x+6) Step 2, Solve the equation. Simplify grouping symbols first.” Students develop procedural fluency in 8.EE.7 (Solve linear equations in one variable).

  • Unit 8: Systems of Linear Equations, Lesson 8-2: Estimate Solutions to Systems of Equations by Graphing, Session 2, Lesson Quiz, Items 1-3, students write and graph systems of equations to find which florists the wedding coordinator should hire. The problem states, “A wedding coordinator is hiring a florist. To decorate for a wedding, Petals Florist charges $22 per hour plus $55 for supplies. Red Roses Florist charges $11 per hour plus $120 for supplies. 1. Let x represent the number of hours the florist works and y represent the total cost. Write a system of equations that models the situation. 2. Graph the systems of equations on the coordinate plane. 3. What is an approximate solution to the system? Explain the meaning of the solution.” Students develop procedural fluency with 8.EE.8b (Solve systems of two linear equations in two variables algebraically, and estimate solutions by graphing the equations. Solve simple cases by inspection.)

  • Unit 9: Irrational Numbers, Exponents, and Scientific Notation, Lesson 9-4: Explore Patterns of Exponents, Session 2, Guided Exploration, students explore and compare values of negative and zero exponents. The Lesson states, “Rules of Exponents: A student is using a calculator to explore negative and zero exponents. How do the values on the calculators compare?” A worked example of the negative exponent rule and zero exponent rule is provided. “Let’s Explore More a. What is the difference between the expressions (3)2(-3)^2 and 323^{-2}? b. Without calculating, which value is greater: 737^{-3} or 838^{-3}?” Students develop procedural fluency of 8.EE.1 (Know and apply the properties of integer exponents to generate equivalent numerical expressions).

Materials provide opportunities for students to independently demonstrate procedural skill and fluency throughout the grade level. Examples include:

  • Unit 5: Patterns of Association, Fluency Practice, the materials state, “Fluency practice helps students develop procedural fluency, that is, the “ability to apply procedures accurately, efficiently, and flexibly.” Because there is no expectation of speed, students should not be timed when completing the practice activity.” Build Fluency section states, “Objective Students build fluency with relating unit rate with slope. As students work to develop fluency with unit rates, have them reflect on and share with classmates the strategies they find the most useful.” Fluency Talk states, “How would you describe the relationship between the slope of a linear graph and the unit rate for the relationship it shows?”

  • Unit 6: Angles, Triangles, and the Pythagorean Theorem, Lesson 6-3: Understand and Use Square Roots, Differentiate, Reinforce Understanding, Independent Work, Exercise 5-8, students practice solving problems involving square roots. “For exercises 5-8, solve each equation and check the solutions. 5. x2=144x^2=144 6. t2=259t^2=\frac{25}{9} 7. m2=25m^2=-25 8. g2=100225g^2=\frac{100}{225}” This activity provides an opportunity for students to develop procedural skill and fluency of 8.EE.1 (Know and apply the properties of integer exponents to generate equivalent numerical expressions.)

  • Unit 8: Systems of Linear Equations, Lesson 8-4: Use Substitution to Solve Systems of Equations, Number Routines, If I Know This…, students build proficiency with operations as they use the solution to an equation to solve equations with the same digits with different base ten values. The materials state, “This routine is similar to the Number String Matrix routine. Students are given a single fact and four or five equations that are related in some way. Students explain how they used the given fact to determine the solutions to the equations.” This activity provides an opportunity for students to develop procedural skill and fluency of 8.EE.8 (Analyze and solve pairs of simultaneous linear equations.)

Indicator 2C
02/02

Materials are designed so that teachers and students spend sufficient time working with engaging applications of the mathematics.

The materials reviewed for Reveal Math 2025 Grade 8 meet expectations for being designed so that teachers and students spend sufficient time working with engaging applications of the mathematics.

There are multiple routine and non-routine application problems throughout the grade level, including opportunities for students to work with teacher support and independently. The materials state, “While single and multi-step application problems are included across various portions of lessons, independent application opportunities are most often found within the Apply section. Many Apply problems provide multiple options, helping to build student agency through choice.” Materials provide opportunities for students to engage with routine application problems throughout the grade level. Examples include:

  • Unit 4: Understand and Analyze Functions, Lesson 4-4: Explore Types of Functions, Session 2, Summarize & Apply, students interpret the equation y=mx+by = mx + b as a linear function and apply it to real-world scenarios. The materials state, “Apply: Types of Functions Fatima wants to invest $200. She is considering two options. For option A, the interest rate is a simple interest rate of 4%. For option B, the interest rate is 3.25% compounded annually. Question: Which option should Fatima choose for her investment if she plans to invest for less than 20 years? Which option is best if Fatima wants to invest for more than 20 years?” (8.F.3)

  • Unit 6: Angles, Triangles, and the Pythagorean Theorem, Lesson 6-4: Understand the Pythagorean Theorem, Session 2, Guided Exploration, Let’s Explore More, students consider how to modify the Pythagorean Theorem equation to find the length of a leg. The materials state, “a. How can you use the Pythagorean Theorem to determine the length of a missing leg, given the lengths of one leg and the hypotenuse? b. Ancient Egyptians discovered that a triangle with side lengths 3, 4, and 5 is a right triangle. How could you use this fact to solve the bridge cable length problem above? c. Using the same 3, 4, 5 relationship, can you name another set of three whole numbers that make a right triangle? Use the Pythagorean Theorem to check your answer.” (8.G.7)

  • Unit 9: Irrational Numbers, Exponents, and Scientific Notation, Mathematical Modeling, Wind Energy is Trending, students develop a proposal to build a wind turbine for a city. The materials state, “You are the owner of a wind turbine company that services single households and cities. An average household in the United States uses 893 kilowatt-hours (kWh) of electricity per month. An average wind turbine generates 8.43x1058.43 x 10^5 kWh per month. The following cities are considering being powered by wind energy. Which city should your company submit a proposal to?” A chart with 4 cities, their electrical usage (kWh) and population is provided. (8.EE.1)

Within the Implementation Guide, Focus, Coherence, Rigor, Application, “Students encounter real- world problems throughout each lesson. The On My Own exercises include rich, application-based question types, including Error Analysis and Extend Thinking. Lesson differentiation provides opportunities for application through the STEM Adventures. The unit performance task and the Mathematical Modeling Project, both found in the Student Edition offer additional opportunities for students to apply their knowledge of math concepts to solve non-routine application problems.” Examples of non-routine application problems include

  • Unit 3: Linear Relationships and Equations, Lesson 3-3: Use Similar Triangles to Determine Slope, Differentiate, STEM Adventures, students compare two different proportional relationships represented in different ways. The materials state, “In this STEM Adventure, biosystems engineers are exploring erosion control solutions for different project sites. Use your linear relationship and equation knowledge to test and interpret which erosion control solutions are most efficient.” (8.EE.5)

  • Unit 5: Patterns of Association, Describe Patterns in Two-Way Tables, Session 2, Lesson Quiz, Exercises 7-11, STEM Connection, students understand that patterns of association can also be seen in bivariate categorical data by displaying frequencies and relative frequencies in a two-way table. The materials state, “An experiment investigates possible side effects of a headache medicine. Study participants are given either a dose of the medicine or a placebo (an inactive treatment). The table shows the results of the study. 7. Complete the two-way table by filling in the totals for each category. 8. Which side effect is most common among participants taking the medicine? Taking the placebo? Among all study participants? 9. What patterns of association do you notice between the two categories? 10. How could this information help the company that makes the headache medicine? 11. Error Analysis One of the researchers says that nausea and fever are the main side effects from the medicine. How do you respond to that researcher?” (8.SP.4)

  • Unit 7: Volume, Mathematical Modeling, There's Volume in Green Buildings, Project Two, students explore the volume of a cylinder through determining how many boards a tree can produce. The materials state, “Green buildings conserve natural resources, which enhances our quality of life. Wood products are a good choice for most new construction green building projects. Wood is renewable, sustainable and recyclable. A company building a green housing development needs to estimate how many trees will be needed to build a home. 1 square foot of a home needs approximately 6.3 boards. It is estimated the mature pine trees used have a height of 70 feet and a circumference of 6 feet. Number of boards = Volume of cylindrical tree trunk ×3\times3. Design a proposal recommending the number of mature pine trees needed for the company to build a 2,000 square foot home.” (8.G.9)

Indicator 2D
02/02

The three aspects of rigor are not always treated together and are not always treated separately. There is a balance of the three aspects of rigor within the grade.

The materials reviewed for Reveal Math 2025 Grade 8 meet expectations in that the three aspects of rigor are not always treated together and are not always treated separately. There is a balance of the three aspects of rigor within the grade.

