7th Grade - Gateway 1

The materials reviewed for Open Up Resources Grade 7 meet expectations for assessing grade-level content and, if applicable, content from earlier grades.

Program assessments include Pre-Unit Diagnostic Assessments, Cool Downs, Mid-Unit Assessments, Performance Tasks, and End-of-Unit Assessments which are summative. According to the Course Guide, “At the end of each unit is the end-of-unit assessment. These assessments have a specific length and breadth, with problem types that are intended to gauge students’ understanding of the key concepts of the unit while also preparing students for new-generation standardized exams. Problem types include multiple-choice, multiple-response, short answer, restricted constructed response, and extended response. Problems vary in difficulty and depth of knowledge.” Examples of summative End-of-Unit Assessment problems that assess grade-level standards include:

• Unit 2: Introducing Proportional Relationships, End-of-Unit Assessment: Version B, Problem 3, “Kiran walked at a constant speed. He walked 1 mile in 15 minutes. Which of these equations represents the distance d (in miles) that Kiran walks in t minutes. A. d = t + 14 B. d = t - 14 C. d = 15t D. d = 115t.” (7.RP.2c)

• Unit 5: Rational Number Arithmetic, End-of-Unit Assessment: Version A, Problem 7, “Jada walks up to a tank of water that can hold up to 10 gallons. When it is active, a drain empties water from the tank at a constant rate. When Jada first sees the tank, it contains 7 gallons of water. Three minutes later, the tank contains 5 gallons of water. 1. At what rate is the amount of water in the tank changing? Use a signed number, and include the unit of measurement in your answer. 2. How many more minutes will it take for the tank to drain completely? Explain or show your reasoning. 3. How many minutes before Jada arrived was the water tank completely full? Explain or show your reasoning.” (7.NS.2 and 7.NS.3)

• Unit 6: Expressions, Equations, and Inequalities, End-of-Unit Assessment: Version A, Problem 3, “Select all expressions that are equivalent to 6x + 1 - (3x - 1). A. 6x + 1 - 3x - 1 B. 6x + (-3x) + 1 + 1 C. 3x + 2 D. 6x - 3x + 1 - 1 E. 6x + 1 + (-3x) - (-1).” (7.EE.1)

• Unit 7: Angles, Triangles, and Prisms, End-of-Unit Assessment: Version B, Problem 5, “Draw as many different triangles as possible that have a side length of 5 units, a 45° angle, and a 90° angle. Clearly mark the side lengths and angles given.” (7.G.2)

• Unit 8: Probability and Sampling, End-of-Unit Assessment: Version B, Problem 4, “A school plans to start selling snacks at their basketball games. They want to know which snacks would be most popular. 1. What is the population for the school’s question? 2. Give an example of a sample the school could use to help answer their question.” (7.SP.1)

The materials reviewed for Open Up Resources Grade 7 meet expectations for giving all students extensive work with grade-level problems to meet the full intent of grade-level standards.

Each lesson is structured into four phases: Warm Up, Instructional Activities, Lesson Synthesis, and Cool Down. This structure ensures thorough engagement with grade-level problems and alignment with educational standards.

The Warm Up phase starts each lesson, helping students prepare for the day’s content and enhancing their number sense or procedural fluency. Following the Warm Up, students participate in one to three instructional activities that focus on the learning standards. These activities, described in the Activity Narrative, form the lesson's core.

After completing the activities, students synthesize their learning, integrating new knowledge with prior understanding. The lesson concludes with a Cool Down phase, a formative assessment to measure student understanding. Additionally, each lesson includes Independent Practice Problems to reinforce the concepts.

Instructional materials engage all students in extensive work with grade-level problems. Examples include:

• Unit 4: Proportional Relationships and Percentages, Section B: Percent Increase and Decrease, Lesson 6: Increasing and Decreasing, students use proportional reasoning and percentages to describe and solve problems involving increases and decreases. Activity 1: More Cereal and a Discounted Shirt, Problem 1, “A cereal box says that now it contains 20% more. Originally, it came with 18.5 ounces of cereal. How much cereal does the box come with now?” Activity 2: Using Tape Diagrams, Problem 1, “Match each situation to a diagram. Be prepared to explain your reasoning (two tape diagrams with 25% shaded are shown, one diagram is longer on the bottom, the second has equal parts on top and bottom). a. Compared with last year’s strawberry harvest, this year’s strawberry harvest is a 25% increase. b. This year’s blueberry harvest is 75% of last year’s. c. Compared with last year, this year’s peach harvest decreased 25%. d. This year’s plum harvest is 125% of last year’s plum harvest.” Practice Problems, Problem 3, “Write each percent increase or decrease as a percentage of the initial amount. The first one is done for you. a. This year, there was 40% more snow than last year. The amount of snow this year is 140% of the amount of snow last year. b. This year, there were 25% fewer sunny days than last year. c. Compared to last month, there was a 50% increase in the number of houses sold this month. d. The runner’s time to complete the marathon was 10% less than the time to complete the last marathon.” Materials present students with extensive work with grade-level problems of 7.RP.3 (Use proportional relationships to solve multistep ratio and percent problems.)

