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 6th Grade

Alignment Summary

The materials reviewed for Reveal Math 2025, Grade 6 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.

6th 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 6 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 6 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 6 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:

  • Benchmark Assessment 2, Item 32, “Four expressions are given. Expression A: 0.32+80.3^2+8, Expression B: 23+0.092^3+0.09, Expression C: 23+0.0322^3+0.03^2, Expression D: 32÷102+233^2\div10^2+2^3. Which expression is not equivalent to the other three? Justify your response. Enter the answer.(6.EE.2)

  • Unit 2: Understanding the World Around Us Through Statistics, Unit Assessment: Form A, Item 1, “Which of the following are statistical questions? Select all that apply. A) How many 5-kilometer races are in Kentucky in October? B) How many pairs of running shoes does each runner own? C) How many miles are in a 5-kilometer race? D) How many feet are in a mile? E) How fast can each person in a running club run? F) What is the finish time for each runner in the race?” (6.SP.1)

  • Unit 3: Ratios and Rates, Lesson 3-6: Ratio Reasoning: Convert Measurements within the Same System, Session 1, Exit Ticket, “Apollo the Great Dane puppy weighs 9 pounds at 1 month old. How can you use the ratio of ounces to pounds to find Apollo’s weight in ounces? Give Apollo’s weight in ounces.” (6.RP.3d)

  • Unit 5: Solve Area, Surface Area, and Volume Problems, Lesson 5-8: Determine Surface Area of Prisms, Session 2, Lesson Quiz, Item 4, “A box in the shape of a square pyramid is going to be painted with spray paint, including the bottom. The box has a base with sides that measure 4 feet and a slant height of 6 feet. A 1-pound can of spray paint covers 30 square feet and costs $7.50. How many cans of spray paint are needed? What is the cost of painting the box? Show and explain your work.” (6.G.4)

  • Benchmark Test 3, Item 14, “The table shows the location of four divers relative to sea level. The integer 0 represents sea level. Jon claims that diver A is the farthest from sea level. Do you agree? Explain.” The item includes a table with two rows. The row labeled “Diver” has four columns A, B, C, and D. The second row is labeled “Depth (ft)” and contains values 2, -5, 0, -3. (6.NS.7)

Above grade-level assessment items are present but could be modified or omitted without significant impact on the underlying structure of the instructional materials. The materials are digital and download as a Microsoft Word document, making them easy to modify or omit items. These items include:

  • Unit 4: Understand and Use Percentages, Unit Assessment: Form A, Item 14, “The regular price of a baseball hat is $14.45. If Carlos buys the baseball hat on sale for 20% off the regular price, how much change will he receive after paying with $20? Explain how you found your answer.” (7.RP.3) The task requires students to use proportional relationships to solve multistep ratio and percent problems e.g. markups and markdowns.

  • End-of-Year Assessment, Item 32, “Eli bought bagels that cost $1.15 each. The total cost c of b bagels is equal to $1.15b. Complete the table to find the number of bagels purchased for each total cost. Enter the answers.” A table with three columns and four rows is provided. The first column is labeled “Input, b” and has three empty rows. The second column is labeled “Rule, 1.15b” and has “1.15b” in each of the three rows. The third column is labeled “Output ($), c” and has 8.05 in the first row, 10.35 in the second row, and 11.05 in the third row. Students are asked to fill out the column labeled “Input, b.” (8.F.1) Function rules and inputs and outputs are not formally introduced until grade 8. The task happens at the end of course assessment and the reasoning for the task is also consistent with 6.EE.9.

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 6 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 2: Understanding the World Around Us Through Statistics, Lesson 2-3: Describe Data Using the Median, Session 1, Guided Exploration, Let’s Explore More, students find the measure of center and the median. Part B states, “How might a value in the data set that is much larger or much smaller than the rest of the data affect the median?” Practice Problems, Exercises 3-4, “Reginald records the number of trees at local parks. The results are shown in the table. 3. What is the median number of trees at the local parks near Reginald? 4. What does the median number tell Reginald?” Lesson 2-4: Represent and Describe Data in a Box Plot, Session 1, Exit Ticket, Item 1, “The box plot shows the number of points a basketball team scores in its games. Use the box plot to determine the measures of the lower extreme, upper extreme, Quartile 1, median, and Quartile 3 for the data. Enter the answer.” The item includes a box plot diagram with a lower extreme of 32, an upper extreme of 50, and a median of 38. In the box plot diagram, Quartile 1 is 34 and Quartile 3 is 44. These problems meet the full intent and give all students extensive work with 6.SP.5c (Summarize numerical data sets in relation to their context, such as by: Giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern…) 

  • Unit 3: Ratios and Rates, Performance Task, students use a table of values to compare trout populations to area and convert square feet to acres to determine if trout levels are within a recommended range. It states, “Lucy works for a local fish commission and is analyzing the numbers of trout stocked in ponds. The table shows the number of trout stocked and the sizes of five ponds. Part A: How do the ratios of trout to pond size compare in the five ponds? Part B: The recommended number of trout in a pond is 1,000 to 1,200 per acre. Which of the ponds have trout levels that are not within the recommended range? How could the number of trout in those ponds be adjusted to put the trout levels within the recommended range? Part C: One acre is equivalent to 43,560 square feet. Suppose Lucy determines that a pond with an area of 65,340 square feet has 1,770 trout stocked. Is this pond within the recommended range?” The table includes a column listing five ponds (A, B, C, D, E), a column listing the number of trout in each pond (1,840; 520; 2,496; 2,112; 1,350) and a column listing the area in acres of each pond (1.6; 0.4; 2.4; 2.2; 1.25). Students are encouraged to use ratio and rate reasoning in a real-world scenario, use tables of equivalent ratios to determine which ponds have the recommended range of trout, and use ratios to convert measurements and units. Lesson 3-5: Compare Ratio Relationships, Lesson Quiz, Item 1 and 2, Item 1, students use tables to compare ratios. “Each table represents an equivalent ratio. Complete the sentences. Based on the cost per fluid ounce, ___ juice is the less expensive drink. It is ___ cents per fluid ounce.” Item 2, “In the last 30 minutes, a car has traveled at a constant speed of 65 miles per hour on a highway. The graph shows the distance a train has traveled in the last 30 minutes. Complete the sentence. The ___ is traveling at a greater speed by ___ miles per hour.” A coordinate plane is pictured with the distance (mi) and time (min) plotted for the train. These practice problems allow students to use ratio and rate reasoning and apply it to speed and unit price and to use both a table and a graph. Unit 4: Understand and Use Percentages, Lesson 4-3: Estimate the Percent of a Number, Practice, Exercise 13 engages students in using percentages with ratio reasoning. “On average, 28% of the students at a certain middle school walk to school. If there are 412 students at the school, approximately how many students walk to school?” These problems meet the full intent and give all students extensive work with 6.RP.3 (Use ratio and rate reasoning to solve real-world and mathematical problems.) 

  • Unit 5: Solve Area, Surface Area, and Volume Problems, Lesson 5-6: Represent Three- Dimensional Figures in Two Dimensions, Session 1, Guided Exploration, students use nets to explore three dimensional figures. It states, “Yuzuki is making a replica of the Pyramids of Giza for a social studies project. She will make the pyramids out of paper. Yuzuki can create a net of each pyramid. A net is a two-dimensional representation of a three-dimensional figure.” Practice Problems, Exercises 4-5 direct students to “draw a net for each figure” (pictures of a cube and a rectangular pyramid are provided). Lesson 5-7: Determine the Surface Area of Prisms, Session 2, Lesson Quiz, Exercise 9, “What is the surface area of a triangular prism that has the triangular base shown and a height of 6 feet?” There is a picture of a right triangle with a height of 8 feet, base of 8 feet, and hypotenuse of 11.3 feet. Lesson 5-8: Determine Surface Area of Pyramids, Session 1, Practice, Exercise 2, “Sheng is covering the square pyramid shown. He does not plan to cover the base. The cost of the material is $5.75 per square meter. His budget for the project is $250. Can Sheng afford to complete his project? Explain.” (A picture of a square pyramid with a height of 5 meters and a base length of 4 meters is provided). These problems meet the full intent and give all students extensive work with 6.G.4 (Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of real-world and mathematical problems.) 