All three aspects of rigor are present independently throughout the grade. Examples where instructional materials attend to conceptual understanding, procedural skill and fluency, or application include:

  • Unit 4: Understand and Analyze Functions, Lesson 4-2: Explore Functions, Session 1, Launch, Be Curious: Notice & Wonder, students build conceptual understanding as they learn that a function is a rule that assigns to each input exactly one output. The materials state, “Students discuss various aspects of a vending machine. What do you notice? What do you wonder? What do the letters and numbers on the keypad mean? How is the keypad related to the snacks in the vending machine? How can you use the keypad to get a particular snack? Why is it important that each combination of letters and numbers gives only one type of snack?” (8.F.1)

  • Unit 6: Angles, Triangles, and the Pythagorean Theorem, Lesson 6-6: Determine Distance on the Coordinate Plane, Practice, students develop procedural fluency while using the Pythagorean Theorem to determine the length of the hypotenuse of a right triangle constructed on the coordinate plane. The materials state, “For exercises 8-14, use the graph to answer the questions. 8. What is the distance between points A and B? 9. What is the distance between points D and F? 10. Which points are the closest to each other? What is the distance between those points?” (8.G.8)

  • Unit 7: Volume, Lesson 7-4: Solve Problems Involving Spheres, Mathematical Modeling, There’s Volume in Green Buildings, students apply their knowledge of volume by developing a proposal for an alternative energy source for the town and determine the amount of space needed for the energy source. The materials state, “Project One One way to conserve water for sustainable living is to use a rainwater harvesting system that stores rainwater in a cylindrical tank. A home development company in Seattle in hiring you to design the tank. Recommended Tank Size A = Area of Roof D = 0.8 = Drainage Coefficient R = Annual Rainfall” Students are provided a chart with years and annual rainfall in inches. (8.G.9)

Multiple aspects of rigor are engaged simultaneously to develop students’ mathematical understanding of a single unit of study throughout the materials. Implementation Guide, Lesson Walk-Through, Rigor, states “Every lesson describes the main rigor focus of each lesson based on the goals and expectations of the standards.” The Apply section states, “The Apply offers students a non-routine problem to solve. Many Apply problems provide multiple options, helping to build student agency though choice. The Teacher Edition offers scaffolded prompts that the teacher can ask students who may need support getting started.” Practice & Reflect states, “Practice & Reflect provides students with practice that address all elements of rigor.” Many lessons include more than one aspect of rigor. Examples include:

  • Unit 2: Congruence and Similarity, Lesson 2-6: Understand Similarity, Session 1, Guided Exploration, Reimagining the Patio, students build conceptual understanding and develop procedural fluency through transformations to show that one two-dimensional figure is similar to another, then describe a sequence of transformations that exhibits the similarity of the figures. The material states, “A client has requested a larger table for his patio. The landscape architect also suggests a new location for the table. How can the architect describe the position and size of the larger table compared to the smaller one?” Let’s Explore More, “a. Are all the rectangles similar? Why or why not? b. How can the side measures help you determine if the tables are similar? c. What does it mean if the scale factor of the dilation in a sequence of transformations is one?” (8.G.4)

  • Unit 3: Linear Relationships and Equations, Lesson 3-5: Describe Solutions to Linear Equations, Session 1, Exit Ticket, students build conceptual understanding, develop procedural fluency, and use application by representing nonproportional linear relationships with an equation and applying the concept of the equation y=mx+by=mx+b to real-world situations. The materials state, “For items 1 and 2, use the graph representing the total cost to ship a package to complete the exercise. 1. Does the graph represent a proportional relationship? Explain. 2. Identify the slope and y-intercept. Explain what the slope represents.” Students are given a graph with an x-axis of Weight (lbs) and a y-axis of Cost ($). There is a ray drawn on the graph. (8.EE.6)

  • Unit 6: Angles, Triangles, and the Pythagorean Theorem, Lesson 6-5: Understand the Converse of the Pythagorean Theorem, Summarize & Apply, students build conceptual understanding, develop procedural fluency, and apply the converse of the Pythagorean Theorem to determine if a triangle is a right triangle. The materials state, “The Ancient Egyptians used a rope loop with 12 equally-spaced knots to check for right angles. Question: How do you think they used this rope loop to make square corners when they surveyed land or built structures?” (8.G.7)

Criterion 2.2: Math Practices

10/10

Materials meaningfully connect the Standards for Mathematical Content and Standards for Mathematical Practice (MPs).

The materials reviewed for Reveal Math 2025, Grade 8 meet expectations for practice-content connections. The materials meaningfully connect the Standards for Mathematical Content and the Standards for Mathematical Practice (MPs).

Indicator 2E
02/02

Materials support the intentional development of MP1: Make sense of problems and persevere in solving them; and MP2: Reason abstractly and quantitatively, for students, in connection to the grade-level content standards, as expected by the mathematical practice standards.

The materials reviewed for Reveal Math 2025 Grade 8 meet expectations for supporting the intentional development of MP1: Make sense of problems and persevere in solving them; and MP2: Reason abstractly and quantitatively, for students, in connection to the grade-level content standards, as expected by the mathematical practice standards. 

Within the Implementation Guide, Math Practices states, “To think like mathematicians, students must build thinking habits that help them develop a problem-solving frame of mind. Reveal Math helps students build proficiency with these important thinking habits and problem-solving skills through the Math is... Prompts found in every lesson. These prompts model the kinds of questions students can ask themselves to become proficient problem solvers and doers of math.” The Standards for Mathematical Practice are identified for teachers in the Lesson Overviews, and within the lesson margins labeled in orange as “Math Practices and Processes” or “MPP”. Although most lessons offer opportunities for students to engage with more than one Standard for Mathematical Practice, this guidance identifies a focus MP within each lesson. The notes also provide lesson-specific information, ideas, and questions teachers can use to deepen students’ engagement with the focus MP. 

MP1 is identified and connected to grade-level content, and there is intentional development of the MP to meet its full intent. Students make sense of problems and persevere in solving them as they work with support of the teacher and independently throughout the modules. Examples include:

  • Unit 1: Math is…, Unit Overview, Math Practices and Processes, Promoting students’ sense-making, thinking, and reasoning states, “In this unit, Lessons 1-2 through 1-5 focus students’ learning on the mathematical habits of mind that are integral to proficiency in mathematics. Each lesson focuses on two specific habits of mind: Lesson 1-2 - Math Is Exploring and Thinking: Students refine their thinking habits related to problem solving. They discuss how they make sense of a problem, analyze givens, and determine an appropriate solution strategy for the problem. They consider how they monitor their progress towards a solution. Students also consider the meaning of quantities and the relationship among the quantities and values in a problem.” 

  • Unit 2-6: Congruence and Similarity, Lesson 2-6: Understand Similarity, Session 1, Activity- Based Exploration, students analyze and make sense of sequences of transformations to show similarity. The materials state, “Encourage students to be flexible in their approach to problems. If a strategy is not leading to a reasonable solution, it is important to regroup and try a new approach. Have students complete the Concluding Questions in their Activity Exploration Journal. How can you tell which types of transformations you should use to show that two triangles are similar? If you change the order of the transformations in a sequence, does that change the image? Explain.” 

  • Unit 4: Understand and Analyze Functions, Lesson 4-6: Compare Functions, Session 1, Guided Exploration, Orthodontic Braces, students analyze and make sense of features of linear functions represented in two different ways. The materials state, “Have students think about factors that make up payment plans. What is the monthly payment for the clear plastic braces? for the metal braces? Students work with a partner to determine the monthly cost of each type of braces. Consider the properties of functions that can be used to compare the pricing for the two types of braces. How can you organize the information to make sense of the problem? Help students see that information presented differently can be organized in the same way to help compare features of functions. Display the following two statements: The cost of metal braces is more expensive than the cost of the clear plastic braces. 1. Students work independently to respond to the statement, providing arguments to support their answers. 2. Students discuss their responses and reasoning with a classmate. Based on feedback from their partner, students revise and strengthen their responses. 3. Ask student-pairs to present their responses to the class. Other students should listen and ask clarifying questions about their justifications.” 

MP2 is identified and connected to grade-level content, and there is intentional development of the MP to meet its full intent. Students reason abstractly and quantitatively as they work with support of the teacher and independently throughout the modules. Examples include:

  • Unit 6: Angles, Triangles, and the Pythagorean Theorem, Lesson 6-7: Apply the Pythagorean Theorem, Session 1, Guided Exploration, Handicap Ramps, students understand the relationships between problem scenarios and mathematical representations of the Pythagorean Theorem and a real-world problem. The materials state, “Have students work with a partner to determine the shapes they see in the sections of the ramp. Students should recognize that the first section is a right triangle, the second and last sections are rectangles, and the third section is a trapezoid. Have students describe the quantities and their importance to solving the problem to a partner. Encourage students to identify the height and the length of each portion of the ramp.” Let’s Explore More states, “1. Set Up: Give students time to respond to the Let’s Explore More question b and to think about what they will say to their partner to explain and justify their strategies and responses 2. What is similar, What is Different: Place students into pairs and ask them to share their responses, looking for similarities and differences. 3. Mathematical Focus: Students work in groups to discuss the relationship between the horizontal and vertical distances covered by the ramp and the total length of the ramp.” 

  • Unit 8: Systems of Linear Equations, Unit Overview, Math Practices, Reason Abstractly and Quantitatively states, “Writing and solving systems of equations is a foundational skill for higher-level mathematics. Helping students to reason abstractly and quantitatively in order to represent and solve mathematical and real-world situations with systems of linear equations will provide them with the skill set they need to be successful in high-school mathematics and beyond. Encourage students to identify the important quantities in a problem and how the quantities are connected. Focus students’ attention to the relationship between quantities in a problem and how they can use the relationships to determine an appropriate solution method. For example, if the coefficients on the same variable in two equations are opposites, then elimination is a good choice.” 

  • Unit 9: Irrational Numbers, Exponents, and Scientific Notation, Lesson 9-5: Use Product and Quotient of Powers Properties, Session 1, Activity-Based Exploration, Properties of Powers, students discuss what the numbers in a Product of Powers and Quotient of Powers Properties represent. The materials state, “Hands On: Students work in groups to find multiple solutions to x0x0=x10x^{0}\cdot x^{0}=x^{10}. Be sure to tell students to use positive and negative integers for the exponents of x. Students compare their solutions with other groups and look for patterns. Then students repeat this process for the equation. How can you connect these problems to math that you already know? Students already know how to write numbers as powers. Encourage students to make connections between the expanded forms of powers and the properties used to find the products of numbers with the same exponential bases. Have students complete the Concluding Questions in their Activity Exploration Journal. How can exponential expressions be simplified when multiplying expressions with the same bases? How can exponential expressions be simplified when dividing expressions with the same bases?”

Indicator 2F
02/02

Materials support the intentional development of MP3: Construct viable arguments and critique the reasoning of others, for students, in connection to the grade-level content standards, as expected by the mathematical practice standards.

