7th Grade - Gateway 1

The materials reviewed for Reveal Math 2025 Grade 7 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: Solve Problems Involving Geometry, Unit Assessment (paper version): Form B, Question 5, “Part A: Draw a triangle with one angle that is greater than 90°, one side length of 5 units, and one side length at 7 units. Part B: Classify the triangle by its sides and angles. Explain your reasoning.” Online version, “Part A: Which triangle has one angle that is greater than 90° and has no congruent side lengths? Choose the correct answer. Students are given four different triangles. Three of the triangles have two sides labeled 5 and 7 and the last triangle has one side labeled 5. Part B: Classify the triangle by its sides and angles. Explain your reasoning. Enter the answer.” (7.G.2)

• Unit 4: Solve Problems Involving Percentages, Performance Task: Managing a Shoe Store, Part B, “A customer buys a pair of shoes at the shoe store. The receipt shows that the cost of the pair of shoes before tax is $119.50 and the cost after tax is $126.67. What is the sales tax rate in the state where the shoe store is located? Explain.” (7.RP.3)

• Unit 5: Sampling and Statistics, Unit Assessment, Form A, Question 2, “The quiz scores of 12 students in a science class are shown. 9, 8, 7, 3, 9, 10, 10, 9, 7, 8, 9, 7 What score would you expect a student in the science class to receive on the next quiz? Explain.” (7.SP.1)

• Unit 6: Solve Problems Involving Operations with Integers and Rational Numbers, Lesson 6-2: Add Integers and Rational Numbers, Lesson Quiz, Question 3, “Amelia is holding a balloon on a string. The balloon is 16 feet high from the ground. As Amelia passes through a door, she moves the balloon down 4.3 feet toward her. What is the height of the balloon as Amelia passes through the door?” (7.NS.1)

• Unit 7: Work with Linear Expressions, Lesson 7-3: Add Linear Expressions, Exit Ticket, Question 2, “Two friends sell handmade jewelry at festivals. The amount earned from selling jewelry at the Apple Festival was (29n+13b) dollars. The amount earned from selling jewelry at the Peach Festival was (26n+11b)dollars. Write an expression that shows the total amount of money earned at the festivals. Then find the total.” (7.EE.1)

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 2: Solve Problems Involving Geometry, Lesson 2-5: Describe Cross Sections of Three-Dimensional Figures, Lesson Quiz, Question 2, “A cylinder is sliced perpendicular to its base. What is the shape of the cross section? a. circle b. rectangle c. semicircle d. square” (G-GMD.4) Content for 7th grade only extends to cross sections of right rectangular prisms and right rectangular pyramids.

The materials reviewed for Reveal Math 2025 Grade 7 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: Solve Problems Involving Geometry, Lesson 2-2: Use Side Lengths and Angle Measures to Draw and Analyze Triangles, Explore, Session 1, Activity-Based Exploration, How Many Triangles, students explore how many triangles they can make given three line segments or three angle measures. It states, “Group students in pairs or small groups. Have students read and respond to the Introductory Questions in their Activity Exploration Journal. Given three line segments, how many triangles do you think you can make with them? Given three angles, how many triangles do you think you can make with them? Hands On Students break spaghetti noodles into 3 pieces and work together to form triangles. Make sure that they measure the lengths of each of the 3 pieces as well as the 3 angles of the triangle that they form and record their observations. Encourage students to find pieces that do not form a triangle.” These problems meet the full intent of 7.G.2 (Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides…) In Lesson 2-6: Solve Problems Involving Area and Surface Area, Lesson Quiz, Question 2, students find the area of a figure composed of a triangle and two rectangles. It states, “Regina draws a plane for two rectangular vegetable garden beds and a triangular rose garden. What is the total area of Regina’s gardens?” These problems meet the full intent of 7.G.6 (Solve real-world and mathematical problems involving area, volume, and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.) In Lesson 2-9: Solve Problems Involving Areas of Circles, Explore, Session 1, Activity-Based Exploration, Rolling and Unrolling, students describe the relationship between the circumference and area of a circle. “Hands-On, Have students cut out the triangles that form the parallelograms on the Area of a Circle Teaching Resources and glue them onto the circles. Encourage students to make as many observations as possible about the relationships they observe. Then, they will reason about the relationship between the dimension of a circle and the dimensions of the parallelogram to find the area of the circle. Encourage the students to record their observations in their Activity Exploration Journal. These problems meet the full intent of 7.G.4 (Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle.)