  • Unit 7: Integers, Rational Numbers, and the Coordinate Plane, Lesson 7-1: Explore Integers and Their Opposites, Session 2, Lesson Quiz, Item 11 states, “Error Analysis, Miguel says that 12 and 24 are opposites because 24 is 12 units away from 12. How do you respond to Miguel?” Students recognize that opposite signs of numbers indicate locations on opposite sides of zero. In Lesson 7-6: Determine the Distance on the Coordinate Plane, Session 1, Practice Exercise 7, students evaluate a fictional student’s thinking about the distance between 1.5 and -1.5 on a graph using absolute value. “Error Analysis, Anwar finds the distance between point A and point B as shown. How do you respond to Anwar? 1.51.5=1.51.5=0|-1.5|-|1.5|=1.5-1.5=0” Students are provided with a coordinate plane with point A plotted at -1.5 and point B plotted at 1.5. In Unit 7: Integers, Rational Numbers, and the Coordinate Plane, Performance Task Part A, students recognize that opposite signs of numbers indicate locations on opposite sides of zero on a number line and can order signed numbers. “The record low temperatures for six cities are shown in the table. Order the temperatures. Which city has the lowest record low temperature? Which city has the highest record low temperature?” There is a table with six cities, “Ashville 0℉, Harmwood -9℉, Newtown 2℉, Richburg -17℉, River City -2℉, Sampson 4℉.” Part B, “In Richburg, the record high temperature is 108℉. Explain how Francisco can use absolute value to determine the difference between the record high temperature and the record low temperature? What is the difference between the temperature?” Part C, “Suppose Francisco wants to graph the low temperature for each month in a city, with months on the horizontal axis and temperatures on the vertical axis. January is represented as month 1. If the low temperature for November is -2℉, what ordered pair represents this on a graph?” Unit Reflect, “How can you find the distance between two points on the coordinate plane that have the same first coordinate?” These problems meet the full intent and give all students extensive work with 6.NS.6a (Recognize opposite signs of numbers as indicating locations on opposite sides of 0 on the number line; recognize that the opposite of the opposite of a number is the number itself, e.g., –(–3) = 3, and that 0 is its own opposite).

  • Unit 9: Relationships Between Two Variables, Lesson 9-1: Explore Relationships Between Two Variables, Session 1, Guided Exploration, students identify dependent and independent variables in real-world scenarios. The materials state, “Akela planted three trays of bean seeds for a science experiment. She records the daily amount of sunlight each tray of seeds receives and average plant height for each tray after 3 weeks of growth. What can Akela say about the relationships between sunlight and plant growth?” An explanation about the two quantities (independent variable and dependent variable) is provided. Let’s Explore More, Part A, “Why do you think the variables that represent the quantities are called independent and dependent variables?” Part B, “Why is the amount of sunlight the independent variable?” In Lesson 9-2: Analyze Graphs of Relationships Between Two Variables, Session 1, Exit Ticket, Item 1, students use a table of values to graph independent and dependent variables. “Millie is keying in data at a rate of 55 words per minute. Part A, Complete the table. Part B Complete the graph.” There is a two column table with one column labeled the “Number of Minutes” with the values 2, 4, 6, 8 and a second column labeled as “Number of Words” which is empty. There is also a graph titled “Words Keyed”, the x-axis is labeled “Number of Minutes”, and the y-axis is labeled “Number of Words.” In Lesson 9-3: Write Equations to Represent Relationships Between Two Variables, Session 2, Lesson Quiz, Exercise 9, students analyze an error in an equation with two variables that change in relationship to one another. “Error Analysis, Claire states that the equation for the relationship shown in the graph is t=20ct=20c, where tt is the number of tickets and cc is the total cost. How do you respond to Claire?” These problems meet the full intent and give all students extensive work with 6.EE.9 (Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity…)

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 6 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 6 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 43 out of 66, approximately 65%.

  • The approximate number of instructional days devoted to major work, including assessments and supporting work connected to the major work is 132 days out of 177, approximately 75%. 

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 75% 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 6 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: Solve Area, Surface Area, and Volume Problems, Lesson 5-4: Apply Area Concepts to Solve Problems, Session 1, Exit Ticket, Item 1, connects the supporting work of 6.G.1 (Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.) to the major work of 6.EE.2c (Evaluate expressions at specific values of their variables. They include expressions that arise from formulas used in real-world problems. They perform arithmetic operations, including those involving whole number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations). Students use the area formula to find the area of a regular pentagon. The materials state, “What is the area of the regular pentagon? Explain how you found your answer.” The item includes a picture of a regular pentagon with a height of 16.4 inches and a base of 12 inches.

  • Unit 6: Numerical and Algebraic Expressions, Lesson 6-8: Generate Equivalent Expressions, Session 1, Exit Ticket, connects supporting work of 6.NS.4 (Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1–100 with a common factor as a multiple of a sum of two whole numbers with no common factor) to the major work of 6.EE.3 (Apply the properties of operations to generate equivalent expressions.) Students simplify to create equivalent expressions. “Write equivalent expressions to simplify 4(6x+3)+2x4(6x+3)+2x. Identify the properties you used for each step.”

  • Unit 7: Integers, Rational Numbers, and the Coordinate Plane, Lesson 7-7: Represent Polygons on the Coordinate Plane, Session 1, Guided Exploration, Polygons on the Coordinate Plane, Let’s Explore More, connects the supporting work of 6.G.3 (Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. Students apply these techniques in the context of solving real-world and mathematical problems.) to the major work of 6.NS.6c (Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane). Students use the area formula to find the area of a regular pentagon on the coordinate plane. Students are provided with four points in Quadrant 1, “a. What operation would you use to determine the side lengths of a square with the vertices shown? b. A certain rectangle has a perimeter of 24 units and an area of 27 square units. Two of the vertices have coordinates (1,2) and (1,5). What could be the coordinates of the other vertices?”

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 6 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 2: Understanding the World Around Us Through Statistics, Unit Assessment Form A, Question 8, states “Kailan surveys her friends to find how often they read each week. The table shows the number of times each friend reads in a typical week. Which box plot best represents the data? Choose the correct answer.” The task includes a table with the following values 6, 4, 12, 4, 0, 5, 6, 12, 8, 8 and four box plots. Students find the median and range for the data and choose the box plot that best reflects this data. Students engage with the supporting work of 6.SP.A (Develop understanding of statistical variability) and the supporting work of 6.SP.B (Summarize and describe distributions).

  • Unit 6: Numerical and Algebraic Expressions, Lesson 6-5: Write and Evaluate Algebraic Expressions, Session 2, Practice Exercise 13, STEM Connection, students solve a one-variable equation with exponents. The problem reads,  “A farm is installing solar panels. The expression 6h×0.82×365126h\times0.8^2\times\frac{365}{12} represents the monthly energy production, in watts, where h is the average number of sunlight on the solar panels each day. If the average number of hours of sunlight each day is 8.6 hours, how much energy will be produced each month?” Students engage with the major work of 6.EE.A (Apply and extend previous understandings of arithmetic to algebraic expressions) and the major work of 6.EE.B (Reason about and solve one-variable equations and inequalities).

  • Unit 8: Equations and Inequalities, Unit Review, Exercises 21 and 22, students graph inequalities on a number line to find solutions for a one-variable inequality. The problem reads, “For exercises 21 and 22, use the inequality. x<13x<\frac{1}{3} 21. Graph the inequality on the number line. 22. Name 3 values of x that are solutions to the inequality.” Students engage with the major work of 6.NS.C (Apply and extend previous understandings of numbers to the system of rational numbers) and the major work of 6.EE.B (Reason about and solve one-variable equations and inequalities).

  • Unit 9: Relationships Between Two Variables, Lesson 9-4: Apply Two-Variable Relationships to Solve Problems, Session 2, Lesson Quiz, Questions 1 and 2, students write an equation with two variables that relate to one another and use their equation to find solutions to a real world scenario. The problem reads, “A gym charges $10 per hour for racquetball. Complete the table to represent the cost for one month at the gym. Enter the answers.” 2. Part A, “Write an equation to represent the relationship between the number of hours of racquetball h and the total cost each month C.” Part B, “What is the cost to play 10 hours of racquetball in one month?” Students engage with the major work of 6.RP.A (Understand ratio concepts and use ratio reasoning to solve problems.) and the major work of 6.EE.A (Apply and extend previous understandings of arithmetic to algebraic expressions.)

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 6 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 4: Understand and Use Percentages, Lesson 4-3: Estimate the Percent of a Number, Lesson Overview, Coherence, connects the current grade level work of 6.RP.3 (Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations) to future work in Grade 7 where “Students solve problems using proportions and percentages.” 

  • Unit 5: Solve Area, Surface Area, and Volume Problems, Unit Overview, Coherence, connects the current grade level work of 6.G.1 “Find the area of parallelograms, rhombuses, triangles, trapezoids, and polygons by composing or decomposing figures into other figures or using a formula” to future work in Grade 7 where “Students solve problems involving area, surface area, and volume.”.

  • Unit 9: Relationships Between Two Variables, Unit Overview, Coherence, connects the current grade level work of 6.EE.9 “Identify independent variables and dependent variables, find the value of the dependent variable given a relationship between two quantities, use tables and graphs to find and analyze the relationships between two quantities and to write an equation to show the relationship between dependent and independent variables, and write an equation to show the relationship between two quantities and use it to solve a problem.” to future work in Grade 7 where students “solve word problems leading to equations of the form px+q=rpx+q=r and p(x+q)=rp(x+q)=r.”

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

  • Unit 2: Understanding the World Around Us Through Statistics, Lesson 2-7: Divide Decimals Using an Algorithm, Lesson Overview, Coherence, connects the current grade-level work “Students divide multi-digit decimals by whole numbers” and “Students multiply by a power of 10 to divide multi-digit decimals by decimals” to prior work where “Students divided multi-digit numbers using strategies based on place value” and “Students divided whole numbers using the algorithm.”