The materials reviewed for Reveal Math 2025 Grade 8 meet expectations for supporting the intentional development of MP3: Construct viable arguments and critique the reasoning of others, for students, in connection to the grade-level content standards, as expected by the mathematical practice standards.

Within the Implementation Guide, Math Practices states, “To think like mathematicians, students must build thinking habits that help them develop a problem-solving frame of mind. Reveal Math helps students build proficiency with these important thinking habits and problem-solving skills through the Math is... Prompts found in every lesson. These prompts model the kinds of questions students can ask themselves to become proficient problem solvers and doers of math.”

Students construct viable arguments and critique the reasoning of others in connection to grade-level content as they work with support of the teacher and independently throughout the units. Examples include:

  • Unit 2: Congruence and Similarity, Lesson 2-5: Explore Dilations, Sessions 1, Activity-Based Exploration, Can You Shrink That?, students construct mathematical arguments as they explore dilations of two-dimensional figures. The materials state, “What changes and what remains the same when you enlarge or shrink a figure? Encourage students to think about strategies they can use to determine whether their answers are reasonable. Ask students to explain how they can use these strategies to reinforce or revise their initial ideas. Have students complete the Concluding Questions in their activity Exploration Journal. How are the triangles in this activity alike? How are they different? How does enlarging or reducing a figure compare to the previous transformations we have studied?” 

  • Unit 3: Linear Relationships and Equations, Lesson 3-3: Use Similar Triangles to Determine Slope, Session 1, Guided Exploration, Triangles on a line, students construct viable arguments while exploring the hypotenuse of similar triangles having the same slope. The materials state, “Triangles ABC and CDE have the measurements shown. How do the slopes of line segments AC and CE compare?” Let’s Explore More states, “a. Why do you think similar triangles are sometimes referenced as slope triangles? b. Would the slope be the same if a third triangle is drawn? Why or why not? There are 2 similar triangles shown with the dimensions of 3,4,5 and 6,8,10.”

  • Unit 4: Understand and Analyze Functions, Lesson 4-3: Represent Functions, Session 1, Activity-Based Exploration, Representing Functions, students critique the reasoning of others as they explore different ways to represent linear functions and determine initial value and rate of change in each representation. The materials state, “Have students respond to the Introductory Question in their Activity Exploration Journal. How can you represent a function in different ways? As student-pairs explore the activities, check that all pairs understand the task. If students need guidance or support, ask: What tools can you use to display the relationship between the number of cups stacked and the height of the cups? What has to be true for a function to have a constant rate of change? How is the initial value represented on a graph, table, and equation? What patterns do you notice in the table and graph? Have students discuss the patterns they notice in the table and graph. Ask volunteers to share their thoughts with the class. Encourage students to think about the relationships between the patterns they see in the table and graph. Have students complete the Concluding Questions in their Activity Exploration Journal. What are the different ways to represent a function? What characteristics can you use to describe a representation of a linear function?”

  • Unit 6: Angles, Triangles, and the Pythagorean Theorem, Lesson 6-3: Understand and Use Square Roots, Session 2, Guided Exploration, Table Size, students justify their choices and estimates while finding the length of a side of a square with an area that is not a perfect square. The materials state, “A table has an area of 2 square meters. How long is each side of the table?” Let’s Explore More, “a. How can you use your knowledge of square numbers to estimate square roots of numbers that are not perfect squares? b. What values would you try that are in the hundredths? c. What do you notice each time you refine your estimates to find identical factors that equal 2?”

Indicator 2G
02/02

Materials support the intentional development of MP4: Model with mathematics; and MP5: Use appropriate tools strategically, for students, in connection to the grade-level content standards, as expected by the mathematical practice standards.

The materials reviewed for Reveal Math 2025 Grade 8 meet expectations for supporting the intentional development of MP4: Model with mathematics; and MP5: Use appropriate tools strategically, for students, in connection to the grade-level content standards, as expected by the mathematical practice standards. 

Within the Implementation Guide, Math Practices states, “To think like mathematicians, students must build thinking habits that help them develop a problem-solving frame of mind. Reveal Math helps students build proficiency with these important thinking habits and problem-solving skills through the Math is... Prompts found in every lesson. These prompts model the kinds of questions students can ask themselves to become proficient problem solvers and doers of math.”

MP4 is identified and connected to grade-level content, and there is intentional development of the MP to meet its full intent. Students model with mathematics as they work with teacher support and independently throughout the modules. Examples include:

  • Unit 4: Understand and Analyze Functions Lesson 4-5: Model Linear Relationship with Functions, Session 2, Activity-Based Exploration, students construct a function to model a real-world situation and then apply the function to answer questions. The materials state, “Facilitate a whole-class discussion of the activity. Using the evidence of student thinking that you gathered, sequence students’ findings to highlight different approaches and thinking strategies used to respond to the Concluding Questions. How can you use the rate of change and initial value to find values for a linear function that are not shown in a table? How can you write an equation for a linear function represented by a table? What are some other representations you could use?”

  • Unit 5: Patterns of Association, Lesson 5-6: Interpret Two-Way Relative Frequency Tables, Session 1, Activity-Based Exploration, Interpret Two-Way Tables, students create and describe what they do with the two-way relative frequency table model and how it relates to the problem situation. The material states, “What questions can you ask to better define the problem? MPP Have students focus on asking questions about how each value in the table relates to the total and the other values in the row or column. Have students complete the Concluding Questions in their Activity Exploration Journal. What information does a two-way table’s relative frequencies provide? How can you tell if there is an association between the two categorical variables represented in a two-way table”

  • Unit 6: Angles, Triangles, and the Pythagorean Theorem, Lesson 6-6: Determine Distance on the Coordinate Plane, Session 1, Guided Exploration, Mountain Biking, students apply the Pythagorean Theorem and check to see whether an answer makes sense. The materials state, “Does your answer/solution make sense in the context of the situation? MPP Students should identify the total bike ride includes three parts. Discuss why the three sides of the triangle represent the length of the bike ride and why the distance from A to B is represented by the longest side of the right triangle.”

  • Implementation Guide, Unit Walk-Through, Mathematical Modeling 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.”

MP5 is identified and connected to grade-level content; however, there are only 4 opportunities for students to develop MP5, as identified in the materials. One of the opportunities is in Unit 1 and focuses on a prior grade-level standard. Two examples are found in Unit 2 and one example in Unit 5. Students choose tools strategically as they work with teacher support and independently throughout the modules. Examples include:

  • Unit 2: Congruence and Similarity, Unit Overview states, “Use Appropriate Tools Strategically The predominant tool that students use throughout this unit is the coordinate plane. Students use this tool to explore and make generalizations about transformations and to show that two figures are congruent or similar. Students also use paper and pencil, concrete models such as patty paper, and rulers or straightedges. Proficiency in choosing tools is a skill that applies to all areas of mathematics. As students use various tools throughout the unit, engage them in conversation about what insight they expect to gain from the tool and any limitations the tool might have.”

  • Unit 2: Congruence and Similarity, Lesson 2-7: Use Angle-Angle Similarity, Session 1, Activity-Based Exploration, For Four Triangles, students consider how protractors can be helpful when completing the activity. The materials state, “As students-pairs explore the activities, check that all the pairs understand the task. If students need guidance or support ask: What do you know about the three interior angles of a triangle? How do two angles determine the shape of a triangle? How did a protractor help you complete the activity? MPP: Make sure students understand that a protractor can help compare the corresponding side lengths and angle measures. Have students complete the Concluding Question in their Activity Exploration Journal. If two angles of one triangle are congruent to two angles of another triangle, what do you know about the two triangles? Why?”

  • Unit 5: Patterns of Association, Lesson 5-1: Construct Scatter Plots, Session 1, Guided Exploration, Lemonade Sales, students gain insights and recognize imitations from using different tools. The materials state, “The manager of a lemonade stand kept track of the daily high temperatures and daily sales of lemonade at a local park. How can you determine whether there is a relationship between temperature and lemonade sales? You can use a scatter plot to determine relationships between two variables. A scatter plot is a graph on the coordinate plane in which values from two variables are plotted.” Below the question is a two way table followed by a scatterplot graph of Temperature versus Lemonade Sales. Let’s Explore More states, “a. What would the managers learn from making this scatter plot and how could they use that information to plan? b. Based on the scatter plot, what is a reasonable estimate of lemonade sales on a day when the temperature is predicted to be 76°F?”

Indicator 2H
02/02

Materials attend to the intentional development of MP6: Attend to precision; and attend to the specialized language of mathematics for students, in connection to the grade-level content standards, as expected by the mathematical practice standards.

The materials reviewed for Reveal Math 2025 Grade 8 meet expectations for supporting the intentional development of MP6: Attend to precision; and attend to the specialized language of mathematics, for students, in connection to the grade-level content standards, as expected by the mathematical practice standards. 

Within the Implementation Guide, Math Practices states, “To think like mathematicians, students must build thinking habits that help them develop a problem-solving frame of mind. Reveal Math helps students build proficiency with these important thinking habits and problem-solving skills through the Math is... Prompts found in every lesson. These prompts model the kinds of questions students can ask themselves to become proficient problem solvers and doers of math.”

Students attend to precision in mathematics, in connection to grade-level content, as they work with teacher support and independently throughout the units. Examples include:

  • Unit 2: Congruence and Similarity, Lesson 2-1: Explore Translations, Session 1, Activity-Based Exploration, Can You Translate that?, students attend to precision as they explore the characteristics of transformations and translations. They observe what changes and what remains the same when a figure slides. The materials state, “Have students read and respond to the Introductory Question in their Activity Exploration Journal. What changes and what remains the same when a figure is slid? What characteristics can you use to describe the figure before it slides? Which of those characteristics remain the same after the figure slides? Which direction will the figure be facing after a slide is performed? What level of precision does the solution require?”

