6th Grade - Gateway 1

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: 0.3^2+8, Expression B: 2^3+0.09, Expression C: 2^3+0.03^2, Expression D: 3^2\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.

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? |-1.5|-|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=20c, where t is the number of tickets and c 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…)

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.

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)+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?”

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\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<\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.)

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=r and p(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.”