  • Unit 3: Ratios and Rates, Lesson 3-1: Understand Ratios, Lesson Overview, Coherence, connects current grade-level work, “Students explore ratio relationships and concepts” to prior work where “Students analyzed and generated equivalent fractions.”

  • Unit 7: Integers, Rational Numbers, and the Coordinate Plane, Lesson 7-1: Explore Integers and Their Opposites, Lesson Overview, Coherence, connects the current grade-level work, “Students explore the locations of integers and their opposites on a number line” to prior work where “Students explored the locations of positive numbers on a number line.”

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 6 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 177 days, broken down as follows:

  • 132 days of content-focused lessons

  • 10 days of Unit Openers with Ignite

  • 20 days of Mathematical Modeling

  • 4 days of Math Probes

  • 8 days of Unit Assessments

  • 3 days of Benchmark Assessments

Grade 6 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 6 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 6 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 6 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:

  • The Unit Overview outlines the three parts of rigor–conceptual understanding, procedural skill & fluency, and application. In the Unit Overview for Chapter 7: Integers, Rational Numbers, and the Coordinate Plane notes “Students understand the locations of integers and rational numbers and their opposites on a number line and understand the absolute value of a number as its distance from zero on a number line.” (6.NS.6 and 6.NS.7)

  • Unit 3: Ratios & Rates, Lesson 3-4: Determine Equivalent Ratios Using Graphs, Session 1, Guided Exploration, students make tables of equivalent ratios relating quantities with whole- number measurements. The problem states, “The organizers of a soccer league ordered 6 of the large bags shown to hold soccer balls. How many soccer balls will the bags hold?” There is a table and a graph provided to demonstrate a ratio of 1 bag to 6 soccer balls. Discussion questions are “What tools or models represent this relationship? How are the table and graph related? Why do you think the graph is a straight line?” (6.RP.3a)

  • Unit 4: Understand and Use Percentages, Lesson 4-2: Relate Fractions, Decimals, and Percents, Be Curious: Notice & Wonder, students use a protocol to discover the relationship between decimals, fractions, and percents. “Which doesn’t belong? 12:80, 80100\frac{80}{100}, 80%, 4 out of 5.” Pose Purposeful Questions, “How can you rewrite these into the same form? How can you actually compare the different values? What would need to happen to compare these values?” (6.RP.3c)

  • Unit 5: Solve Area, Surface Area, and Volume Problems, Lesson Lesson 5-1: Determine the Area of Parallelograms and Rhombuses, Session 2, Guided Exploration, Tiling a Backsplash, students explore ways to find the area of a rhombus by decomposing and rearranging it. The problem reads, “Facilitate Mathematical Discourse. Can you think of another way to decompose the rhombus and compose the pieces into a rectangle? Will the area of your rectangle be different from the area of the rectangle shown? How can you decompose and rearrange the parts to justify the formula for area?” Let’s Explore More states, “Is area always represented in square units (u2)(u^2)? Explain.” (6.G.1)

  • Unit 7: Integers, Rational Numbers, and the Coordinate Plane, Lesson 7-1: Explore Integers and Their Opposites, Session 1, Be Curious: Notice & Wonder uses a real-life example of sea level for students to understand that positive and negative numbers are used together to describe quantities having opposite directions or values; use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation. the problem shows a picture of Death Valley National Park with Telescope Peak labeled at 3,368 meters and Badwater Basin labeled below the line of Sea Level is provided. Students are asked, “What do you notice? What do you wonder?” Pose Purposeful Questions state, “Which features of Death Valley National Park are shown? Which feature has an elevation nearest to sea level? How can you represent the location of each of the features?” (6.NS.5)

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

  • Unit 3: Ratios and Rates, Lesson 3-2: Understand Rates and Unit Rates, Session 1, Activity-Based Exploration, students “explore problems involving rates and unit rates” in the “Hands-On'' section. It states, “Students use the Blank Number Lines Teaching Resource to create a double number line to solve the problem. Students will use what they know about the relationship between quantities to label a double number line and use it to answer the question.” Activity Exploration Journal states, “Yelina needs to ride the metro train into the city each day for one week. She needs to decide whether she wants to purchase seven one-day passes or one seven-day pass. The one-day pass costs $6.25 per pass. The seven-day pass costs $35 per pass. Which pass do you recommend Yelina choose? Why?” (6.RP.3b)

  • Unit 4: Understand and Use Percentages, Lesson 4-1: Understand Percent, Session 1, Be Curious: Notice & Wonder, students compare the total number of each color card in an array of 20 colored cards to find a percent of a quantity as a rate per 100. The problem states, “Pose Purposeful Questions, How does the number of each color compare to the others? How does the number of each color compare to the whole? How can you express the ratio of the color to the whole consistently? Pause & Reflect Students consider how the quantities of cards can be expressed. They think about the relationship between individual colors and the total number of cards. How can you express the ratio of pink cards to the total number of cards?” (6.RP.3c)

  • Unit 6: Numeric and Algebraic Expressions, Lesson 6-8: Generate Equivalent Expressions, Session 1, Activity-Based Exploration, students create algebraic expressions by adding, rearranging, and deleting algebra tiles to model expressions. Students use digital algebra tiles to answer “In how many more ways can you represent 12x+138+4x+2212x+138+4x+22 so that its value does not change?”(6.EE.3)

  • Unit 7: Integers, Rational Numbers, and the Coordinate Plane, Lesson 7-5: Represent Rational Numbers on the Coordinate Plane, Session 1, Activity-Based Exploration “Students explore how rational numbers can be represented in the four regions on the coordinate plane.” The hands-on activity states, “Students label the coordinates of the locations shown on the map. Then they will fold the map to see if any points match up. Students can notice and wonder about the coordinates of the reflected points.” Then teachers ask, “What do you notice about the way the regions are numbered? What do you notice about the numbers in the ordered pairs in the first region? In the second region? In the third region? In the fourth region?” Finally, students journal the answer to “What does it mean if two ordered pairs differ only by their signs?” (6.NS.6b)

  • Unit 8: Equations & Inequalities, Lesson 8-5: Understand Inequalities and Their Solutions, Session 1, Activity-Based Exploration, students graph inequalities on a number line to understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? “How can you represent an inequality on a number line? You will explore how to represent the solution to each of the following inequalities on a number line. x>4x>-4, , x<6x<6, x6x\geq6. How can you represent the solution of an inequality?” (6.EE.5)

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 6 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 2: Understanding the World Around Us Through Statistics, Lesson 2-6: Divide Multi Digit Numbers Using an Algorithm, Session 2, Guided Exploration, students explore using an algorithm to divide multi-digit whole numbers that do not divide easily. The materials state, “In the U.S., public schools calculate the amount spent on each student in a year. The typical amount spent for each student each year is shown. How much do schools typically spend on each student each month? You can abbreviate the values when using an algorithm to make calculations simpler. The equation 12630÷12=a12630\div12=a represents the problem. Divide the numbers in each place value position from left to right. Start at the highest place value. You can extend the dividend to decimal places to address a remainder.” Students develop procedural fluency of 6.NS.2 (Fluently divide multi-digit numbers using the standard algorithm).

  • Unit 3: Ratios & Rates, Lesson 3-4: Determine Equivalent Ratios Using Graphs, Session 1, Exit Ticket, students explore the concept of equivalent ratios through ratio tables and graphs. The materials state, “The table shows the cost of notebooks at the school store. 1. Use the table to plot the points on the coordinate plane. 2. What does the point at (3,15) on the coordinate plane represent?” A table with two rows is included. The first row is labeled “Number of Notebooks” and the second row is labeled “Cost ($).” Students develop procedural fluency and conceptual understanding of 6.RP.3a (Make tables of equivalent ratios relating quantities with whole- number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios).

  • Unit 6: Numerical and Algebraic Expressions, Lesson 6-3: Explore Numerical Expressions with Exponents, Session 2, Summarize & Apply states that, “You can use exponents to represent a repeated multiplication expression. An expression written with an exponent is a power. You can evaluate a power using multiplication. Apply: Biology James is studying the growth rate of a specific type of bacteria. He places three cells in a Petri dish and records the number of bacteria every five hours. The table shows his results. Question 1: What powers represent the number of bacteria recorded every 5 hours? Question 2: What power would represent the number of bacteria after 25 hours? Choose a question to answer. Then answer it in the space below.” Students develop procedural fluency of 6.EE.1 (Write and evaluate numerical expressions using whole number exponents).

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

  • Unit 4: Understand and Use Percentages, Fluency Practice, students practice dividing decimals using the algorithm. The materials state, “Divide decimals using an algorithm. Multiply the divisor by a power of 10 so the divisor is a whole number. Divide. Annex zeros, if necessary. Place the decimal in the quotient directly above the decimal in the dividend. 9÷2.43=3.759\div2.43=3.75.” After completing practice items, students are asked, “How would you explain to a classmate when to annex zeros?” This activity provides an opportunity for students to develop procedural skill and fluency of 6.NS.2 (Fluently divide multi-digit numbers using the standard algorithm.)