  • Unit 7: Volume, Lesson 7-3: Solve Problems Involving Cones, Session 2, Activity-Based Exploration, Coney Island, students attend to precision as they explore how the volume of a cylinder compares to the volume of a cone. The materials state, “What must be the same about a cylinder and a cone for the volume of the cone to be one-third the volume of the cylinder? How can you find the volume of a cone?” “Which symbols are appropriate to solve this problem?” 

  • Unit 8: Systems of Linear Equations, Lesson 8-2: Estimate Solutions to Systems of Equations by Graphing, Session 2, Guided Exploration, students attend to precision as they explore systems of equations. The materials state, “Rafael wants to determine the solution to a system of equations, but the intersection point was not on a grid line. What is an estimated solution to the system of equations y=2.5x1y=2.5x-1 and y=0.5x+2y=0.5x+2?” Teacher guidance states, “Does the problem call for an estimate or an exact solution? As students think about if the solution requires an estimate or an exact solution, have them consider if there are better ways to find an estimate and what to do with that estimate.”

Students attend to the specialized language of mathematics, in connection to grade-level content, as they work with teacher support and independently throughout the units. Examples include:

  • Unit 5: Patterns of Association, Lesson 5-4: Use Linear Models to Solve Problems, Session 1, Guided Exploration, Advertising Costs and Sales, students attend to the specialized language of mathematics as they write an equation that represents a line of fit, use it to make a prediction, and explain their thinking. The materials state, “The scatter plot shows the relationship between the amount of money a company spends on advertising and the amount of money they make in sales over several months. Jada drew a line she thinks represents a linear fit to the data. How much should the company expect to make in sales if they spend $50,000 in advertising?” Let’s Explore More states, “a. What is the meaning of the slope in this situation? b. What is the meaning of the y-intercept in this situation? c. The company is considering a $3 million ad during the Super Bowl. What would the company project for sales and do you think the linear relationship will still be valid? Explain your thinking.”

  • Unit 8: Systems of Linear Equations, Lesson 8-2: Estimate Solutions to Systems of Equations by Graphing, Lesson Overview, Focus, Language Objectives states, “Students will distinguish between, and use, coordinating and subordinating conjunctions. To optimize output, students will participate in MLR: Co-Craft Questions and Problems and MLR: Information Gap.” Session 1, Launch, Be Curious: Notice & Wonder, Students attend to the specialized language of mathematics as they share their thinking, “What trends or patterns do you see in the graph? What do you think the graph could be representing? What do you think might occur if the lines on the graph continue farther to the right?” 

  • Unit 9: Irrational Numbers, Exponents, and Scientific Notation, Lesson 9-3: Compare and Order Rational and Irrational Numbers, Lesson Overview, Focus, Language Objectives states, “Students will organize steps in sequential order orally and in writing. To optimize output, students will participate in MLR: Stronger and Clearer Each Time, MLR: Discussion Supports and MLR Co-Craft Problems” Session 1, Launch, Be Curious: Notice & Wonder, students attend to precision as they discuss what is the same and different about the two circles, “How are they the same? How are they different? What do the different marks and labels suggest about the circles? How are the two numbers related to the circles? How are the measurements related to one another? Are these circles more alike than different?”

Indicator 2I
02/02

Materials support the intentional development of MP7: Look for and make use of structure; and MP8: Look for and express regularity in repeated reasoning, for students, in connection to the grade-level content standards, as expected by the mathematical practice standards.

The materials reviewed for Reveal Math 2025 Grade 8 meet expectations for supporting the intentional development of MP7: Look for and make use of structure; and MP8: Look for and express regularity in repeated reasoning, for students, in connection to grade-level content standards, as expected by the mathematical practice standards.

Within the Implementation Guide, Math Practices states, “To think like mathematicians, students must build thinking habits that help them develop a problem-solving frame of mind. Reveal Math helps students build proficiency with these important thinking habits and problem-solving skills through the Math is... Prompts found in every lesson. These prompts model the kinds of questions students can ask themselves to become proficient problem solvers and doers of math.”

MP7 is identified and connected to grade-level content, and there is intentional development of the MP to meet its full intent. Students look for and make use of structure as they work with teacher support and independently throughout the modules. Examples include:

  • Unit 2: Congruence of Similarity, Lesson 2-4: Understand Congruence, Session 2, Guided Exploration, Transforming Figures, students look for patterns while transforming figures on the coordinate plane to determine whether two figures are congruent. The materials state, “Is quadrilateral EFGH congruent to quadrilateral IJKL? Two figures are congruent if there is a sequence of rigid motion transformations that can be used to generate one figure from the other.” Let's Explore More states, “a. How can you determine whether quadrilateral A is congruent to quadrilateral B? b. What sequence of transformations can be used to transform quadrilateral A onto quadrilateral B?”

  • Unit 3: Linear Relationships and Equations, Lesson 3-5: Describe Nonproportional Linear Relationships, Summarize & Apply: Describe Nonproportional Linear Relationships, Apply: Erosion Control, students look for and explain structure as they write a linear equation in the form y=mx+by=mx+b. The materials state, “A lakeshore is eroding each year and there are two mitigation options available. A development team is deciding which method of erosion control they wish to use to cover 5,000 square feet of lakeside over the next 20 years. Mulch must be replaced every two years. The erosion blankets must be replaced every five years. Question: Which method should the team use if they have a budget of $5,000 per year? What limitations will this have?” Students are given a chart of cost per square feet for the mulch and the erosion blankets. 

  • Unit 4: Understand and Analyze Functions, Lesson 4-4: Explore Types of Functions, Practice, Item 12, students look for and explain structure as they identify if a function is linear or nonlinear based on multiple representations. STEM Connection states: “The Mars 2020 Perseverance Rover is traveling across the surface of Mars collecting samples and information to learn about ways to support life on the planet. The rover moves at a constant speed of 120 meters per hour for an hour. It stops to collect soil samples and take pictures for 20 minutes The rover then starts moving to ist next location over a rougher terrain at a constraint speed of 60 meters per hour for 40 minutes.” Error Analysis states, “A classmate says that if Perseverance had continued moving at a constant speed of 120 meters per hour after it stopped to collect samples, then the relationship would represent a linear function. How would you respond to the student?” 

MP8 is identified and connected to grade-level content, and there is intentional development of the MP to meet its full intent. Students look for and express regularity in repeated reasoning as they work with teacher support and independently throughout the modules. Examples include:

  • Unit 3: Linear Relationships and Equations, Lesson 3-4: Describe Proportional Linear Relationships, Session 1, Activity-Based Exploration, students look for and express regularity in repeated reasoning as they explore the relationship between slope, the equation of a line, and ordered pairs on a line. The materials state, “When you calculate the slope of a line, does it matter which two points on the line you pick?” Teacher Guidance states, “As student-pairs explore the activities, check that all pairs understand the task. If students need guidance or support, ask: How can you use two points to determine the slope of the line? How can you use the slope to find any ordered pair on the graph? Math is… Looking for Patterns How is looking for patterns helpful in solving this problem? Have students discuss the patterns they notice. Connect the patterns they notice to their understanding of proportional relationships. Encourage students to consider how they may use these patterns to create an equation that represents a proportional relationship. Have students complete the Concluding Question in their Activity Exploration Journal. How can you create an equation that represents a proportional relationship?” 

  • Unit 7: Volume, Lesson 7-1: Understand and Use Cube Roots, Session 1, Guided Exploration, Puzzle Cube, students evaluate the reasonableness of their answers and thinking as they find the side length of a cube given its volume. The materials state, “How can you find the side length of any cube if you know the volume?” Let’s Explore More states, “a. How are cube roots and square roots similar? How are they different? b. What are the perfect cubes from 1 to 1,000?” MPP, “Have students discuss the calculations involved when finding the volume of a cube. Make sure students recognize that raising a value to the third power involves repeated multiplication. The base of the power is multiplied by itself three times.”

  • Unit 9: Irrational Numbers, Exponents, and Scientific Notation, Lesson 9-1: Represent Rational Numbers in Decimal Form, Session 1, Activity-Based Exploration, Fractions as Decimals, students evaluate the reasonableness of their answers and thinking as they explore the relationship between rational numbers and repeating decimals. Students convert a series of fractions to decimals and record the patterns that they find. The materials state, “Have students review the steps used to convert fractions to decimals. They should note any calculations that are repeated. Make sure students understand that if the remainder equals the dividend when dividing a fraction by a decimal, the pattern will repeat. Have students complete the Concluding Question in their Activity Exploration Journal. How can you express a rational number as a decimal?” Hands-On, “Students work with a partner to write unit fractions ranging from 12\frac{1}{2} to 125\frac{1}{25} and then convert each fraction to a decimal. Students record patterns and draw conclusions about unit fractions written as decimals.”

Overview of Gateway 3

Usability

The materials reviewed for Reveal Math 2025, Grade 8 meet expectations for Usability. The materials meet expectations for Criterion 1: Teacher Supports and Criterion 2: Assessment; and partially meet expectations for Criterion 3: Student Supports.

Criterion 3.1: Teacher Supports

09/09

The program includes opportunities for teachers to effectively plan and utilize materials with integrity and to further develop their own understanding of the content.

The materials reviewed for Reveal Math 2025, Grade 8 meet expectations for Teacher Supports. The materials: provide teacher guidance with useful annotations and suggestions for enacting the student and ancillary materials; contain adult-level explanations and examples of the more complex grade-level concepts and concepts beyond the current grade so that teachers can improve their own knowledge of the subject; include standards correlation information that explains the role of the standards in the context of the overall series; provide explanations of the instructional approaches of the program and identification of the research- based strategies; and provide a comprehensive list of supplies needed to support instructional activities. 

Indicator 3A
02/02

Materials provide 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.