• Unit 5: Rational Number Arithmetic, Section B: Adding and Subtracting Rational Numbers, Lesson 7: Adding and Subtracting to Solve Problems, students add and subtract rational numbers to solve problems in unfamiliar contexts. Warm-Up: Positive or Negative, Problem a. “Without computing: is the solution to -2.7 + x = -3.5 positive or negative?” Activity 1: Phone Inventory, “A store tracks the number of cell phones it has in stock and how many phones it sells. The table shows the inventory for one phone model at the beginning of each day last week. The inventory changes when they sell phones or get shipments of phones into the store. a. What do you think it means when the change is positive? Negative? b. What do you think it means when the inventory is positive? Negative? c. Based on the information in the table, what do you think the inventory will be at on Saturday morning? Explain your reasoning. d. What is the difference between the greatest inventory and the least inventory?” Students are given a table of data that shows the daily inventory and change for Monday through Friday. Practice Problems, Problem 3, “a. How much higher is 500 than 400 m? b. How much higher is 500 than -400 m? c. What is the change in elevation from 8,500 m to 3,400 m? d. What is the change in elevation between 8,500 m and -300 m? e. How much higher is -200 m than 450 m?” Materials present students with extensive work with grade-level problems of 7.NS.3 (Solve real-world and mathematical problems involving the four operations with rational numbers.)

• Unit 6: Expressions, Equations, and Inequalities, Section D: Writing Equivalent Expressions, Lesson 19: Expanding and Factoring, students use the distributive property to write equivalent expressions. Activity 1: Factoring and Expanding with Negative Numbers, “In each row, write the equivalent expression. If you get stuck, use a diagram to organize your work. The first row is provided as an example. Diagrams are provided for the first three rows.” Students complete missing information in the table of factored and expanded expressions. Cool Down: Equivalent Expressions, “If you get stuck, use a diagram to organize your work. a. Expand to write an equivalent expression: -\frac{1}{2}(-2x + 4y) b. Factor to write an equivalent expression: 26a - 10.” Practice Problems, Problem 1, “a. Expand to write an equivalent expression: -\frac{1}{4}(-8x + 12y) b. Factor to write an equivalent expression: 36a - 16.” Materials present students with extensive work with grade-level problems of 7.EE.1 (Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients).

Instructional materials provide opportunities for all students to engage with the full intent of grade-level standards. Examples include: 

• Unit 2: Introducing Proportional Relationships, Section C: Comparing Proportional and Nonproportional Relationships, Lesson 8: Comparing Relationships with Equations, students determine whether relationships are proportional. Activity 3: All Kinds of Equations, “Here are 6 different equations. y = 4 + x, y = \frac{x}{4}, y = 4x, y = 4^x, y = \frac{4}{x}, y = x^4. a. Predict which of these equations represent a proportional relationship. b. Complete each table using the equation that represents the relationship. c. Do these results change your answer to the first question? Explain your reasoning. d. What do the equations of the proportional relationships have in common?” Cool Down: Tables and Chairs, “Andre is setting up rectangular tables for a party. He can fit 6 chairs around a single table. Andre lines up 10 tables end-to-end and tries to fit 60 chairs around them, but he is surprised when he cannot fit them all. a. Write an equation for the relationship between the number of chairs and the number of tables when: 1. the tables are apart from each other: 2. the tables are placed end-to-end: b. Is the first relationship proportional? Explain how you know. c. Is the second relationship proportional? Explain how you know.” Practice Problems, Problem 2, “Decide whether or not each equation represents a proportional relationship. a. The remaining length (L) of a 120-inch rope after x inches have been cut off: 120 - x = L b. The total cost (t) after 8% sales tax is added to an item’s price (p): 1.08p = tc. The number of marbles each sister gets (x) when m marbles are shared equally among four sisters: x = \frac{m}{4} d. The volume (V) of a rectangular prism whose height is 12 cm and base is a square with side lengths s cm: V = 12$$s^2$$”. The materials meet the full intent of 7.RP.2 (Recognize and represent proportional relationships between quantities.)