  • Unit 5: Solve Area, Surface Area, and Volume Problems, Fluency Practice, gives the students the following instructions: “Add or subtract decimals. Align the decimal points. Annex zeros, if needed. Add or subtract. Multiply decimals. Multiply. Place the decimal point so the product has the same number of decimal places as the addends. Divide decimals. Multiply so that the divisor is a whole number. Divide. Place the decimal in the quotient directly above the decimal in the dividend. Evaluate each expression. 1. 6.2+9.36.2+9.3, 2. 8.922.478.92-2.47, 3.1.5×2.63. 1.5\times2.6.” This activity provides an opportunity for students to develop procedural skill and fluency of 6.NS.3 (Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.) 

  • Benchmark Assessment 2, Item 31, students determine the error in the claim made by the fictitious student and then correct the error. The problem states, “For the school bake sale, members of the cheerleading squad bake the number of cookies shown in the table. A student claims that Robert and Melanie bake the same number of cookies and Alicia and Joe bake the same number of cookies. Find the error made by the student and correct it. Sample answer: The student may have multiplied 3×43\times4 instead. Alicia baked 3×4=123\times4 = 12 cookies, but Joe baked 34=3×3×3×3=813^4=3\times3\times3\times3= 81 cookies." This activity provides an opportunity for students to independently develop procedural skill and fluency of 6.EE.1 (Write and evaluate numerical expressions using whole number exponents).

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 6 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 Use Percentages, Lesson 4-3: Estimate the Percent of a Number, Session 2, Lesson Quiz, Item 1, students use rate and reasoning to solve real-world and mathematical problems. The item states, “Just Shirts has 90 shirts on sale. Of those 90 shirts, 55 shirts are polo shirts. Which is the best estimate for the percent of the shirts sold that are polo shirts? A. 50% B. 55% C. 60% D. 75%” (6.RP.3c)

  • Unit 5: Solve Area, Surface Area, and Volume Problems, Lesson 5-2: Determine the Area of Triangles, Session 1, Practice, Item 5, students find the area of triangles and apply these techniques to real-world scenarios. Item 5 states, “STEM Connection: A pipestem triangle is a piece of lab equipment that holds a beaker while it is being heated. What is the area inside the pipestem triangle shown?” (6.G.1)

  • Unit 6: Numerical and Algebraic Expressions, Lesson 6-1: Division Expressions with Fractions and Whole Numbers, Session 2, Extend Thinking, students interpret and make comparisons between fraction division problems. The materials state, “For exercises 1 and 2, find the quotient by drawing a model. 1. 13÷4\frac{1}{3}\div4 and 2. 16÷2\frac{1}{6}\div2 For exercises 3-5, answer the questions. 3. What do you notice about the quotient 13÷4\frac{1}{3}\div4 and the quotient 16÷2\frac{1}{6}\div2? 4. How does 13\frac{1}{3} compare to 16\frac{1}{6}? 5. How does 4 compare to 2?” (6.NS.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: Ratios and Rates, Lesson 3-2: Understand Rates and Unit Rates, Session 2, Summarize & Apply, students solve unit rate problems and use ratio and rate reasoning to solve real world problems. The materials state, “Yelina’s mother’s current budget for commuting to and from her job is shown. She is considering purchasing a monthly public transportation pass that costs $145. Her walk from the train station to her office would be about 25 minutes. Question: What is your recommendation for Yelina’s mother for her daily commute?” (6.RP.2)

  • Unit 5: Solve Area, Surface Area, and Volume Problems, Mathematical Modeling, students find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems. The materials state, “Your school has adopted a one-acre (43,560 square feet), parallelogram-shaped plot of land for reforestation. A local conservation group sent the table below of recommended trees for the climate of the area. You and your classmates will decide on a planting plan for the site. The conservationists recommend selecting no more than 3 types of trees and to include a mixture of trees with different growth rates. Your plan should include the number of each type of tree and a diagram showing where each type of tree will be planted. Be sure to consider the area of the plot of land when making your decisions.” Six tree options are pictured and include captions with spacing requirements and growth rate of each type of tree. (6.G.1)

  • Unit 7: Integers, Rational Numbers, and the Coordinate Plane, Lesson 7-6: Determine Distance on the Coordinate Plane, Session 1, Activity-Exploration, students explore determining the distance between two points on the coordinate plane. The materials state, “Students plan the locations of different features by plotting points on a coordinate plane map of a town (Coordinate Plane 2 Teaching Resource). Students have freedom as to where they place these features, as long as they follow the criteria listed in the Activity Exploration Journal.” (6.NS.8)

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 6 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 2: Understanding the World Around Us Through Statistics, Lesson 2-6: Divide Multi-Digit Numbers Using an Algorithm, Session 2, Lesson Quiz, Item 4, students develop procedural fluency with the standard algorithm for division. Item 4 states, “A deli owner buys 12 pounds of smoked salmon for $333 from the fish market. What is the cost of smoked salmon per pound?” (6.NS.2)

  • Unit 8: Equations and Inequalities, Lesson 8-1: Understand Equations and Their Solutions, Session 1, Exit Ticket, Item 1, students engage in conceptual understanding as they use variables to represent numbers and write equations when solving real-world problems. Item 1 states, “Each stack of newspapers is 3123\frac{1}{2} inches high. Write an equation you can use to find how many 3123\frac{1}{2} inch stacks s of newspapers make a stack 49 inches high.” (6.EE.6)

  • Unit 10: Math Is…, Lesson 10-1: Math is Everywhere, Session 2, Summarize & Apply, students apply ratio and rate reasoning in a real-world scenario. The materials state, “Did you know that leaving the water running while brushing your teeth wastes an average of four gallons versus only turning the water on to rinse? How much water would you save each year if every person in your house ran water only to rinse? How does your savings compare to a household of 3, 4, 5, and 8 people?” (6.RP.3)

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. The materials state, “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 offers, “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: Understanding the World Around Us Through Statistics, Mathematical Modeling, students build conceptual understanding, use application, and develop procedural fluency as they analyze the results of three water analysis tests to determine which contaminant, if any, violates the maximum contaminant level by using mean and fluently dividing numbers using the standard algorithm. The materials state, “Project One The table shows the average amount of water consumed each day in an indoor household in the United States by appliance or device. A local family has made the commitment to reduce their water consumption by 15\frac{1}{5}. What recommendations can you make to the family? Which appliance or device would you recommend they use less frequently? Develop a plan that could get them to their goal.” (6.NS.2, 6.SP.5)

  • Unit 3: Ratios and Rates, Lesson 3-1: Understand Ratios, Session 2, Guided Exploration, students build conceptual understanding and application as they use ratio and rate reasoning to solve real-world and mathematical problems. The materials state, “Making Salad Dressing, Tahira is making a salad dressing using the recipe shown. She plans to use 4 tablespoons of vinegar. How can she determine the amount of olive oil she will need to keep the taste of the salad dressing the same? One Way Use a tape diagram. The vinegar and olive oil are both parts of the salad dressing. Multiply the quantities of vinegar and olive oil by 4 to maintain the same ratio. Another Way, Use a double number line. A double number line shows the ratio relationships on two number lines. With 4 tablespoons of vinegar, 12 tablespoons of olive oil are needed. Let’s Explore More, a. How can Tahira determine the amount of salad dressing she will have if she uses 6 tablespoons of vinegar? b. Tahira added 4 teaspoons of mustard to the 4 tablespoons of vinegar. How will her salad dressing taste?” (6.RP.3) 

  • Unit 7: Integers, Rational Numbers, and the Coordinate Plane, Lesson 7-6: Determine Distance on the Coordinate Plane, Session 2, Summarize & Apply, students build procedural fluency and application as they solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. The materials state, “You can use the coordinates and absolute values to find distances between points with the same first coordinate or the same second coordinate. When two points are in the same quadrant, subtract the absolute values of the coordinates to determine the distance. When the points are in different quadrants, add the absolute values of the coordinates to determine the distance. Apply: Deon’s Errands The table shows the locations for several places in town. The grid shows a map of the town where each unit labeled on the grid represents one mile. Deon needs to go to the dry cleaner, which is 34\frac{3}{4} mile west and 1141\frac{1}{4} miles north of the library. Question: What are the coordinates of the dry cleaner?” The item includes a table with location coordinates. (6.NS.8)

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 6 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 6 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, the materials state, “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 3: Ratios and Rates, Lesson 3-5: Compare Ratio Relationships, Session 1, Activity- Based Exploration, students use a variety of strategies to compare ratios. The materials state, “Two friends create shades of purple paint. Reginald uses 3 parts red and 5 parts blue to make his shade of purple. Anwar uses 2 parts red and 3 parts blue to make his shade of purple. Whose mixture contains the most blue paint? Use the space below to record your findings with descriptions, drawings, and representations. Be prepared to share your findings. Concluding Question 1. What methods can you use to compare two ratios that are not equivalent?” 

  • Unit 6: Numerical and Algebraic Expressions, Unit Overview, Math Practices states,“Making sense of quantities and their relationships in problem situations is a key skill in working with numeric and algebraic expressions. Students will use sense-making and perseverance throughout the unit. For example, to evaluate numerical expressions with exponents, students use the order of operations to plan a solution pathway, to identify if two expressions are equivalent, students look for entry points such as identifying which, if either, expression can be simplified or analyzing the parts of each expression. When simplifying algebraic expressions, students may check that the original and simplified expressions are equivalent by substituting a value for the variable in each.” The Unit Overview discusses how the mathematical content in this unit is enriched by MP.1: make sense of problems and persevere in solving them. 