The materials reviewed for Reveal Math 2025 Grade 8 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 2: Congruence and Similarity, Lesson 2-2: Explore Reflections, Lesson Overview, Lesson Pacing states, “Session 1, Lesson Instruction 45 min; Launch Notice & Wonder; Explore Choose Your Option Activity-Based Exploration Can You Reflect That? or Guided Exploration Rearranging Furniture; Wrap Up AEJ Concluding Questions or Assess Exit Ticket.”

  • Unit 8: Systems of Linear Equations, Lesson 8-5: Use Elimination to Solve Systems of Equations, Session 1, Guided Exploration, Restaurant Owner, teachers are provided with questions to ask during the guided lesson. The materials state, “How will you choose which variables to use and what they represent? Why do you think it is important to multiply the terms in one equation by a constant value? Is there another constant value you can multiply each term in an equation to eliminate a variable term? Which equation should we manipulate?”

  • Unit 9: Irrational Numbers, Exponents, and Scientific Notation, Lesson 9-6: Use Power of a Power and Product Properties, Lesson Overview, Orchestrating Rich Mathematical Discourse states, “In this lesson, students explore how to simplify expressions with powers of powers or powers of products. It is important that students have opportunities to engage in discussion about these concepts as they build their understanding of them. These suggestions can help optimize the discussion about exponent properties 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 previous knowledge of exponents and exponents properties your students are likely to use and misconceptions some students may have. Guided Exploration: As you plan for the lesson, review the questions in the teacher presentation and anticipate student responses to those questions. Think about questions students may have about rewriting expressions and different ways students may visualize expressions.”

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, “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.”

Indicator 3B
02/02

Materials contain adult-level explanations and examples of the more complex grade-level/course-level concepts and concepts beyond the current course so that teachers can improve their own knowledge of the subject.

The materials reviewed for Reveal Math 2025 Grade 8 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 the 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 3: Linear Relationships and Equations, Unit Overview, Focus, A Deep Dive into Linear Relationships and Equations states, “The concept of linear relationships is an integral part of instruction form middle school through high school, not only in math but also in other disciplines such as science and engineering. Linear relationships are defined by the straight-line graph that represents the relationship between the independent (x) and dependent (y) variables and are represented as y = mx + b. The defining characteristics of a particular linear relationship are its rate of change (slope, m), and initial value (y-intercept, b). When b = 0, a linear relationship is also a proportional relationship. Linear equations set the foundation for high-school mathematics concepts including functions, modeling and geometry.”

  • Unit 5: Patterns of Association, Lesson 5-2: Interpret Scatter Plots, Lesson Overview, Lesson Highlights and Key Takeaways states, “In this lesson, students will explore the relationships between two quantitative variables. They will be asked to represent the data on a scatter plot, They will then be asked to determine the association between variables. Students are encouraged to use repeated reasoning to approach the task. Scatter plots are used to interpret and investigate patterns in bivariate data.”

  • Unit 6: Angles, Triangles, and the Pythagorean Theorem, Unit Overview, Focus, A Deep Dive into the Pythagorean Theorem states, “The Pythagorean Theorem is among the most familiar geometric concepts; even those who do not remember what it means will recognize the name. The Pythagorean Theorem relates the length of the longest side of a right triangle (the hypotenuses) to the lengths of the other sides (the legs). Represented visually, the area of the square with a side length equal to the hypotenuse is equal to the sum of the squares with side lengths equal to the legs. Represented algebraically, c2=a2+b2c^{2}=a^{2}+b^{2}. The converse is also true: if the square of the hypotenuse is equal to the sum of the squares of the legs, then the triangle is a right triangle. Understanding the Pythagorean Theorem sets the foundation for analytic geometry and trigonometry that frames high school mathematics, starting with the concepts of trigonometric ratios and deriving the equations of conic sections and extending to trigonomic functions and proving geometric theorems algebraically.”

  • Unit 9: Irrational Numbers, Exponents, and Scientific Notation, Lesson 9-7: Use Powers of 10 to Estimate Quantities, Lesson Highlights and Key Takeaways state, “In this lesson, student explore rewriting numbers as products of a number between 1 and 10 times a power of 10 and using those numbers to estimate and compare very large and very small quantities. Powers of 10 can be used to estimate quantities.”

Indicator 3C
02/02

Materials include standards correlation information that explains the role of the standards in the context of the overall series.

The materials reviewed for Reveal Math 2025 Grade 8 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 8: Systems of Linear Equations, Lesson 8-4: Use Substitution to Solve Systems of Equations, Standard: 8.EE.8 is identified for this lesson.

  • Unit 8: Systems of Linear Equations, Lesson 8-5: Use Elimination to Solve Systems of Equations, Major standards 8.EE.8, 8.EE.8.b, and 8.EE.8.c; and Math Practices and Processes, MPP: Reason abstractly and quantitatively are identified for this lesson. 

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

  • Unit 2: Congruence and Similarity, Lesson 2-8: Solve Problems Using Similar Triangles, Lesson Overview, Math Background states, “Students’ study of similar triangles draws on concepts and skills students have gained in previous grades and units. Classify and Measure Triangles Grade 4 students drew and identified types of angles in two-dimensional figures. This is an important development to compare triangles and determine similarity. Classify Triangles by Side Lengths Grade 5 students classified triangles based on their side lengths: equilateral, isosceles, and scalene. As students classify triangles based on their properties, the use of tick marks shows sides of equal length. This work lays the foundation for identifying similar triangles. Draw Geometric Shapes Grade 7 students drew two-dimensional figures with given conditions. This practice leads to an understanding of the relationship of side lengths and angles in triangles.”

  • Unit 3: Linear Relationships and Equations, Lesson 3-2: Compare Proportional Relationships, Lesson Overview, Coherence, Previous states, “Students recognized and represented proportional relationships between quantities.” Now states, “Students graph and compare proportional relationships, interpreting the unit rate as the slope of the line.” Next states, “Students will relate the slope of a line to similar triangles.”

  • Unit 6: Angles, Triangles, and the Pythagorean Theorem, Unit Overview, A Deep Dive into the Pythagorean Theorem states, “The Pythagorean Theorem is among the most familiar geometric concepts; even those who do not remember what it means will recognize its name. The Pythagorean Theorem relates the length of the longest side of a right triangle (the hypotenuse) to the lengths of the other sides (the legs). Represented visually, the area of the square with a side length equal to the hypotenuse is equal to the sum of the squares with side lengths equal to the legs. Represented algebraically, c2=a2+b2c^{2}=a^{2}+b^{2}. The converse is also true: if the square of the hypotenuse is equal to the sum of the squares of the legs, then the triangle is a right triangle. Understanding the Pythagorean Theorem sets the foundation for analytic geometry and trigonometry that frames high school mathematics, starting with concepts of trigonometric ratios and deriving the equations of conic sections and extending to trigonometric functions and proving geometric theorems algebraically.”

  • Unit 7: Volume, Unit Overview, Focus, Math Background states, “The geometric measurement learning progression begins in Grade 3 as students connect multiplication with the area of rectangles and recognize that area is additive. The progression continues in Grade 5 with volume as students derive and apply the formulas for the volume of a rectangular prism and recognize that, like area, volume is additive. Grade 6 students applied properties of figures to find the area of triangles, special quadrilaterals, and polygons and used nets to find the surface area of prisms and pyramids. Grade 7 students used formulas to find the area of a circle and solved real-world problems involving area, volume, and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.”

Indicator 3D
Read

Materials 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 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.”

Indicator 3E
02/02

Materials provide explanations of the instructional approaches of the program and identification of the research-based strategies.

The materials reviewed for Reveal Math 2025 Grade 8 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 4: Understand and Analyze Functions, Unit Overview, Effective Mathematics Teaching Practices, Pose Purposeful Questions states, “As students progress through the unit, pose purposeful questions to assess students' understanding of functions and to advance students' reasoning and sense making about the key ideas of the unit use students' responses to inform instruction and determine what kinds of practice and review might be necessary. In early lessons, as students learn to define and represent functions, pose questions that assess foundational understanding, such as the definition of a function and how key values are shown in different representations of functions. Use students' responses to inform instruction and determine what kinds of practice and review might be necessary. Later, as students progress to differentiating between linear and nonlinear functions, modeling with functions, and comparing functions, pose questions that advance students' reasoning and sense making. For example, in order to advance students' sense making, pose questions that help students decontextualize problem situations and write equations to represent quantities. Also pose questions that help students contextualize representations of functions and use descriptions and labels provided to interpret tables and graphs. In Lesson 6, students compare functions represented in different ways. Pose questions that advance students' sense making about how the initial value and rate of change are shown in each representation and their reasoning about comparing the two functions.” 

  • Unit 7: Volume, Unit Opener, Preparing for the Explore and Develop, “How Do I Choose? To decide which exploration to implement for the lessons in this unit, consider the following: Activity-Based Exploration (ABE) Much of the content is new for students and conceptual in nature. 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 7-3 and 7-4 offer particularly strong opportunities for students to explore volume. Students who need practice working in pairs or small groups could benefit from the Activity-eased Explorations in this unit. As students work in their groups, circulate to ensure that students are working together. Encourage students to participate in the group and listen to their group members. Guided Exploration The lessons in which students apply foundational concepts from prior grades could be opportunities for students to explore the concepts with more guidance. Lesson 7-2 connects finding the volume of a cylinder to finding the volume of a prism and could be an opportunity to implement the Guided Exploration if your students do not have a solid foundation in finding the volume of a prism. Guided Exploration can be beneficial when students are engaged during class discussions. The Collaborate & Connect activities in the Guided Explorations also provide opportunities for students to work in pairs. Circulate as students work in pairs to encourage effective collaborations.”