• Unit 7: Angles, Triangles, and Prisms, Section A: Angle Relations, Lesson 1: Relationships of Angles, students use reasoning about adjacent angles to determine angle measures. Activity 2: More Pattern Block Angles, “Use pattern blocks to determine the measure of each of these angles.” Students measure an obtuse, exterior, and straight angle (which are pictured). Activity 3: Measuring Like This or Like That, “Tyler and Priya were both measuring angle TUS. Priya thinks the angle measures 40 degrees. Tyler thinks the angle measures 140 degrees. Do you agree with either of them? Explain your reasoning.” Pictured is an acute angle on a protractor. “Cool Down: Identical Isosceles Triangle, “Here are two different patterns made out of the same five identical isosceles triangles. Without using a protractor, determine the measure of ∠x and ∠y. Explain or show your reasoning.” Practice Problems, Problem 3, “Here is a square and some regular octagons. In this pattern, all of the angles inside the octagons have the same measure. The shape in the center is a square. Find the measure of one of the angles inside one of the octagons.” The materials meet the full intent of 7.G.B (Solve real-life and mathematical problems involving angle measure, area, surface area, and volume.)

• Unit 8: Probability and Sampling, Section B: Probability of Multi-step Events, Lesson 8: Keeping Track of All Possible Events, students determine the total possible outcomes of a compound event. Warm-Up: How Many Different Meals?, “How many different meals are possible if each meal includes one main course, one side dish, and one drink?” A table is shown with main courses (grilled chicken, turkey sandwich, pasta salad), side dishes (salad, applesauce), and drinks (milk, juice, water). Activity 2: How Many Sandwiches?, Problem 1, “A submarine sandwich shop makes sandwiches with one kind of bread, one protein, one choice of cheese, and two vegetables. How many different sandwiches are possible? Explain your reasoning. You do not need to write out the sample space. Breads: Italian, white, wheat, Proteins: Tuna, ham, turkey, beans, Cheese: Provolone, Swiss, American, none, and Vegetables: Lettuce, tomatoes, peppers, onions, pickles.” Cool Down: Random Points, “Andre is reviewing proportional relationships. He wants to practice using a graph that goes through a point so that each coordinate is between 1 and 10. a. For the point, how many outcomes are in the sample space? b. For how many outcomes are the x-coordinate and the y-coordinate the same number?” The materials meet the full intent of 7.SP.8b (Represent sample spaces for compound events using methods such as organized lists, tables, and tree diagrams…)

The materials reviewed for Open Up Resources Grade 7 meet expectations that, when implemented as designed, the majority of the materials address the major clusters of each grade. 

When implemented as designed, the majority (at least 65%) of the materials, when implemented as designed, address the major clusters of the grade. For example: 

• The approximate number of units devoted to major work of the grade (including assessments and supporting work connected to the major work) is 5 out of 8, approximately 63%.

• The number of lessons devoted to major work of the grade, including supporting work connected to major work is 76 out of 110, approximately 69%. 

• The number of instructional days devoted to major work of the grade and supporting work connected to major work (includes required lessons and assessments) is 81 out of 118, approximately 69%. 

An instructional day analysis is most representative of the materials, including the required lessons and End-of-Unit Assessments from the required Units. As a result, approximately 69% of materials focus on major work of the grade.

The materials reviewed for Open Up Resources Grade 7 meet expectations that supporting content enhances focus and coherence simultaneously by engaging students in the major work of the grade.

Each lesson contains Learning Targets that provide descriptions of what students should be able to do after completing the lesson. Standards being addressed are identified and defined. Materials connect learning of supporting and major work to enhance focus on major work. Examples include:

• Unit 2: Introducing Proportional Relationships, Section C: Comparing Proportional and Nonproportional Relationships, Lesson 8: Comparing Relationships with Equations, Activity 2: Total Edge Length, Surface Area, and Volume, Problems 1-3, connects the supporting work 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) to the major work of 7.RP.1 (Compute unit rates associated with ratios of fractions, including ratios of lengths, areas, and other quantities measure in like or different units) and 7.RP.2 (Recognize and represent proportional relationships between quantities). Students determine whether or not relationships between the quantities are proportional as they reinforce their understanding of edge length, surface area, and volume.) “Here are some cubes with different side lengths. Complete each table. Be prepared to explain your reasoning. a. How long is the total edge length of each cube? b. What is the surface area of each cube? c. What is the volume of each cube?” Problem 2, “Which of these relationships is proportional? Explain how you know.” Problem 3, “Write equations for the total edge length E, total surface area A, and volume V of a cube with side length s.” Students are shown pictures of cubes with side lengths 3, 5, and 7$$\frac{1}{2}$$.