  • Unit 9: Relationships Between Two Variables, Lesson 9-4: Apply Two-Variable Relationships to Solve Problems, Session 1, Guided Exploration, students analyze, make sense, and compare quantities in two-variable relationships. The materials state, “An assembly line at an automobile manufacturing plant is run in 8-hour shifts and produces 2.5 cars per hour. The manufacturer has received the order shown. Should the manufacturer accept the order?” The task includes a picture of a purchase order for 1,000 black cars in a production time of 3 weeks. 

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 2: Understanding the World Around Us Through Statistics, Lesson 2-4: Represent and Describe Data in a Box Plot, Session 2, Guided Exploration, students represent situations symbolically as they compare data using two box plots. The materials state, “The sixth graders and seventh graders want to compare their finish times in the 5-kilometer race. How do the finish times of the students in the two grades compare?” The task includes two tables with data. The teacher materials prompt teachers to “Have students work with a partner to determine how they can represent the relationship between quantities. Students may mention that they can use and compare box plots to interpret the relationship.” 

  • Unit 4: Understand and Use Percentages, Lesson 4-4: Find and Compare with Percentages, Session 2, Lesson Quiz, Items 9-10, students understand the relationships between problem scenarios and mathematical representations as they use ratio and rate reasoning to solve real-world and mathematical problems. The materials state, “A group of sixth-grade students were asked to choose a vegetable snack. The table shows the number of students that chose each type of vegetable. 9. How can you determine what percent of students chose celery? 10. What percent of students chose broccoli?” The items include a table of different vegetables and the number of students. 

  • Unit 8: Equations and Inequalities, Unit Overview, Math Practices states, “Reason Abstractly and Quantitatively Writing and solving algebraic equations and inequalities 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 equations and inequalities will provide them with the skill set they need to be successful in high-school mathematics and beyond. Encourage students to think about problems they have solved in the past when making sense of new problems. This can help them identify appropriate solution methods. Focus students attention on the relationships between quantities in a problem and how they can use the relationships to determine an appropriate solution method. For example, have students name the operation used in the given equation, identify the inverse operation, and name the Property of Equality they will use to solve the equation.”

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 6 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: Understanding the World Around Us Through Statistics, Lesson 2-9: Describe Data by Mean Absolute Deviation, Session 1, Activity-Based Exploration, students construct viable arguments and critique the reasoning of others as they describe variability of a data set. The materials state, “Have students work with a partner to discuss what they can listen for as others share their arguments. These can include listening for viable arguments and critiquing the reasoning of others. In this problem situation, students can describe the circumstances in which data sets might have the same mean value but have deviations that are significantly different. Have students complete the Concluding Question in their Activity Exploration Journal. How does the average amount that each data value deviates from the mean describe the spread of a data set?

  • Unit 5: Solve Area, Surface Area, and Volume Problems, Lesson 5-8: Determine the Surface Area of Pyramids, Session 1, Guided Exploration, students construct viable arguments as they explore how to determine the surface area of a pyramid. The materials state, “Let’s Explore More a. Why are the heights of the triangles in a square pyramid congruent? b. The triangular faces in a square pyramid are congruent. Is this true for all pyramids

  • Unit 6: Numerical and Algebraic Expressions, Lesson 6-3: Explore Numerical Expressions with Exponents, Session 1, Guided Exploration, students critique the reasoning of others as they explore writing addition and multiplication expressions in different ways. The materials state, “Let’s Explore More: a. How does the value of 4×54\times5 compare to the value of 545^4? b. Can you write the expression 25+25+25\frac{2}{5}+\frac{2}{5}+\frac{2}{5} as a power?” Teacher Guidance states, “Have students think about how they know they have understood the argument presented. Help students listen intently to the argument. Encourage them to write down any parts of the argument they would like clarified.” 

  • Unit 7: Integers, Rational Numbers, and the Coordinate Plane, Lesson 7-2: Represent Rational Numbers and Their Opposites on the Number Line, Session 1, Activity-Based Exploration, students construct arguments and critique the reasoning of others as they explore rational numbers and their opposites by plotting numbers on a number line. The materials state, “Introductory Question: How can you plot a non-integer number on a number line? Concluding Question 1. How can you determine whether the opposite of a fraction or a decimal number will be positive or negative?” The Teacher Guidance states, “Students can share out their ideas about the relationships between fraction and decimal numbers and their opposites. Ask students to think about the questions they have about their classmates’ ideas. Have students share anything they want to add on or critique their classmates’ ideas.”

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 6 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 5: Solve Area, Surface Area, and Volume Problems, Lesson 5-1: Determine the Area of Parallelograms and Rhombuses, Session 1, Activity-Based Exploration students check to see whether an answer makes sense and change the model when necessary to find the area of special quadrilaterals. Teacher Guidance states, “Hands-On: Students determine which figure on the Area of Quadrilaterals Teaching Resource has the greatest area. Students can cut the paper and move the pieces around to form squares or rectangles if needed. Have volunteers share their responses while others listen respectfully. Guide students to see the value in pausing to check their work and determine whether their answer is reasonable. Encourage students to take the time to check their work throughout the unit.”

  • Unit 8: Equations and Inequalities, Lesson 8-3: Write and Solve Equations Using Multiplication or Division, Session 2, Summarize & Apply, students model the situation with an appropriate representation to write and solve one step equations. The materials state, “The student council buys snacks in bulk to sell during lunch. One box of snacks contains the types and quantities of snacks shown below. The first month, the student council sold 115 bags of snacks, including 50 bags of cheese crackers. Question: How many boxes of snacks would you recommend the student council order for next month?” Teacher guidance, “Elicit Evidence of Student Understanding How does creating models such as tape diagrams help you write multiplication and division equations involving variables? How does understanding of the Multiplication Property of Equality and Division Property of Equality make you a more efficient problem solver?” 

  • Unit 9: Relationships Between Two Variables, Lesson 9-3: Write Equations to Represent Relationships Between Two Variables, Session 2, Guided Exploration, students write an equation from a graph, describe what they do with a model and how it relates to the problem situation. The materials state, “Let’s Explore More: a. Which representation do you find most helpful when representing the relationship between two variables: a table, a graph, or an equation? b. How are the graph and equation related?” Teacher Guidance states, “How can you apply mathematics to model the context? Listen to students’ responses and make sure that they know that they are applying mathematics to model the context when they use a table, graph, or an equation.”

  • 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, and there is intentional development of the MP to meet its full intent. Students choose tools strategically as they work with teacher support and independently throughout the modules. Examples include:

  • Unit 4: Understand and Use Percentages, Lesson 4-3: Estimate the Percent of a Number, Session 2, Guided Exploration, students recognize the insight to be gained from different tools and strategies as they estimate the percent of a number using rounding or compatible numbers. The materials state, “What is another tool that would be helpful in approaching this problem? Have volunteers share the tools that would be helpful in approaching this problem. As needed, help students brainstorm other tools, while keeping a list for all to reference. Making a rough sketch of a pie chart, using different colors to shade in hundredths’ decimal grid, or making a labeled table with percents and quantities are some other tools that may help students understand the problem.”

  • Unit 6: Numerical and Algebraic Expressions, Lesson 6-2: Division Expressions with Fractions and Mixed Numbers, Session 2, Summarize & Apply, students recognize the insight to be gained through the use of certain tools, models or equations to divide fractions and mixed numbers by fractions and mixed numbers. The materials state, “Summarize: Divide Fractions and Mixed Numbers You can use models or equations to divide fractions or mixed numbers by fractions and mixed numbers. How many 14\frac{1}{4}s are in 2382\frac{3}{8}?” Teacher guide, “Elicit Evidence of Student Understanding How would you explain to a friend a scenario in which you might divide a fraction by a fraction? What is beneficial about using a visual model to find the quotient? Why is writing an equation to find a quotient helpful?” 

  • Unit 7: Integers, Rational Numbers, and the Coordinate Plane, Lesson 7-3: Understand Absolute Value of Rational Numbers, Session 1, Guided Exploration, students recognize the insights gained from using a number line as they explore the absolute value of rational numbers. The materials state, “Claire is performing a science experiment with two liquids. The temperatures of the two liquids in degrees Celsius are shown. She needs to use the beaker with the temperature that is closer to 0℃. Which beaker should Claire use? You can graph the temperatures on a number line to compare.” Teacher guidance, “Have students work with a partner to find the distance each point is from 0. Student-pairs may want to recreate the number line using the Blank Open Number Lines Teacher Resource. As students work on the activity and answer the question, encourage them to explain how they found their solutions. How does this tool help solve the problem? Have students discuss how a thermometer is the same and different than a number line. Ask students to consider how each tool can be used to help them determine how far a rational number is from zero.”