  • Unit 9: Irrational Numbers, Exponents, and Scientific Notation, Lesson 9-7: Use Powers of 10 to Estimate Quantities, Activity-Based Exploration, The Power of 10, the teacher guide states, Support Productive Struggle, “As student-pairs explore the activities, check that all pairs understand the task If students need guidance or support, ask: How can you compare MB to GB? How can you express the numbers using powers of 10? Hands On: Have students determine the number of ants it would take to lift a car. Explain that an ant weighs 2.5 milligrams and can lift 50 times their body weight A car weighs approximately 1360 kilograms. Encourage students to rewrite each amount as a power of ten using the same unit of measure.” Support Productive Struggle, “If students need guidance or support, ask How can you compare milligrams to kilograms? How can you express the numbers using powers of 10?”

Indicator 3F
01/01

Materials provide a comprehensive list of supplies needed to support instructional activities.

The materials reviewed for Reveal Math 2025 Grade 8 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 1: Math Is…, Unit Planner, Materials To Gather states, “Math is Mine Teaching Resource, photographs of varying sizes, ruler, straight-edge, Sudoku Teaching Resource”

  • Unit 2: Congruence and Similarity, Lesson 2-7: Use Angle-Angle Similarity, Lesson overview, Materials states, “The materials may be for any part of the lesson. Two Angles Teaching Resources, protractor, patty paper, scissors”

  • Unite 8: Systems of Linear Equations, 8-2: Estimate Solutions to Systems of Equations by Graphing, Lesson Overview, Materials states, “The materials may be for any part of the lesson. Graph paper, straightedge, Transportation Cards Teaching Resources”

  • Unit 9: Irrational Numbers, Exponents, and Scientific Notation, Unit Planner, Materials To Gather states, “Calculator, Blank Number Lines Teaching Resource, Blank Open Number Lines Teaching Resource, Order Rational and Irrational Numbers Teaching Resource, Exponential Patterns Teaching Resource, small squares of paper, note cards”

Indicator 3G
Read

This is not an assessed indicator in Mathematics.

Indicator 3H
Read

This is not an assessed indicator in Mathematics.

Criterion 3.2: Assessment

10/10

The program includes a system of assessments identifying how materials provide tools, guidance, and support for teachers to collect, interpret, and act on data about student progress towards the standards.

The materials reviewed for Reveal Math 2025, Grade 8 meet expectations for Assessment. The materials identify the content standards and mathematical practices assessed in formal assessments. The materials provide multiple opportunities to determine students' learning and sufficient guidance to teachers for interpreting student performance, and suggestions for following-up with students. The materials include opportunities for students to demonstrate the full intent of grade-level standards and mathematical practices across the series.

Indicator 3I
02/02

Assessment information is included in the materials to indicate which standards are assessed.

The materials reviewed for Reveal Math 2025 Grade 8 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:

  • Unit 2: Congruence and Similarity, Lesson 2-3: Explore Rotations, Assess to Inform Differentiation, Lesson Quiz, Item 3 states, “Rectangle PQRS has vertices at P (-1,6), Q(4,6), R(4,-2), and S(-1,-2). If PQRS is rotated 270° counterclockwise about the origin to create P’Q’R’S’, what are the coordinates of the image?” In the Item Analysis, the question is aligned to 8.G.1, 8.G.1.a, 8.G.1b, 8.G.1c "Write rotation rule" and MP 1, Make sense of problems and persevere in solving them.

  • Unit 3: Linear Relationships and Equations, Unit Review, Performance Task states, “For each Part A through C, answer the question and include justifications. William works for a park. Over several months, he studies the amount Of beach erosion on a lake. Part A. In 6 months, 15 feet of beach is lost to erosion. What is the monthly rate of erosion? How can you model the erosion with a linear equation? Part B. At the beginning of the study, there was 40 feet of beach. How can you model the amount of beach remaining with a linear equation? Part C. When the amount Of beach remaining equals 15 feet, the park needs to close to make repairs. What can William do to determine when the park will need to close? If the erosion continues at the same rate, when will the park close? Unit Reflect: How can you use the relationship between two variables to write a linear equation?” In the Item Analysis, the question is aligned to 8.EE.6, 8.EE.7, 8.EE.7b “Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane.”

  • Unit 5: Patterns of Association, Unit Assessment, Items 2 and 3 state, “2. The scatter plot shows the relationship between the number of meals eaten in restaurants each week and the number Of miles driven in a car. Describe the relationship shown in the scatter plot. 3. Does the scatter plot show a positive, negative, or no association? ___ association” In the Item Analysis, the question is aligned to 8.SP.1 "Clusters in Scatter Plots, Positive and Negative Associations", MP 2, Reason abstractly and quantitatively, and MP 7, Look for and make use of structure, for students.

  • Program Overview: Course Assessments, Benchmark Assessment, Benchmark Test 1: Course 3, Item 24 states, “Celinda scored 2 more than 3 times as many strikes as Teresa did while they were bowling. Celinda scored 8 strikes. Part A Let x represent the number Of strikes Teresa scored. Write an equation to model the situation. Part B Solve the equation for x. How many strikes did Teresa have? ___ strike(s)” In the Item Analysis, the question is aligned to 8.EE.7 “Solve a two-step equation”

Indicator 3J
04/04

Assessment system 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 materials reviewed for Reveal Math 2025 Grade 8 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: Congruence and Similarity, Readiness Diagnostic, “Administer the Readiness Diagnostic to determine your students' readiness for this unit.” Item 1 states, “What is the value of -10 + (-11)?” Targeted Intervention states, “Use the Intervention Lessons recommended in the table to provide targeted intervention to students who need it. These lessons are available in the Digital Teacher Center and are assignable.” 

  • Unit 4: Understand and Analyze Functions, Performance Task, Hospital Wait Times states, “Answer each part with justification. Julissa works for a company that advises hospitals on efficient methods to serve emergency patients. She developed a plan with Metro Hospital to reduce the average time a patient waits in the emergency room. The table shows the average wait time per patient for the first 3 months of implementing the new plan. Part A: How can you describe the relationship between the average wait time and the months? Is the relationship a function? Justify your answer.” Students are given a table that has Month, x over Average Wait Time (min), y. The table has the x values of 0, 1, 2, and 3 and the y values of 75, 71.5, 68, and 64.5. The rubric states, “2 POINTS Work reflects proficiency. Student correctly identifies relation as a function and explains rationale. 1 POINT Work reflects progressing proficiency. Student correctly identifies relation as a function but fails to explain rationale. 0 POINTS Work reflects weak proficiency. Student fails to identify relation as a function and explain rationale.”

  • Unit 6: Angles, Triangles, and the Pythagorean Theorem, Math Probe, Analyze the Probe, 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 select whether each statement concerning the angle measures in the figures is true or false, and explain their choice. Targeted Concept: Understand the relationship between angles formed by intersecting lines and angles within triangles.” Target Misconceptions: “Students may rely completely on the way the figure is drawn to determine the size of an angle. Students may use the length of the rays that form an angle to determine its size. Students may believe they cannot compare angle measures without knowing the numeric measures of the angles.” Angle Measures, “Use the figure to select whether each statement is true or false. If there is not enough information, select not enough information. Then, explain your choice.” Figure 1 is a picture of parallel lines cut by a transversal.

  • Unit 9: Irrational Numbers, Exponents, and Scientific Notation, Unit Assessment, Unit Assessment: From A, Item 2 states, “During the soccer season, the starting forward made 10 out of 27 shots on goal. At this rate, how many goals would the forward make next season if he takes 35 shots on goal? Explain.” Sample Answer states, “The forward’s rate is 1027\frac{10}{27}= 0.3700.\overline{370} or about 37%. 37% of 35 is 12.95, so the starting forward will make about 13 goals next season.” Item Analysis, “Item 2, DOK 2, Lesson 9-1, Guided Support Intervention Lesson Terminating & Repeating Decimal Numbers, Standard 8.NS.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.

Indicator 3K
04/04

Assessments include opportunities for students to demonstrate the full intent of grade-level/course-level standards and practices across the series.

The materials reviewed for Reveal Math 2025 Grade 8 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 2: Congruence and Similarity, Lesson 2-5: Explore Dilations, Session 2, Assess to Inform Differentiation, Lesson Quiz, Item 5, students are assessed with a writing task by describing the effects of scale factor on two-dimensional figures. The task reads, “Harold believes that any scale factor written as a fraction will result in a reduction in size of an image. Is Harold correct? Explain your reasoning.” (8.G.3 and MP3)

  • Unit 3: Linear Relationships and Equations, Lesson 3-2: Compare Proportional Relationships, Assess to Inform Differentiation, Lesson Quiz, Item 3, students use information from a graph to determine the unit rate. The item reads, “A local charity is selling pies to raise money. The amount the charity received y for x pies is modeled by y = 6x. The charity is also selling cakes, and the money it raises from cake sales is shown in the graph. Complete the sentences. The pies sell for $ ___ each. The cakes sell for $ ___ each. The ___ raise more money per unit sold.” (8.EE.5 and MP2)

  • Unit 4: Understand and Analyze Functions, Unit Assessment, Item 1, students determine which scenarios can be modeled by a linear function. The item reads, “Which situation cannot be modeled by a linear function? A. Jimmy is 50 miles from his home and driving 20 miles per hour on an electric scooter. B. There are 2 water lilies in a pond on Day 1, 4 on Day 2, 8 on Day 3, and 16 on Day 4. C. An investor puts $600 into an account and then adds $100 per week. D. A book has 650 pages and Billy reads 20 pages each night.” (8.F.3 and MP4) 

  • Benchmark 3, Item 12, students are assessed by constructing and interpreting a two-way table. The item reads, “A survey of 220 students showed that 46 seventh graders are attending the science fair. A total of 105 students are attending the fair. Among those surveyed were 108 eighth graders. Part A: Complete the two-way table. Part B: How many more eighth graders than seventh graders are attending the fair? ___ more eighth graders” (8.SP.4 and MP4)

Indicator 3L
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Assessments offer accommodations that allow students to demonstrate their knowledge and skills without changing the content of the assessment.

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.

Criterion 3.3: Student Supports

07/08

The program includes materials designed for each student’s regular and active participation in grade-level/grade-band/series content.