• Unit 3, Lesson 3-3: Use Graphs to Determine Proportionality, Session 1, Practice, Exercises 1-3, students graph the relationship of a real-life situation on a coordinate plane. It states, “At a breakfast stand, you can purchase two breakfast bars for $5.00 or seven for $17.50. 1. Graph the relationship on the coordinate plane. Is the cost of breakfast bars proportional to the number of bars purchased? Explain how you know. 2. What does the point (0,0) represent on the graph? 3. What point represents the unit rate? What is the unit rate?” These problems meet the full intent of 7.RP.2a (Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the line is a straight line through the origin), 7.RP.2b (Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships), 7.RP.2d (Explain what a point (x,y) on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0,0) and (1,r) where r is the unit rate.) In Lesson 3-5: Describe Proportional Relationships, Develop, Session 2, Guided Exploration, Tension on the Trampoline, “A trampoline spring stretches 3 inches for every 77 pounds of weight pulling on it. How far would the spring stretch if 100 pounds of weight were put on it? You can use the constant of proportionality to solve the problem. The constant of proportionality is 3:77 or \frac{3}{77} because the spring stretches 3 inches for every 77 pounds of weight placed on it. One Way: Use a graph. Another Way: Use an equation.” These problems meet the full intent of 7.RP.2b (Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships) and 7.RP.2d (Explain what a point (x,y) on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0,0) and (1,r) where r is the unit rate.) In the Performance Task, students solve a variety of problems where they recognize and represent proportional relationships between quantities. “Karima is a mechanical engineer that works on designs for air purifiers. The table shows the square footage for the air purifiers she has designed and the number of cubic feet they purify. Part A Is the relationship between the advertised square footage of an air purifier and the number of cubic feet it can purify proportional? If so, what is the constant of proportionality and what does it represent in this situation? Part B A coworker states to Karima that an air purifier that can purify 3,600 cubic feet should have an advertised square footage of 400. Is the coworker correct? If not, what should the advertised square footage be? Part C Karima wants to write an equation that she can use to calculate the cubic feet purified for any advertised square footage. What equation should she use?” These problems meet the full intent 7.RP.2a (Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the line is a straight line through the origin) and 7.RP.2b (Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships).

• Unit 6, Lesson 6-2: Add Integers and Rational Numbers, Session 1, Exit Ticket, Question 2, students solve real-world problems by adding and subtracting integers. It states, “A contestant has -200 points on a game show. The contestant answers a question correctly and earns 500 points. What is the contestant’s score now?” In Lesson 6-3: Understand Additive Inverses, Session 1 Guided Exploration, Agriculture, Let’s Explore More, students explore the additive inverse and absolute value. “An agricultural engineer uses a drone to suspend water throughout a greenhouse. The drone moves back-and-forth to water each plant twice. From its starting position, the drone travels 5 feet to the left. a. Use your own words to describe additive inverse. b. What do you notice about the absolute value of inverses like -152 and 152?” Lesson 6-4: Subtract Integers and Rational Numbers, Session 2, Guided Exploration, Roving on Mars, Let’s Explore More, students apply properties of operations to rational signed numbers. “One of NASA’s rovers on Mars recorded a high temperature of 95\degree Fahrenheit and a low temperature of -166\degree Fahrenheit. What is the range in temperature on Mars? a. How would the range change if the high temperature was -95\degreeF, instead of 95\degreeF? Explain your thinking. ” These problems meet the full intent and give all students extensive work with 7.NS.1d (Apply properties of operations as strategies to add and subtract rational numbers.) 

• Unit 7, Lesson 7-1: Combining Like Terms, Practice, Exercise 8-10, students add, subtract, factor, and expand linear expressions with rational coefficients. It states, “For exercises 8-10, write the expression in simplest form. 8. 8a+4b-6a+7b 9. -4m+3n+5n-4+3m 10. 4m-9m+3n+7+2n+5n.” In Lesson 7-4: Subtract Linear Expressions, Session 1, Guided Exploration, Budgeting, Let’s Explore More, students explore the real-world context for a linear expression. “Isaiah has $150 in his checking account. This week, he has x dollars to deposit. He puts 5% of his deposit into his savings account and the rest in his checking account. a. Explain in your own words what $(0.95x+100) means. b. How does the process of adding linear expressions compare to the process of subtracting linear expressions?” In Lesson 7-5: Factor Linear Expressions, Session 1, Exit Ticket, Question 1, students are given an expression that needs to be written in factored form, “Write the expression 9x+36y in fully factored form.” These problems meet the full intent and give all students extensive work with 7.EE.1 (Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.) 