• Unit 3: Measuring Circles, SectionC: Let’s Put It to Work, Lesson 11: Stained-Glass Windows, Activity 2: A Bigger Window, connects the supporting work of 7.G.1 (Solve problems involving scale drawings of geometric figures) and 7.G.4 (Know the formulas for the area and circumference of a circle and use them to solve problems) and major work of 7.EE.3 (Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form using tools strategically). Students use their cost computations from the previous activity to find the cost of an enlarged version of the stained glass window, scaled by a factor of 3, “A local community member sees the school’s stained glass window and really likes the design. They ask the students to create a larger copy of the window using a scale factor of 3. Would $450 be enough to buy the materials for the larger window? Explain or show your reasoning.” Students are given a picture of the stained glass window, which consists of semi-circles and diamond-shaped pieces. 

• Unit 7: Angles, Triangles, and Prisms, Section B: Drawing Polygons with Given Conditions, Lesson 6: Building Polygons (Part 1), Activity 2: Building Diego’s and Jada’s Shapes, Problem 1, connects the supporting work of 7.G.2 (Draw geometric shapes with given conditions), to the major work of 7.NS.1 (Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers). Students build polygons given descriptions of side lengths, “Diego built a quadrilateral using side lengths of 4 in, 5 in, 6 in, and 9 in. a. Build such a shape (students use applet in presentation mode). b. Is your shape an identical copy of Diego’s shape? Explain your reasoning.”

The materials reviewed for Open Up Resources 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.

Each lesson contains Learning Targets that describe what the students should be able to do after completing the lesson. Standards being addressed are identified and defined.

Materials connect major work to major work throughout the grade level when appropriate. Examples include.

• Unit 4: Proportional Relationships and Percentages, Section A: Proportional Relationships with Fractions, Lesson 5: Say It with Decimals, Activity 1: Repeating Decimals, Problems 1 and 2 connects the major work of 7.NS.A (Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers.) to the major work 7.RP.A (Analyze proportional relationships and use them to solve real-world and mathematical problems.) Students convert ratios written as fractions to decimals that repeat or terminate, “Use long division to express each fraction as a decimal. a. \frac{9}{25} b. \frac{11}{30} c. \frac{4}{11} What is similar about your answers to the previous question? What is different?” 

• Unit 5: Rational Number Arithmetic, Section E: Solving Equations When They are Negative Numbers, Lesson 15: Solving Equations with Rational Numbers, Activity 2: Trip to the Mountains, Problem 1, connects the major work of 7.EE.B (Solve real-life and mathematical problems using numerical and algebraic expressions and equations.) to the major work 7.NS.A (Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers.) Students solve equations using inverse operations with negative values, “The Hiking Club is on a trip to hike up a mountain. The members increased their elevation 290 feet during their hike this morning, Now they are at an elevation of 450 feet. a. Explain how to find their elevation before the hike. b. Han says the equation e + 290 = 450 describes the situation. What does the variable e represent? c. Han says that he can rewrite the equation as e = 450 + (-290) to solve for e. Compare Han’s strategy to your strategy for finding the beginning elevation.” 

• Unit 6: Expressions, Equations, and Inequalities, Section D: Writing Equivalent Expressions, Lesson 18: Subtraction in Equivalent Expressions, Activity 2: Organizing Work, Problem 2, connects the major work of 7.EE.A (Use properties of operations to generate equivalent expressions.) to the major work of 7.NS.A (Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers.) Students use distributive property to write equivalent expressions with negative numbers, “Use the distributive property to write an expression that is equivalent to \frac{1}{2}(8y + -x + -12). The boxes can help you organize your work.” Students are shown a rectangle with a width of \frac{1}{2} and segmented lengths of 8y, -x and -12. 

Materials provide connections from supporting work to supporting work throughout the grade-level when appropriate. Examples include:

• Unit 7: Angles, Triangles, and Prisms, Section A: Angle Relationships: Lesson 4: Solving for Unknown Angles, Activity 2: What’s the Match? connects the supporting work of 7.G.A (Draw, construct, and describe geometric figures and describe the relationships between them.) to the supporting work of 7.G.B (Solve real-life and mathematical problems involving angle measure, area, surface area, and volume.) Students match relationships between angles in a figure with equations that can represent those relationships, “Match each figure to an equation that represents what is seen in the figure. For each match, explain how you know they are a match. 1. g + h = 180 2. g = h 3. 2h + g = 90 4. g + h + 48 = 180 5. g + h + 35 = 180” Students are given five figures to match.