The materials reviewed for Reveal Math 2025, Grade 8 partially meet expectations for Student Supports. The materials met expectations for: multiple extensions and/or opportunities for students to engage with grade- level mathematics at higher levels of complexity; providing varied approaches to learning tasks over time and how students demonstrate their learning; opportunities for teachers to use varied grouping strategies; providing strategies and supports for students who read, write, and/or speak in a language other than English to support their regular and active participation in learning grade-level mathematics; and manipulatives, both virtual and physical, are accurate representations of the mathematical objects they represent and, when appropriate, are connected to written methods. The materials partially meet expectations for: providing strategies and supports for students in special populations to support their regular and active engagement in learning grade-level mathematics; providing guidance to encourage teachers to draw upon student home language to facilitate learning; and providing supports for different reading levels to ensure accessibility for students.

Indicator 3M
01/02

Materials provide strategies and supports for students in special populations to support their regular and active participation in learning grade-level/series mathematics.

The materials reviewed for Reveal Math 2025 Grade 8 partially meet expectations for providing strategies and supports for students in special populations to support their regular and active participation in learning grade-level/series mathematics.

Within the Implementation Guide, Unit Features, 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 is 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” 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.” 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 states, “Targeted intervention resources are available to assign students 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.” 

While suggestions are outlined within the Unit Overview, and individual lessons include Effective Mathematics Teaching practices, the materials lack specific strategies and supports for differentiating instruction to meet the needs of students in special populations during the Explore phase of the lesson. Additionally, within the Activity-Based Exploration and Guided Exploration, there is no information or strategies regarding supports for special populations. Differentiation and targeted intervention opportunities are available after students take the Lesson Quiz, but not during the lessons. Examples of supports for special populations include: 

  • Unit 3: Linear Relationships and Equations, Lesson 3-1: Describe the Slope of a line, Session 2, Differentiate, Lesson Quiz Recommendations state, “If students score At least 4 of 5 Then have students do Any B or E activity. If students score 3 of 5 Then have students do Any B or E activity. If students score 2 or fewer of 5 Then have students do Any R or B activity.” Reinforce Understanding states, “Take Another Look Lesson Assign the interactive lesson to reinforce targeted skills. The Slope of a Line Find the unit Rate” Build Proficiency, “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. Operations on Rational Numbers in the Real World” Extend Thinking states, “STEM Adventures In this STEM Adventure, biosystems engineers are exploring erosion control solutions for different project sites. Use your linear relationship and equation knowledge to test and interpret which erosion control solutions are most efficient.”

  • Unit 5: Patterns of Association, Readiness Diagnostic, Teacher Guidance states, “Administer the Readiness Diagnostic to determine your students’ readiness for this unit. Targeted Intervention Use the Intervention Lessons recommended in the table to provide targeted intervention to students who need it. These lessons are available in the Digital Teacher Center and are assignable.” In the Item Analysis table for the Readiness Diagnostic, the Item, DOK, and Skill are listed in a table with a corresponding Guided Support Intervention Lesson and Standard. 

  • Unit 6: Angles, Triangles, and the Pythagorean Theorem, Unit Overview, Effective Teaching Practices, Support Productive Struggle in Learning Mathematics states, “This unit introduces two big ideas to students that are foundational for higher-level mathematics: angle relationships and the Pythagorean Theorem. As students progress through the unit, provide opportunities and supports for them to engage in productive struggle with these mathematical ideas and relationships. As students learn about and apply angle relationships and the Pythagorean Theorem, there are multiple opportunities to engage them in productive struggle. Students may grapple with: identifying congruent angle pairs formed when a transversal crosses parallel lines. applying the relationships among interior and exterior angles of a triangle to find missing angle measures. understanding and applying the relationship among the side lengths of a right triangle. finding the distance between points on the coordinate plane. Allow students to struggle productively as they work through the concepts and problems; however, provide support and scaffolding as needed to prevent students from becoming frustrated. For example, if students struggle to apply the relationships between interior and exterior angles of a triangle, ask guiding questions about supplementary angles and straight lines or have students trace and manipulate the figures. If students struggle with the concept of using the Pythagorean Theorem to find the distance between two points on the coordinate plane, help them connect the line segment with the hypotenuse of a right triangle and provide support as they find the horizontal and vertical side lengths.”

  • Unit 7: Volume, Lesson 7-1: Understand and Use Cube Roots, Number Routines, Orchestrating Rich Mathematical Discourse states, “In this lesson, students explore finding the side length of a cube, given its volume. It's important that students have opportunities to engage in discussion about this concept as they build their understanding of them. These suggestions can help optimize the discussion about cube roots 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. Some students may attempt to multiply by 3 instead of using the exponent of 3. Other students may think that a cube root can be found using division. Guided Exploration: As you plan for the lesson, review the questions in the teacher presentation and anticipate student responses to those questions. Think about which questions may pose challenges for students. Some students may struggle to find the side length, given the volume, as much of their previous experience has been finding the volume given the side length.”

Indicator 3N
02/02

Materials provide extensions and/or opportunities for students to engage with grade-level/course-level mathematics at higher levels of complexity.

The materials reviewed for Reveal Math 2025 Grade 8 meet expectations for providing extensions and/or opportunities for students to engage with grade-level/course-level mathematics at higher levels of complexity.

Advanced students have opportunities to think differently about learning with extension activities and are not required to do more assignments than their classmates. The Implementation Guide, Professional Learning Resources (page 65) states, “Extend Thinking: The STEM Adventures and Websketch activities powered by Geometer’s Sketchpad offer students opportunities to solve non-routine problems in a digital environment. The print-based Extend Thinking activity master offers an enrichment or extension activity.” Specific recommendations are routinely part of the Differentiate and STEM sections of lessons and Units, as noted in the following examples: 

  • Unit 2: Congruence and SImilarity, Lesson 2-2: Explore Reflections, Session 2, Differentiate, Extend Thinking, STEM Adventures, students extend their thinking of 8.G.3, describe the effect of dilations, translation, rotations, and reflections on two-dimensional figures using coordinates. The materials state, “In this STEM Adventure, game designers are creating a video game to help students learn about renewable energy types. Students use their knowledge of transformations to complete the building design for the game city. Use indirect measurement and proportions to complete the table. This chart contains information about various observers and tall buildings. use proportions and your calculator to complete the chart Of tall buildings Of the world.” Students are given a chart with column headings: Height of observer, Length of Shadow, Building Location, Height of Building, Length of Shadow. Students are provided 4 out of the 5 columns of information and they must find the missing value. 

  • Unit 4: Understand and Analyze Functions, Lesson 4-3: Represent Functions, Session 2, Differentiate, Extend Thinking, STEM Adventures, students extend their thinking of 8.F.1, understand that a function is a rule that assigns to each input exactly one output… “In this STEM Adventure, students explore waste management. Your understanding of functions will help you as you manage a waste management facility. For exercises 1 - 6, state whether the given values describe a discrete or a continuous function. 1. The number of homework problems assigned each day for a week. 2. The temperature in a city over a 5-hour period. 3. The number of desks in a classroom. 4. The distance traveled by a biker on a 3-hour training ride. 5. The number of shells collected each day during a 7-day vacation. 6. The weight of a baby from birth to 6 months of age.”

  • Unit 8: Systems of Linear Equations, Unit Opener: Explore Through STEM, Tree Advice, students extend their thinking of 8.EE.8, analyze and solve pairs of simultaneous linear equations. The materials state, “When selecting trees to plant for either conservation or economic benefits, people might turn to the USDA National Agroforestry Center for advice. They can find information about the attributes of different species and even comparisons of those attributes in order to select the best trees for the intended purpose.” Think About It states, “What makes a tree or shrub better suited for a given area of the country? Throughout this unit students will explore agroforestry and the role it plays in environmental engineering. Have students notice and wonder about the image. Ask: In what kind of surroundings was this photo taken? What are the people in the photo doing? How do you know? How is planting trees related to environmental engineering?”

  • Unit 9: Irrational Numbers, Exponents, and Scientific Notation, Lesson 9-6: Use Power of a Power and Product Properties, Session 2, Differentiate, Extend Thinking, STEM Adventures, students extend their thinking 8.EE.1, know and apply the properties of integer exponents to generate equivalent numerical expressions. The materials state, “In this STEM Adventure, students use their understanding of real numbers to explore harnessing the natural power of the wind to generate electricity.” Extend Thinking, “The power of a power and product properties can be used in geometry to find volume and area. Given a cube with sides that are 626^{2} centimeters long, you can find the volume of the cube as shown below. (62)3=66(6^{2})^{3}=6^{6} or 46,656 cm3\textit{cm}^{3}. Given the side length of each cube, find the volume. 1. 333^{3} inches.”

Indicator 3O
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Materials 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.

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 WebsketchTM 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 WebsketchTM 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?”

Indicator 3P
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Materials provide opportunities for teachers to use a variety of grouping strategies.

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.”

Indicator 3Q
02/02

Materials provide 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.

The materials reviewed for Reveal Math 2025 Grade 8 meet expectations for providing strategies and supports for students who read, write, and/or speak in a language other than English to regularly participate in learning grade-level mathematics.