• Unit 9, Lesson 9-1: Understand Probability, Session 1, Guided Exploration, Rain or Shine, Let’s Explore More, students understand the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring. It states, “a. Suppose there is a 0% chance that it will rain on Saturday. Is it possible that it will rain on Saturday? b. Arrange the probabilities 99%, \frac{5}{10}, 0.34, 11%, and \frac{9}{10} from impossible to certain. Then describe a real-world example of when this skill would be important.” In Lesson 9-3: Theoretical Probability of Simple Events, Session 2, Guided Exploration, Shirt Choices, Let’s Explore More, students explore theoretical probability with a real-world scenario. “Quan has the number of each type of shirt shown in his closet that he can choose from to wear to school. a. Is it more likely that Quann will randomly choose a button-down shirt or T-shirt? Explain your reasoning. b. There are two types of shirts in Quan’s closet, long-sleeved and short sleeved. Explain why the probability that Quan will select a short-sleeved shirt from his closet is not 50%.” In the Performance Task: Winning Gift Cards, Part A and Part B, students are given a real-world scenario and asked to find the theoretical probability and determine the likelihood of the event occurring. The materials state, “Zion is the manager of a bicycle store. To encourage customers to come to the store, Zion decides to let one customer play a game each day to win a $500 gift card to the store. Each day Zion writes a number from 1 to 20 on a piece of paper. If the customer correctly guesses the number, they win the gift card. Part A What is the theoretical probability that a customer wins the gift card on any particular day? Explain how to find the answer. Part B-Describe the chance that a customer wins the gift card on any particular day as impossible, unlikely, equally likely, likely, or certain. Explain your reasoning.” These problems meet the full intent and give all students extensive work with 7.SP.5 (Understand the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring. Larger numbers indicate greater likelihood. A probability near 0 indicates an unlikely event, a probability around \frac{1}{2} indicates an event that is neither unlikely or likely, and a probability near 1 indicates a likely event.)

The materials reviewed for Reveal Math 2025 Grade 7 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 6.5 out of 10 units, approximately 65%.

• The approximate number of lessons devoted to major work, and supporting work connected to major work of the grade is 41 out of 62, approximately 66%.

• The approximate number of instructional days devoted to major work, including assessments and supporting work connected to the major work is 110 days out of 169, approximately 65%. 

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 65% of the instructional materials focus on major work of the grade.

The materials reviewed for Reveal Math 2025 Grade 7 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 2: Solve Problems Involving Geometry, Lesson 2-4: Solve Problems Involving Angle Relationships, Session 2, Guided Exploration, Vertical Flight, connects the supporting work of 7.G.5 (Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure.) to the major work of 7.EE.4 (Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities.) as students “Solve word problems leading to equations and use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure.” For example, “Knife-edge flight is a regular part of aerobatic performances where a plane’s wings form a 90-degree angle with the horizon. How many more degrees must the plane in the photo roll to be in this position?” Students are encouraged to use an equation to find the measure of the angle.

• Unit 5: Sampling and Statistics, Lesson 5-3: Draw Inferences from Samples, Session 1, Guided Exploration, Who’s the Winner?, connects the supporting work of 7.SP.2 (Use data from a random sample to draw inferences about a population with an unknown characteristic of interest. Generate multiple samples (or simulated samples) of the same size to gauge the variation in estimates or predictions.) to the major work of 7.RP.3 (Use proportional relationships to solve multistep ratio and percent problems.) as students “Use proportional relationships to solve multistep ratio problems and use data from a random sample to draw inferences about a population.” For example, “Quan, Rebekah, and Javier are running for the seventh-grade class president in a class of 413 students. They randomly poll 40 seventh-grade students to ask which candidate will get their vote. The results are shown in the table. What is a possible inference you could make about who is most likely to win the actual election? You can use the results from the sample to estimate the percent of the vote each candidate will receive.” Students are encouraged to use a proportion to estimate each candidate’s percent of vote.

• Unit 9: Probability, Lesson 9-3: Theoretical Probability of Simple Events, Session 1, Practice, Question 7, connects the supporting work of 7.SP.7 (Develop a probability model and use it to find probabilities of events. Students compare probabilities from a model to observed frequencies; if the agreement is not good, explain possible sources of the discrepancy.) to the major work of 7.RP.3 (Use proportional relationships to solve multistep ratio and percent problems.) as students “Use proportional relationships to solve multi-step ratio and percent problems.” For example, “A quality engineer determines that the probability that a randomly-selected product from the assembly line is defective is 3%. If she randomly selects a sample of 400 products, how many are likely to be defective?”