• Unit 8: Probability and Sampling, Section D: Using Samples, Lesson 15: Estimating Population Measures of Center, Activity 2: Who’s Watching What? 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.) Students compute the means for sample ages to determine what shows might be associated with each sample and assess the accuracy of population estimates, “Here are three more samples of viewer ages collected for these same 3 television shows. Sample 4: 57, 71, 5, 54, 52, 13, 59, 65, 10, 71 Sample 5: 15, 4, 4, 5, 4, 3, 25, 2, 8, 3 Sample 6: 6, 11, 9, 56, 1, 3, 11, 10, 11, 2. a. Calculate the mean for one of these samples. Record all three answers. b. Which show do you think each of these samples represents? Explain your reasoning. c. For each show, estimate the mean age for all the show’s viewers. d. Calculate the mean absolute deviation for one of the shows’ samples. Make sure each person in your group works with a different sample. Record all three answers. e. What do the different values for the MAD tell you about each group? f. An advertiser has a commercial that appeals to 15- to 16-year-olds. Based on these samples, are any of these shows a good fit for this commercial? Explain or show your reasoning.

The materials reviewed for Open-Up Resources 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.

The Course Guide contains a Scope and Sequence explaining content standard connections. Some Unit Overviews, Lesson Narratives, and Activity Syntheses describe the progression of standards for the concept being taught. Each Lesson contains a Preparation section identifying learning standards (Building on, Addressing, or Building toward). Content from future grades is identified and related to grade-level work. Examples include:

• Unit 2: Proportional Relationships, Unit 2 Overview, “In grades 6–8, students write rates without abbreviated units, for example as ‘3 miles per hour’ or ‘3 miles in every 1 hour.’ Use of notation for derived units such as \frac{mi}{hr} waits for high school—except for the special cases of area and volume. Students have worked with area since grade 3 and volume since grade 5. Before grade 6, they have learned the meanings of such things as sq cm and cu cm. After students learn exponent notation in grade 6, they also use {cm}^2 and {cm}^3.”

• Unit 4: Proportional Relationships and Percentages, Section C: Applying Percentages, Lesson 15: Error Intervals, Lesson Narrative, “This material gives students a solid foundation for future work in statistics. It is not necessary at this stage to emphasize the idea of a margin of error which defines a range of possible values. It is enough for students to see the values falling into that range, as preparation for future learning.”

• Unit 7: Angles, Triangles, and Prisms, Section B: Drawing Polygons with Given Conditions, Lesson 6: Building Polygons (Part 1), Activity 1 Synthesis, “The purpose of this discussion is to establish what is meant when we say two shapes are identical copies. While students don’t use the word congruent until grade 8, they should recognize that two shapes are identical only when they can match perfectly on top of each other by movements that don’t change lengths or angles.”

Materials relate grade-level concepts explicitly to prior knowledge from earlier grades. Examples include:

• Course Guide, Scope and Sequence, Unit 1: Scaled Drawings, “In grade 3, students distinguished between perimeter and area. They connected rectangle area with multiplication, understanding why (for whole-number side lengths) multiplying the side lengths of a rectangle yields the number of unit squares that tile the rectangle. They used area diagrams to represent instances of the distributive property. In grade 4, students applied area and perimeter formulas for rectangles to solve real-world and mathematical problems, and learned to use protractors. In grade 5, students extended the formula for the area of a rectangle to include rectangles with fractional side lengths. In grade 6, students built on their knowledge of geometry and geometric measurement to produce formulas for the areas of parallelograms and triangles, using these formulas to find surface areas of polyhedra.”

• Course Guide, Scope and Sequence, Unit 3: Measuring Circles, “In this unit, students extend their knowledge of circles and geometric measurement, applying their knowledge of proportional relationships to the study of circles. They extend their grade 6 work with perimeters of polygons to circumferences of circles, and recognize that the circumference of a circle is proportional to its diameter, with constant of proportionality π. They encounter informal derivations of the relationship between area, circumference, and radius.”

• Unit 5: Rational Number Arithmetic, Section A: Interpreting Negative Numbers, Lesson 1: Interpreting Negative Numbers, Lesson Narrative, “In this lesson, students review what they learned about negative numbers in grade 6, including placing them on the number line, comparing and ordering them, and interpreting them in the contexts of temperature and elevation (MP2). The context of temperature helps build students’ intuition about signed numbers because most students know what it means for a temperature to be negative and are familiar with representing temperatures on a number line (a thermometer). The context of elevation may be less familiar to students, but it provides a concrete (as well as cultural) example of one of the most fundamental uses of signed numbers: representing positions along a line relative to a reference point (sea level in this case). The number line is the primary representation for signed numbers in this unit, and the structure of the number line is used to make sense of the rules of signed number arithmetic in later lessons.”