7th Grade - Gateway 1

The instructional materials reviewed for Open Up Resources 6-8 Math, Grade 7 meet expectations that they assess grade-level content. The assessments are aligned to grade-level standards.

For example:

• Unit 5 End-of-Unit Assessment Problem 7 assesses student understanding of adding and subtracting rational numbers (7.NS.3) by presenting a scenario that describes a bank account in which students must calculate the balances and transaction amounts. Problems are presented with a relevant context for standards that require a real-world context.

• In Unit 3 End-Unit Assessment Problem 4, students decide if circumference and radius (7.G.4) are proportional based on the given graph and ordered pairs (7.RP.2): “A class measured the radius and circumference of various circular objects. The results are plotted on the graph. 1) Does there appear to be a proportional relationship between the radius and circumference of a circle? Explain or show your reasoning. 2) Why might the measured radii and circumferences not be exactly proportional?”

Assessments are located in the teacher materials in each of the first eight units. Unit 9 Putting It All Together is an optional culminating unit and contains no assessments. Assessments are limited to seven problems but are often broken into multiple prompts and assess numerous standards. Unit 6 also contains a Mid-Unit Assessment for a total of nine assessments.

The instructional materials reviewed for Open Up Resources 6-8 Math, Grade 7 meet expectations for spending a majority of instructional time on major work of the grade.

• The approximate number of units devoted to major work of the grade, including assessments and supporting work, is five out of eight, which is approximately 62.5%.
• The number of lessons devoted to major work of the grade, including assessments and supporting work, is 81 out of 121 total non-optional lessons, or approximately 67%.
• The number of days devoted to major work, including assessments and supporting work, is 92 out of 138 days, which is approximately 67%.

A lesson-level analysis is most representative of the instructional materials because this calculation includes all lessons with connections to major work with no additional days factored in. As a result, approximately 67% of the instructional materials focus on major work of the grade. An analysis of days devoted to major work includes 17 days for review and assessment, but the materials do not dedicate items to be used for the review.

The instructional materials reviewed for Open Up Resources 6-8 Math, Grade 7 meet expectations that supporting work enhances focus and coherence simultaneously by engaging students in the major work of the grade.

Supporting standards/clusters are connected to the major standards/clusters of the grade. The lessons are designed in a way that supporting standards are interwoven into the lessons and activities that maintain a focus on the major work of the grade. The Grade 7 materials include multiple examples of supporting work being used to support the focus and coherence of the major work of the grade, especially in the area of proportional relationships.

• Standard 7.G.6 supports major work standard 7.RP.2. In Unit 2 Lesson 8 Activity 3, students analyze relationships between side length and total edge length, volume, and surface area and determine if they are proportional or nonproportional. Students also practice calculating volume and surface area of three-dimensional figures (7.G.6) while exploring, discussing, and proving whether relationships are proportional.

• Standard 7.G.4 supports major work standard 7.RP.2a. In Unit 3 Lesson 3 Activities 1 and 2, students measure and plot the diameter and circumference of circles, determine if they are in a proportional relationship, and then find the constant of proportionality. In Activity 2, students are provided one measurement (diameter or circumference) and use the derived constant of proportionality to determine the other.

• Unit 3 Lesson 5 (optional) 7.G.4 supports 7.RP.2a, 7.RP.2c, and 7.RP.3. The Activities include contexts in which students use diameter and circumference relationships to calculate how far wheels (circles) can roll to reach certain distances and explore rotations per second and time traveled. In Lesson 7 of Unit 3, students explore the proportionality between diameter and area to determine that they are not proportional.

• Unit 7 Lesson 16 standard 7.G.6 supports 7.RP.A. The Activities provide students with complex surface area and volume contexts in which students use proportional relationships situated in real-world problems. In Activity 2, students are given some dimensions and the area of a base of a hexagonal prism. Students then find the total amount of bags of sand that were poured into the prism to reach a certain height. Students use concepts related to surface area, volume, and proportional reasoning to answer subsequent questions, including determining how many more bags would be necessary to fill the prism (sandbox) an additional 3 inches.