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 6 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 3: Ratios and Rates, Lesson 3-7: Ratio Reasoning: Convert Measurements Between Systems, Session 2, Guided Exploration, students attend to precision as they explore the concept of converting Customary measures to metric measures. The materials state, “What units of measure are needed to be precise? Have students discuss why the correct unit must be identified when using measurements. Mask sure they understand that mathematicians use notation, including symbols, to communicate ideas accurately.”

  • Unit 5: Solve Area, Surface Area, and Volume Problems, Lesson 5-5: Determine the Volume of Rectangular Prisms, Session 1, Activity-Based Exploration, students attend to precision as they find the volume of a rectangular prism by filling it with 12\frac{1}{2} inch unit cubes. The materials state, “What units of measure are needed to be precise? Ask for volunteers to share their thoughts on the level of precision. Have students consider how their results would change if they used 14\frac{1}{4} inch unit cubes, 1-inch unit cubes, or 2-inch unit cubes. Have students complete the Concluding Questions in their Activity Exploration Journal. How do you find the volume of a rectangular prism when it is filled with 12\frac{1}{2} inch unit cubes? You can also use the formula V=lwh to find volume. How is filling a rectangular prism with 12\frac{1}{2} inch unit cubes related to this formula?” 

  • Unit 7: Integers, Rational Numbers, and the Coordinate Plane, Lesson 7-6: Determine Distance on the Coordinate Plane, Session 1, Guided Exploration, students attend to precision as they find the distance between two points on a coordinate plane that have the same y-coordinate and use appropriate units to label graphs accurately. The problem states, “What unit of measure is needed to be precise? Have students consider how the information given in the problem statement can be used to determine the needed unit of measure. The problem statement mentions that one unit on the coordinate plane is equal to one kilometer. Students should notice that they should label their answer of 4.5 with kilometers, so that the answer makes sense in the context of the problem.” 

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 2: Understanding the World Around Us Through Statistics, Lesson 2-5: Describe Data by Range and Interquartile Range, Session 1, Activity-Based Exploration, students use specific mathematical language to describe a data set by giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation). The materials state, “Ask for volunteers to share the math terms they used during the activity. Listen for students to mention the following terms: spread, variability, difference, first quartile, third quartile, lower extreme, and upper extreme. Have students complete the Concluding Questions in their Activity Exploration Journal. What does the variability of the middle half of the data describe? How would changing values in a data set affect the variability of the whole and middle half of the data set?

  • Unit 6: Numerical and Algebraic Expressions, Lesson 6-5: Write and Evaluate Algebraic Expressions, Session 2, Activity Based Exploration, students use specific mathematical language to write and evaluate expressions with unknown quantities. The materials state, “During the whole-class discussion, connect students’ understanding of writing and evaluating algebraic expressions to these new key terms and concepts: An algebraic expression is an expression with at least one variable and one operation. A variable represents an unknown quantity that can change or vary. Variables can be letters or symbols. The Substitution Property of Equality states that is a=ba = b, then b may be substituted for a in any expression containing a. Each part of an algebraic expression that is separated by a plus or minus sign is a term. Terms that contain the same variable, with the same exponent, are called like terms. The numerical factor of each term that contains a variable is a coefficient. A term without a variable is a constant. What mathematical terminology can you use to convey understanding? Have students work with a partner to identify the mathematical language they can use to describe how to write an expression.” 

  • Unit 9: Relationships Between Two Variables, Unit Opener: Ignite, Building the Language of Mathematics, students use specific mathematical language while using a graphic organizer throughout the unit to build understanding of and proficiency with key mathematical terms and concepts. The materials state, “Building the Language of Mathematics Relationships Between Two Variables.” A graphic organizer is provided and “Multiple Representations of Relationships Between Two Variables'' is in the middle. There are four boxes around the middle that state, “Situation A conveyor belt moves objects at 100 feet per minute. Equation y=100xy = 100x, Graph and Table.” At the bottom of the graphic organizer, it says “In my example relationship, ___ is the dependent variable and ___ is the independent variable.”

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 6 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: Understanding the World Around Us Through Statistics, Lesson 2-8: Describe Data Using the Mean, Session 2, Activity-Based Exploration, students look for and make use of structure as they describe data using the mean and discover how changing a value in a data set impacts the mean. The materials state, “Arihi has these five bags of marbles. She wants to share them with four friends so that each person, including herself, has the same number of marbles. How many marbles does each person get? Explain your problem-solving strategy in the space below. Concluding Questions 1. How does the mean of a data set summarize the data set? 2. How can adding a value to a data set greater than all other values affect the mean of the data set?” Teacher Guidance states, “Math is… Looking for Structure How does exploring patterns help you solve problems? Have students work with a partner to discuss solving problems by exploring patterns. Ask for volunteers to share their responses with the class. Make sure that students understand the relationship among the data values, representations, and the mean. Recognizing this relationship can help solve the problem.”

  • Unit 3: Ratios and Rates, Lesson 3-1: Understand Ratios, Session 1, Activity-Based Exploration, students look for and make use of structure in part-to-part and part-to-whole relationships among quantities in real-world scenarios. The materials state, “You will represent and describe the relationship between two quantities in each scenario shown using a tape diagram and a double number line. 1. Tahira is making a dressing for a salad. The recipe calls for 1 tablespoon of vinegar for every 3 tablespoons of olive oil. Tahira plans on using 4 tablespoons of vinegar. How many tablespoons of olive oil will she need? 2. If two cups of apple juice are needed to make 10 cups of a fruit drink, how many cups of apple juice are needed to make 20 cups of the fruit drink?” Teacher Guidance states, “How can you connect mathematical ideas to representations? Students think about how some problems can be represented in different ways. These ways include tape diagrams and double number lines. Some students may also suggest colored counters or tiles, one color representing one quantity and the other the other quantity. Encourage students to describe how each model they make represents the problem and the advantages of each point of view.”

  • Unit 4: Understand and Use Percentages, Unit Overview, Look for and Make Use of Structure, Teacher Guide states, “Analyzing and understanding the structure of percentages is a foundational skill for statistical analysis in middle school and beyond. Helping students see the structure of percent relationships and the structure of percent equations will increase their fluency in percent calculations. Help students connect percentages to ratio reasoning by reinforcing the idea of percent as a ratio out of 100. By solving percent problems as equivalent fractions, students apply a known structure to a new concept. When students represent percent relationships with equations, engage students in discussion how the components of the equation relate to the part, the whole, and the percent in the situation. Help students connect the equation to other representations such as double number lines.”

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 5: Solve Area, Surface Area, and Volume Problems, Lesson 5-7: Determine Surface Area of Prisms, Session 1, Guided Exploration, students look for and express regularity in repeated reasoning to explore the surface area of a rectangular prism using a net and a formula. The problem states, “James is putting a special restorative stain on the entire surface of the wooden chest. One can of stain covers about 35 square feet. How many cans of stain will James need?” Teacher Guidance states, “How can generalizing be helpful in solving this problem? Ask for volunteers to share their responses while others listen respectfully. Students should be able to generalize the connection between the prism and its net.”

  • Unit 6: Numerical and Algebraic Expressions, Lesson 6-7: Find Factors and Multiples, Session 1, Guided Exploration, students look for and express regularity in repeated reasoning to explore how to use a greatest common factor to solve a real-world problem. The materials state, “The school store manager plans to sell a combo pack as a back-to-school item. Each combo pack will have an equal number of pencils and an equal number of notebooks. What is the greatest number of combo packs that he can make using all the pencils and notebooks?” Teacher Guide states, “Are there calculations that are being repeated? Have students discuss what calculations they repeated to list all the factors or to create the factor trees.”

  • Unit 8: Equations and Inequalities, Lesson 8-4: Write and Represent Inequalities, Session 1, Activity-Based Exploration, students look for and express regularity in repeated reasoning as they determine what part of the process is repeating. The materials state, “Students use a number line to represent several possible solutions for each scenario shown on the Inequalities Table Teaching Resource. For each scenario, students should plot at least 10 points on a number line. Students record the points and circle the inequality that represents the scenario.” The Teacher Guide states, “What about the process is repeating? Ask volunteers to share their responses with the class while others listen respectfully. Students should recognize that each value needs to be compared in the inequality to determine if it is a solution of the inequality.”

Overview of Gateway 3

Usability

The materials reviewed for Reveal Math 2025, Grade 6 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 6 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 6 meet expectations for providing teacher guidance with useful annotations and suggestions for how to enact the student materials and ancillary materials, with specific attention to engaging students in order to guide their mathematical development.

Materials provide comprehensive guidance found in a variety of sections within the Implementation Guide, including the Overview, Why, Achievement Descriptors Overview, and Lesson Structure. Examples include:

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

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

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

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

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

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

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

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

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

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

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

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 6 meet expectations for including standards correlation information that explains the role of the standards in the context of the overall series.

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

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

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

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

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

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

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

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

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 6 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), “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 states, “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 6 meet expectations for providing explanations of the instructional approaches of the program and identification of the research-based strategies.

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

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

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

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

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

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

Indicator 3F
01/01

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

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

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

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

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

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

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

Indicator 3G
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This is not an assessed indicator in Mathematics.

Indicator 3H
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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 6 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 6 meet expectations for having assessment information included in the materials to indicate which standards are assessed.