Within the Implementation Guide, Support for Multilingual Learners, Unit-Level support (page 50) states, “At the unit level are three features that provide support for teachers as they prepare to teach English Learners. The Designated Language Support feature offers insights into one of the four areas of language competence — reading, writing, listening, and speaking — and strategies to build students’ proficiency with language.” Lesson-level support Language Objectives state, “In addition to a content objective, each lesson has a language objective that identifies a linguistic focus of the lesson for English Learners.” Multilingual Learner Scaffolds state, “Multilingual Learner Scaffolds provide teachers with scaffolded supports to help students participate fully in the instruction. The three levels of scaffolding within each lesson — Entering/Emerging, Developing/Expanding, and Bridging/Reaching are based on the 5 proficiency levels of the WIDA English Language Development Standards. With these three levels, teachers can scaffold instruction to the appropriate level of language proficiency of their students.” Support for active participation in grade-level mathematics is consistently included within lessons. Examples include:

  • Unit 1: Math Is…Unit Overview, Multilingual Learner Scaffolds, “Entering/Emerging Reference the Spanish cognates sujeto, verbo, and objeto as needed. For the writing portions of the activity, allow students to "draft" sentences orally and receive feedback before writing them. Check the written sentences for correct grammar and punctuation. Developing/Expanding: Help students practice revising by having them trade sentences with a partner. Tell them to add information to drafts in ways that stay true to the original meaning/structure. Remind them that they can invert subject-verb order by writing questions. Bridging/Reaching Guide: students to explore sentence construction by using compound subjects and predicates, and forming compound sentences. Then challenge them to form complex sentences that feature subordinate clauses. Exemplars of these can be found throughout the student edition.”

  • Unit 4: Understand and Analyze Functions, Unit Overview, Multilingual Learner Scaffolds state, “Entering/Emerging Support students if they struggle with distinguishing between infinitives and other verbals- Point out that while I like swimming and / like to swim are interchangeable, I decided going home and I decided to go home are not. Developing/Expanding Encourage students to vary the placement of the adverb phrases in their sentences: beginning, middle, and end. Bridging/Reaching: Explain that more than one infinitive can appear in a sentence. Present: They wanted to learn how to plot ordered pairs. Guide students to understand the role of the second infinitive (to plot) as an adverb phrase.”

  • Unit 6: Angles, Triangles, and the Pythagorean Theorem, Lesson 6-2: Understand Angle Relationships and Triangles, Session 1, Guided Exploration, Triangles in Bridges, Multilingual Learner Scaffolds state, “Entering/Emerging Support students in answering the first Let's Explore More question, explaining that it calls for them to describe a mental process. Model possible responses by providing sentence frames with sequence words: First, I can (add)...; Then, I can (subtract).... Developing/Expanding Ensure that students understand vocabulary by explaining that the verbs in form a straight line and create a triangle are essentially synonymous. Point out that the construction is made up of in the first sentence also provides a related alternative. Bridging/Reaching Help students respond to the second Let's Explore More question by reviewing generalizations as well as related word forms and constructions (l can generalize that...). Encourage them to use content area vocabulary such as sum and supplementary angles.”

  • Unit 8: Systems of Linear Equations, Lesson 8-4: Use Substitution to Solve Systems of Equations, Session 1, Guided Exploration, Data Prices, Multilingual Learner Scaffolds, “Entering/Emerging Pre-Teach unfamiliar vocabulary, such as hotspot and gigabytes. Reinforce comprehension of key representations/terms, such as expression, quantities, and equation by saying them aloud. Have students indicate examples in the text. Help students use them orally in sentences. Developing/Expanding: Have students practice speaking and listening skills by conducting a brief teaching demonstration. Pair students and direct one to deliver oral directions for Step 1 while the partner indicates the correct representations. Then have them reverse roles for Step 2. Bridging/Reaching: Allow students to elaborate on their responses to the second Let's Explore More question by adding a key visual representation—a graph. Have them walk a partner through their reasoning orally as they reference the graph and any other representations.”

Indicator 3R
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Materials provide a balance of images or information about people, representing various demographic and physical characteristics.

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.”

Indicator 3S
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Materials provide guidance to encourage teachers to draw upon student home language to facilitate learning.

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.]”

Indicator 3T
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Materials provide guidance to encourage teachers to draw upon student cultural and social backgrounds to facilitate learning.

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.

Indicator 3U
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Materials provide supports for different reading levels to ensure accessibility for students.

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.”

Indicator 3V
02/02

Manipulatives, both virtual and physical, are accurate representations of the mathematical objects they represent and, when appropriate, are connected to written methods.

The materials reviewed for Reveal Math 2025 Grade 8 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: Congruence and Similarity, Lesson 2-4: Understand Congruence, Session 1, Activity-Based Exploration, Are They the Same?, Implement Tasks That Promote Reasoning and Problem Solving states, “Students use transformations to show that two figures have the same size and shape. The goal is to have students understand that two figures are the same size and shape if there is a rigid motion, or a sequence of rigid motions, that maps one figure onto the other. Materials state, “Digital: Activity Exploration Journal, pp. AEJ19—AEJ20, 1 per student Hands-On: Unit Squares Teaching Resource, 1 per student; scissors, 1 per pair; Activity Exploration Journal, pp. AEJ19—AEJ20, 1 per student” Directions state, “Have students read and respond to the Introductory Question in their Activity Exploration Journal. What transformations maintain a figure's shape and size? Group students in pairs to work on this activity. Today we will explore using transformations to show two figures have the same size and shape. Digital: Students explore using a sequence of transformations to determine if two figures have the same size and shape. Before students begin the first activity, have them explore the WebsketchTM tools they will be using. Ensure that they can perform translations, reflections, and rotations. Hands-On: Have each student use the Unit Squares Teaching Resource to draw as many figures as they can with an area of 4 square units. Students compare their drawings to those of their partners, keeping track of the total number of figures they created. Students then cut out their figures and compare them to their partners to see how many distinct shapes they constructed.”

  • Unit 3: Linear Relationships and Equations, Lesson 3-3: Use Similar Triangles to Determine Slope, Session 1, Activity-Based Exploration, Slopes and Similar Triangles, Implement Tasks That Promote Reasoning and Problem Solving state, “Students explore the slope of the hypotenuses of similar triangles.” Materials, “Digital: Activity Exploration Journal, 1 per student; Hands-On: 20 x 20 Grids Teaching Resource, 1 per student; colored pencils, 1 set per student-pair; Activity Exploration Journal, 1 per student.” Directions state, “Have students read and respond to the Introductory Question in their Activity Exploration Journal. What does it mean to say that two triangles are similar? Group students in pairs to work on this activity. Today we will explore the relationship between the hypotenuses of similar triangles. Digital: Students explore how similar triangles whose hypotenuse lies on the same line have the same slope. Before students begin the activity, have them explore the WebsketchTM tools they will be using. Be sure they can drag the points. Hands-On: Have students draw a straight continuous line on the 20 x 20 Grids Teaching Resource. One student uses a colored pencil to draw a triangle whose hypotenuse lies on the line. The other student uses a different color to draw a different triangle whose hypotenuse lies on the same line. Students repeat this process several times, comparing and contrasting the different triangles.”

  • Unit 7: Volume, Lesson 7-3: Solve Problems Involving Cones, Session 1, Activity-Based Exploration, Cone-y Island, Implement Tasks That Promote Reasoning and Problem Solving state, “Students explore how the volume of a cylinder compares to the volume of a cone.” Materials, “Digital: Activity Exploration Journal, 1 per student Hands-On: Net of Cone Teaching Resource; Net of Cylinder Teaching Resource; ruler; scissors, 1 per student-pair; tape, 1 roll per student-pair; popcorn kernels or rice; Activity Exploration Journal, 1 per student.” Directions state, “Have students respond to the Introductory Question in their Activity Exploration Journal. What is the relationship between the volumes of a cone and a cylinder if their height and radius are the same? Group students in pairs to work on this activity. Today we will explore the connection between the volumes of cylinders and cones with equivalent heights and radii. Digital: Students examine the relationship between a cone and a cylinder with the same base and height. Before students begin the activity, have them explore the WebsketchTM tools they will be using. Ensure they understand dragging P changes the area of the base and Q changes the height of the cylinder. Be sure students also understand how to use the Calculate tool prior to beginning the activity.”

  • Unit 8: Systems of Linear Equations, Lesson 8-4: Use Substitution to Solve Systems of Equations, Session 1, Activity-Based Exploration, I Can’t Believe it’s Not Math! Implement Tasks That Promote Reasoning and Problem Solving state, “Students explore puzzles where they use logic and substitution to determine the value of different shapes.” Materials state, “Digital: Activity Exploration Journal, 1 per student Hands-On: Tangrams or pattern blocks, 1 set per student-pair; Tangam Puzzle Teaching Resource; Activity Exploration Journal, 1 per student” Directions state, “Have students respond to the Introductory Question in their Activity Exploration Journal. How can you find the solution to a system of equations without using a graph? Group students in pairs to work on this activity. Today we will explore how to solve a system of equations without using a graph. Digital: Students explore finding the values of each shape in a puzzle. Before beginning the activity, you may want to discuss how the shapes in each row or column have values that add up to the amounts shown when the students click show sum. Reinforce that each shape has the same value for each instance in that puzzle. Hands-On: Provide students with the Tangram Puzzle Teaching Resource. Have students place tangram pieces or pattern blocks in the boxes on their Activity Exploration Journal and write the sums for each row and column provided. Then have students find the value of each type of shape. Note that for the puzzle provided, the answers are: circle: 9, square: 8, triangle: 6, hexagon: 3. This activity can be repeated with more or less difficult puzzles as needed.”

Criterion 3.4: Intentional Design

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The program includes a visual design that is engaging and references or integrates digital technology, when applicable, with guidance for teachers.

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 standards; include or reference digital technology that provides opportunities for teachers and/or students to collaborate with each other; have a visual design that supports students in engaging thoughtfully with the subject that is neither distracting nor chaotic; and provides teacher guidance for the use of embedded technology to support and enhance student learning. 

Indicator 3W
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Materials 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.

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 WebsketchTM 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?”

Indicator 3X
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Materials include or reference digital technology that provides opportunities for teachers and/or students to collaborate with each other, when applicable.

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.”

Indicator 3Y
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The visual design (whether in print or digital) supports students in engaging thoughtfully with the subject, and is neither distracting nor chaotic.

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.

Indicator 3Z
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Materials provide teacher guidance for the use of embedded technology to support and enhance student learning, when applicable.

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.”