8th Grade - Gateway 1

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

• Unit 9: Irrational Numbers, Exponents, and Scientific Notation, Lesson 9-1: Represent Rational Numbers in Decimal Form, Explore, Session 1, Guided Exploration, Let’s Explore More, Problems a and b, connect the supporting work of 8.NS.1 (Know that numbers that are not rational are called irrational. Students understand informally that every number has a decimal expansion; for rational numbers show that the decimal expansion repeats eventually, and convert a decimal expansion which repeats eventually into a rational number.) to the major work of 8.EE.2 (Use square root and cube root symbols to represent solutions to equations of the form x^2=p and x^3=p, where p is a positive rational number. They evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that 2 is irrational.) as students “convert fractions into decimals so that they learn that every number has a decimal expansion; for rational numbers show that the decimal expansion repeats eventually” For example, “a. What does 5.4\oline{0} mean? b. is 5.\oline{0}4 possible?”

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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