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

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

  • Unit 4: Understand and Use Percentages, Unit Assessment, Form A, Item 7 states, “Jordan completes 58\frac{5}{8} of his homework assignment. What percent of his homework does he complete?” In the Item Analysis, the question is aligned to 6.RP.3c "Ratios with Unknown Parts" and MP6, Attend to precision.

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

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

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 6 meet expectations for including an assessment system that provides multiple opportunities throughout the grade, course, and/or series to determine students' learning and sufficient guidance to teachers for interpreting student performance and suggestions for follow-up.

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

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

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

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

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

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 6 meet expectations for providing assessments that include opportunities for students to demonstrate the full intent of grade-level/course-level standards and practices across the series.

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

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

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

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

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

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 6 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 6 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 6 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 2: Understand the World Around Us Through Statistics, Lesson 2-10: Choose Appropriate Measures, 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, “Assign the interactive lessons to reinforce target skills. Outliers and Patterns Shapes of Data Distributions Select a Measure of Center or Variation” Build Proficiency states, “Spiral Review Assign students either the print or digital version to review these concepts and skills. Find Whole-Number Quotients of Whole Numbers with up to Four-Digit Dividends and Two-Digit Divisors (2 of 2)” Extend Thinking states, “STEM Adventures In this STEM Adventure, students display, describe, and analyze data about daily household water consumption. Then they use statistics to investigate how water consumption is affected by wasteful or conserving behaviors and compare data sets.” 

  • Unit 4: Understand and Use Percentages, 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: Numerical and Algebraic Expressions, Unit Overview, Effective Mathematics Teaching Practice, Build Procedural Fluency from Conceptual Understanding states, “If students struggle with practice problems throughout this unit, use students’ work to assess whether the student lacks conceptual understanding. If so, provide additional instruction. Otherwise, provide additional opportunities to use the skill and develop fluency. For example, if students understand conceptually that they need to write mixed numbers as fractions before dividing but struggle to do so, provide additional practice with writing mixed numbers as fractions. In Lesson 6-8, if students struggle with generating equivalent expressions, determine whether their struggle stems from a lack of conceptual understanding about applying properties of operations or from a lack of fluency in finding common factors and multiples to apply the Distributive Property. Provide review or additional practice as appropriate.”

  • Unit 7: Integers, Rational Numbers, and the Coordinate Plane, Lesson 7-5: Represent Rational Numbers on the Coordinate Plane, 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 Lessons Assign the interactive lessons to reinforce targeted skills. Identify Points in the Coordinate Plane Graph in the Coordinate Plane Reflected Points” Build Proficiency states, “Interactive Additional Practice Assign students either the print or digital assignment to practice lesson concepts. The digital assignment includes algorithmic exercises.” Extend Thinking states, “STEM Adventures Is extreme weather random or are there patterns to be observed? In this STEM adventure students apply their understanding of integers and rational numbers to investigate.”

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 6 meet expectations for providing extensions and/or opportunities for students to engage with grade-level/course-level mathematics at higher levels of complexity.

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

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

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

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

  • Unit 8: Equations and Inequalities, Lesson 8-1: Understand Equations and Their Solutions, Differentiate, Extend Thinking, students extend their learning of 6.EE.6, use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number. The materials state, “For exercises 1-8, substitute the values into the equation to determine which one is the solution to the equation. Show your work. Use your answers to finish the joke’s punchline. If there is no solution, leave a blank. 1. 48+x=10048 + x = 100 A. 52 B. 62 C. 72.”

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 6 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), “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: Understand the World Around Us Through Statistics, Lesson 2-2: Represent and Describe Data in a Histogram, Session 1, Activity-Based Exploration states, “Digital: Group students into pairs of small groups. Before students begin the Digital activity, hand out the Histo-what? Teaching Resource for students to reference. Using WebsketchTM, students create histograms. Ensure that they can move the bars up and down. Hands-On: Group students into the same large groups they were in for Lesson 1. Have students organize their data from Lesson 1 into a table showing the frequency of the data values. Students use the data from their tables to create a histogram on the Histograms Teaching Resource.”

  • Unit 3: Ratios and Rates, Lesson 3-1: Understand Ratios, Session 2, Activity-Based Exploration states, “Invite volunteers to describe the patterns shown in the models they have created. Have students describe how the patterns in the models help them identify the structure in the problem and how that helps them find a solution. Facilitate Mathematical Discourse: Ask students to share their responses to the Concluding Question. How can your representations show the relationships between the quantities in each situation? As students share their representations and descriptions, connect them to these new key terms and concepts: A ratio is a relationship in which for every a unit of one quantity, there are b units of another quantity. A ratio always has two terms. You can represent a ratio using numbers: a to b, a : b, and ab\frac{a}{b}. A part-to-whole ratio compares one part of a group to the whole group. The apple juice to fruit drink is a part-to-whole ratio. A part-to-part ratio compares one part of a group to another part of the same group. The vinegar to olive oil is a part-to-part ratio.”

  • Unit 4: Understand and Use Percentages, Unit Opener, What Do I Already Know? states, “Place a checkmark (✔) in each row that corresponds with how much you already know about each term and topic before starting this unit. At the end of the unit, place a checkmark in each row that corresponds with how much you know about each term and topic. Terms benchmark percentages; equivalent ratios; percent; rate; ratio.” The three possibilities for check marks are “I don’t know; I’ve heard of it; I know it.” 

  • Unit 6: Numerical and Algebraic Expressions, Lesson 6-7: Find Factors and Multiples, Session 2, Summarize & Apply state, “Elicit Evidence of Student Understanding: What is one method you can use to explain to a classmate how to find the greatest common factor of two whole numbers? What is one method you can use to explain to a classmate how to find the least common multiple of two numbers? How can you explain the similarities and differences of finding greatest common factors and least common multiples to a student that has been absent during these lessons?”

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 6 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 2: Understand The World Around Us Through Statistics, Unit Opener, Preparing for Explore and Develop, How Do I Choose? states. “The lessons that introduce new math skills could be opportunities for students to explore the concepts with more guidance. Lessons 2-6 and 2-7 involve using algorithms to divide and could be opportunities to implement the Guided Exploration if your students struggle with operations with multi-digit whole numbers or decimals. Consider whether students need practice presenting ideas to the entire class. Guided Exploration provides opportunities to pause the instruction and have students speak to the group.”

  • Unit 5: Solve Area, Surface Area, and Volume Problems, Unit Opener, Ignite states, “Students can work in pairs or groups of three to work on the Ignite questions… Facilitate Discourse As student-groups share their designs for a tree farm, ask other students to think about similarities and differences among the different designs. Focus on students’ rationales for the shape of the design. What similarities do you notice in the different designs? What differences do you notice? Which ideas for other designs would you want to think about adding to your design?” 

  • Unit 7: Integers, Rational Numbers, and the Coordinate Plane, Lesson 7-2: Represent Rational Numbers and Their Opposites on the Number Line, Session 1, Guided Exploration states, “Collaborate and Connect: How can you represent the depths of the roots? Have students work with a partner to plot the depth of the roots on a number line using the Blank Open Number Lines Teaching Resource. Then have students discuss why the value is a negative number. Let’s Explore More Compare and Connect: Compare and Contrast Solution Strategies 1. Set-Up: Give students 5-7 minutes to answer the Let’s Explore More questions on their own. 2. What is Similar, What is Different: Have students read the problems and share their solutions with a partner. They should use mathematical language as they identify, compare, and contrast their two approaches to solving the problems. Students should reflect on how to distinguish contexts requiring positive rational numbers from contexts that require negative rational numbers. Each time they share, the partners develop a deeper understanding of the problem situation. 3. Mathematical Focus: Have students compare and contrast rational numbers and integers.”

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 6 meet expectations for providing strategies and supports for students who read, write, and/or speak in a language other than English to regularly participate in learning grade-level mathematics.

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

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

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

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

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

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 6 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 2: Understand and Use Statistics to Understand the World Around Us, Lesson 2-1: Understand Statistical Questions, Session 2, Guided Exploration states, “Ayasha conducted a survey about the number of pets the students in her class have. The results of her survey are shown. How can Ayasha display the data to help her summarize her findings?”

  • Unit 4: Understand and Use Percentages, Unit Overview, Math History Minute states, “Graciano Ricalde Gambo (1873-1942) was a Mexican mathematician who, in 1910, achieved recognition for calculating the orbit of Halley’s Comet. His precise calculations proved that the comet would not hit Earth, which was of great concern at the time. Halley’s Comet follows a highly elliptical path and can be seen from Earth every 74-79 years.”

  • Unit 5: Solve Area, Surface Area, and Volume Problems, Unit Opener, What Do I Already Know? states, “Benjamin Banneker (1731-1806) was an African-American mathematician, astronomer, inventor, and writer. When he was 22, he used his own drawings and calculations to construct a working clock that was made almost entirely out of wood.”

  • Unit 9: Relationships Between Two Variables, Lesson 9-3: Write Equations to Represent Relationships Between Two Variables, Session 1, Guided Exploration states, “Miguel is interested in joining a recreation center. Recreation World charges the monthly fee shown on the flyer. How can Miguel determine the cost of being a member of Recreation World for any number of months?”