The materials reviewed for Reveal Math 2025 Grade 7 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: Solve Problems Involving Geometry, Lesson 2-5: Describe Cross Sections of Three-Dimensional Figures, Session 2, Lesson Quiz, Problem 10 connects the supporting work of 7.G.A (Draw, construct, and describe geometrical figures and describe the relationship between them.) to the supporting work of 7.G.B (Solve real-life and mathematical problems involving angle measure, area, surface area, and volume.) as students describe the two-dimensional figures that result from slicing three-dimensional figures and solve real-world and mathematical problems involving areas of two- and three-dimensional objects. The problem reads, “A student in your class states that the area of a cross section of a pyramid that is parallel to the base of the pyramid is equal to the area of the base of the pyramid. What can you tell this student about the cross section of the pyramid?”

• Unit 4: Solve Problems Involving Percentages, Lesson 4-3: Solve Percent Change Problems, Session 1, Guided Exploration, Arctic Sea Ice Extent, connects the major work of 7.RP (Ratios and Proportional Relationships) to the major work of 7.EE (Expressions and Equations) as students use proportional relationships to solve multistep ratio and percent problems that involve real-life problems posed with positive and negative rational numbers in any form. The problem reads, “From 2000 to 2020, the Arctic sea ice extent decreased from an area of 5,512,000 square miles to 3,360,000 square miles. By what percent has the area of the Arctic sea ice extent decreased over the 20-year period?”

• Unit 5: Sampling and Statistics, Lesson 5-5: Assess Visual Overlap, Session 1, Guided Exploration, Rice Production connects the supporting work of 7.SP.A (Use random sampling to draw inferences about a population.) to the supporting work of 7.SP.B (Draw informal comparative inferences about two populations.) as students use data from a random sample to draw inferences about a population with an unknown characteristic of interest and use measures of centers and variability for numerical data from random samples to draw informal comparative inferences about two populations. The problem states, “The number of rice farms is decreasing. However, because of improved civilization methods, the amount of rice production appears to be increasing. What can you conclude about annual rice yields by analyzing the box plots of the 2000 and 2022 rice yields?”

• Unit 8: Solve Problems Using Equations and Inequalities, Lesson 8-3: Solve Equations p(x + q) = r, Session, Guided Exploration, Kennel Up connects the major work of 7.EE.A (Use properties of operations to generate equivalent expressions.) to the major work of 7.EE.B (Solve real-life and mathematical problems using numerical and algebraic expressions and equations.) as students apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients and use solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form. The problem reads, “An animal hospital wants to install 7 kennels that will cover 162.5 square feet of floor space. Each kennel will be 5 feet deep and will be separated by a 2-inch-wide-wall. What will the width of the kennel be? Students are expected to define a variable, write an equation to represent the situations, and solve the equation.”

The materials reviewed for Reveal Math 2025 Grade 7 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: Solve Problems Involving Geometry, Unit Overview, Coherence, What Students Will Learn Next, connects the current grade-level work as, “Students use relationships among angles to find unknown angle measures,” to future work where “Students explore the relationships among the angles in a triangle and among the angles formed when parallel lines are cut by a transversal. (Grade 8)”

• Unit 8: Solve Problems Using Equations and Inequalities, Unit Overview, Coherence, What Students Will Learn Next, connects the current grade-level work as, “Students solve two-step equations of the form px+q=r and the form p(x+q)=r,” to future work where “Students solve linear equations in one variable and pairs of simultaneous linear equations. (Grade 8).”

• Unit 9: Probability, Unit Overview, Coherence, What Students Will Learn Next, connects the current grade-level work as, “Students find the probability of an event by expressing it as number between 0 and 1 and classify the likelihood of an event happening,” to future work where “Students explore concepts of independence and conditional probability. (High School)”

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

• Unit 3: Proportional Relationships, Unit Overview, Coherence, connects the current grade-level work as, “Students determine the constant of proportionality,” to prior knowledge where “Students understood rates as a kind of ratio that compares quantities that may have different units. (Grade 6)”

• Unit 5: Sampling and Statistics, Unit Overview, Coherence, connects the current grade-level work as, “Students analyze the means of multiple samples, predict the population mean, and describe the variability of the distribution of sample means.” to prior knowledge where “Students described data using measures of center and variability. (Grade 6)”

• Unit 7: Work with Linear Expressions, Unit Overview, Coherence, connects the current grade-level work, “Students expand linear expressions using the Distributive Property.” to prior knowledge where “Students applied the Distributive Property to multiply and divide. (Grade 6)”