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 6 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 1, Course 1, 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: absolute value (Lesson 7-3) The distance between a number and zero on a numberline. Español: valor absoluto Distancia estre un número y cero en la recta numérica.”

  • Unit 1: Math Is…, Spanish Unit Resources, Carta para la familia [Family Letter] states, “En esta unidad, Matemáticas es..., los estudiantes pensarán y hablarán sobre qué significa trabajar con las matemáticas y verse a sí mismos trabajando con ellas. Se los alentará a observar y preguntarse cómo se usan las matemáticas en la vida diaria, a hablar de sus ideas y a reflexionar sobre sus experiencias con las matemáticas. [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.]”

  • Unit 3: Ratios and Rates, Lesson 3-1: Understand Ratios, Session 2, Activity-Based Exploration, Multilingual Learner Scaffolds states, “Entering/Emerging As students complete the MLR, allow them to explain their representations and descriptions in their home language, though they should use English to report out. Give them a Venn diagram to record the similarities and differences between their representations and their partner’s. Provide sentence frames, such as I represented it this way because I think…”

  • Unit 10: Math Is…, Lesson 10-1: Math Is Everywhere, Session 2, Activity-Based Exploration, Multilingual Learner Scaffolds states, “Entering/Emerging As students complete the MLR, allow them to explain their answers in their home language, though they should use English to report out. Give them a Venn diagram to record the similarities and differences between their answers and their partner’s. Provide sentence frames such as I answered in this way because I think…”

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 6 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, French, Formulas, provides formulas used in the curriculum in French such as the formula for the area of a cube, “Aire totale d'une surface, Cube, T=6s2T=6s^2.”

  • Unit 3: Ratios and Rates, Lesson 3-1: Understand Ratios, Session 2, Summarize & Apply, “Apply: Middle School Fundraiser Some sixth-grade students will make 50 bags of honey granola to sell at a fundraising event. They will put 2 cups of granola in each bag and will sell each back for $5. The table shows the recipe the students will use. Question 1 How many cups of rolled oats will the students need to buy? Question 2 One pound of almonds costs $9.99 and contains 3 cups of almonds. How much will the students need to budget for almonds? Choose a question to answer. Then answer it in the space below.”

  • Unit 5: Solve Area, Surface Area, and Volume Problems, Lesson 5-7: Determine Surface Area of Prisms, Session 1, Be Curious: Notice & Wonder states, “Purpose Students share their thinking about a partially wrapped box. What do you notice? What do you wonder? Teaching Tip Students may have little to no experience with wrapping a gift using a box and wrapping paper. Have volunteers share when they have wrapped a box in the past and what the process entails. Pose Purposeful Questions What do you think is happening in the picture? What can you infer about the box seeing that it is only partially wrapped. Pause & Reflect Students think about the relationship between the sides of the box and the amount of paper needed to cover the box. What would you need to know about the box to make sure you had enough paper to cover it entirely?”

  • Unit 9: Relationships Between Two Variables, Unit Overview, Math Mindset states, “Understanding Others When students understand others’ perspectives and viewpoints, they are better able to appreciate diversity and treat everyone with respect. Strategies that might help students understand others include: encourage students to describe their understanding of their own experiences. encourage students to describe their identities. encourage students to describe shared group norms.”

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 6 partially provides supports for different reading levels to ensure accessibility for students.

Within the Reveal Math 2025 materials, 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 2: Understanding the World Around Us Through Statistics, Unit Opener, Building the Language of Mathematics states, “As students work through each lesson, have them complete the graphic organizer to build understanding of and proficiency with key mathematical terms and concepts. Encourage students to come up with their own definitions and descriptions of terms. When students generate their own definitions or descriptions of terms, they are most likely to remember them long term. Word Wall If there is a Math Word Wall in the classroom, ask students to add their words, examples, and counter examples of statistics to the wall. As they share them, have each student explain their entry.”

  • Unit 8: Equations and Inequalities, Unit Overview, Math Language Development states, “Using Transitional Words In this unit, students will compare, connect, support, and analyze the connections between and among processes and ideas. They will explain how prior knowledge contributes to their understanding of new information. While lesson vocabulary can provide the words students need to describe, define, or identify, students will also need words that help them communicate the relationships between and among ideas. Expanding expressive vocabulary with transitional words will add variety and clarity to students’ speech and writing.”

  • Unit 9: Relationships Between Two Variables, Lesson 9-3: Write Equations to Represent Relationships Between Two Variables, Session 1, Guided Exploration, the teacher guidance states, “MLR Three Reads: Values/Units Chart 1. First Read: Students underline any words or phrases that represent a known or unknown value or amount. They list these numbers, unknowns, and variables in the left column of the first table on the Tables Teaching Resource (Values). 2. Second Read: In the right column (Units), students write the meaning of the value in context. 3. Third Read: Students use the information from the teaching resource to write an equation that represents the situation.”

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 6 meet expectations for providing manipulatives, both virtual and physical, that are accurate representations of the mathematical objects they represent and, when appropriate, are connected to written methods.

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

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

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

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

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

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 6 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 6 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, Postal Sort: Understanding the World Around Us Through Statistics, Description states, “This interactive game provides practice with mean and median.” Instructions state, “Help sort the mail into boxes for delivery. There are 24 pieces of mail that need sorting. Use the arrows on the right and left side of the screen to move between the two shelves to see all the envelopes. To start, click a box at the bottom of the screen to see the category labels. Click and drag a category to label the box. Click and drag envelopes that fit the category label into the box. Click a box to edit its category label or to deliver it. For some categories, you need to tape the envelopes together before you deliver a box.”

  • Unit 3: Ratios and Rates, Lesson 3-2: Understand Rates and Unit Rates, Session 1, Lesson Opener, Number String Matrix states, “Students build fluency with operations as they use the solution to an equation to solve equations with the same digits with different-base ten values.” There is a digital platform for the number string matrix. The materials state, “A Number String is a list of related equations. Students use the solution strategy for the first equation to solve the subsequent equations. A number string matrix is a set of related problems that are presented in rows and columns. Students pick a row or column and solve the equations.”

  • Unit 6: Numerical and Algebraic Expressions, Lesson 6-5: Write and Evaluate Algebraic Expressions, Session 2, Differentiate, Digital Game Center, teachers can assign students a variety of enrichment, interventions, and reinforcement. The materials state, “The Digital Game Center offers students anytime access to all the digital games for Reveal Math 68. These games are designed to help students build proficiency with key middle school concepts and skills. Among the skills practiced are operations with rational number and integers, ratio and proportional reasoning, and foundational linearity. Teachers may opt to assign games to students through the Digital Teacher Center.” 

  • Unit 7: Integers, Rational Numbers, and the Coordinate Plane, Lesson 7-7: Represent Polygons on the Coordinate Plane, Session 2, Differentiate, teachers can assign tasks that build proficiency for students, 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. Understanding Ordered Pairs on a Coordinate Graph.”

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 6 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 states, “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 6 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 1-5: Math Is Finding Patterns, Session 1, Summarize & Apply, the curriculum provides images and graphics that support student learning without being visually distracting. The material states, “Sei whales, a kind of baleen whale, measure 4.5 meters long at birth and grow about 2.5 centimeters each day. An adult sei whale averages 15 meters in length. Question: At what age would the sei whale reach 15 meters in length?” An image is included of a baby sei whale labeled as 4.5 m and an adult sei whale labeled as 15 m long.

  • Unit 5: Solve Area, Surface Area, and Volume Problems, Lesson 5-3: Determine the Area of a Trapezoid, Session 1, Guided Exploration, the curriculum provides images and graphics that support student learning without being visually distracting, “The top of a table is in the shape of an isosceles trapezoid. What is the area of the tabletop? What are the important quantities in the problem?” The task includes an image of a trapezoid shaped table with measurements of each side of the table and images of a decomposed trapezoid with the same measurements. 

  • Unit 8: Equations and Inequalities, Lesson 8-3: Write and Solve Equations Using Multiplication or Division, Session 1, Guided Exploration, the curriculum provides images and graphics that support student learning and engagement without being visually distracting. “Ayasha’s House The distance from Ayasha’s house to the mountains is shown. The distance from her house to the mountains is four times as far as the distance from her house to the lake. What is the distance from Ayasha’s house to the lake?” The task includes an image of a map with the distance between Ayasha’s house and the mountains labeled 140 mi.

  • Unit 10: Math Is…, Lesson 10-5: Math is Boundless, Session 1, Guided Exploration, the curriculum provides images and graphics that support student learning and engagement without being visually distracting. “What are the elements of geometric design? Math can help us find and create designs that include repetition and patterns. The first element in creating a design is repetition. Repetition involves a repeated object, shape, or form. Because it involves one object, shape, or form, it has predictability. The second element is a pattern. A pattern is a combination of objects, shapes, or forms, repeated in a regular arrangement. A pattern has a pattern unit. It also has predictability.” With the definitions, there is an image of each concept. Repetition has a picture of four identical pink circles and an image of six identical clocks. Pattern has an image of three shapes in a recurring pattern and an image of a geometric textile design.

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 6 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 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 state, “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.”