• The standards in cluster 7.SP.C support 7.RP.A in Unit 8 Lessons 4, 7, 16 and 20, where statistical work with simulations and populations is used in coordination with proportional reasoning as students explore experimental probability and statistical sampling.

• Standard 7.G.5 supports major work standard 7.EE.4 in Unit 7 Lesson 5 Activities. Tasks involve students using equations to represent angle relationships and solve for unknown angles. Angle relationships involve setting up simple and multi-step equations.

Instructional materials for Open Up Resources 6-8 Math, Grade 7 meet expectations that the amount of content designated for one grade level is viable for one year.

The suggested amount of time and expectations for teachers and students of the materials are viable for one school year as written and would not require significant modifications. As designed, the instructional materials can be completed in 162 days.

• From the provided scope and sequence found in the Course Guide, Grade 7 includes materials for 138 instructional days. There are 121 non-optional lessons, nine summative assessments, and eight review days included.

• 119 of these non-optional lessons are designed to address grade-level standards. Two non-optional lessons do not explicitly address grade-level standards but provide problem contexts and activities that prepare students for the unit.

• Ten optional lessons are also present throughout the first eight units. Unit 9 Putting it All Together includes 13 optional lessons that require up to 13 additional days depending on the number of lessons completed. There are 162 instructional days if all optional materials are used.

• Each unit is comprised of 11 to 22 lessons. Within each unit, lessons contain a Warm-Up, two or three Activities, Lesson Synthesis, and a Cool-Down. Guidance regarding the number of minutes needed to complete each component of the lesson is provided in the teacher materials.

The instructional materials for Open Up Resources 6-8 Math, Grade 7 meet expectations for the materials being consistent with the progressions in the standards.

The instructional materials clearly identify content from prior and future grade levels and use it to support the progressions of the grade-level standards. The instructional materials also relate grade-level concepts explicitly to prior knowledge from earlier grades.The materials are intentionally designed to address the standards the way they are laid out in the progressions, and the Unit Overview clearly explains how the standards and progressions are connected for educators. Units begin with lessons connected to the standards from prior grades that are relevant to the current topic. Standards from the grade level and prior grades, and standards that will be addressed later in the year are identified in the sections as “addressing,” “building on,” and “building towards,” respectively. For example:

• In the Grade 7 Scope and Sequence document, Unit 1 Scale Drawings is connected to geometry and geometric measurement found in earlier grades. The tasks in the unit are built upon work “composing, decomposing, and identifying shapes” in Grades 1 and 2, “distinguishing area and perimeter” from Grade 3, “[applying] area and perimeter formulas” in Grade 4, “[extending] the formula for the area of a rectangle to include rectangles with fractional side lengths” in Grade 5, and finally, generating formulas for the area of parallelograms and triangles in Grade 6. The unit addresses Grade 7 work with scale drawings as students “reason about the scaled copies of figures” leading to work with proportions in Unit 4 and extends this knowledge in Grade 8 when they will work with transformations.

• Unit 5 Lesson 5 identifies 1.OA.4 as the standard that the lesson is “building on,” the standard the lesson is “addressing” is 7.NS.1c, and the standard the lesson is “building toward” is 7.NS.1. The lesson builds on Grade 1 understanding of subtraction and extends it to adding and subtracting rational numbers in the first lessons in the unit. By Lesson 15, rational numbers are embedded in expressions and equations. The following explanation is provided for teachers: “The purpose of this lesson is to get students thinking about how to solve equations involving rational numbers. In Grade 6, students solved equations of the form px=q and x+p=q and saw that additive and multiplicative inverses (opposites and reciprocals) were useful for solving them. However, that work in Grade 6 did not include equations with negative values of p or q or with negative solutions. This lesson builds on the ideas of the last lesson and brings together the work on equations in Grade 6 with the work on operations on rational numbers from earlier in Grade 7.”

The Warm-Ups in lessons frequently work with prior-grade standards in ways that support learning of grade-level problems and make connections to progressions from previous grades. For example:

• The Unit 2 Lesson 7 Warm-Up includes equivalent ratio context (6.RP.3) that builds to an expectation of students using proportional relationship language in context (7.RP.2). These precede two lessons where students explore the difference between proportional and nonproportional relationships.

• The Unit 5 Lesson 9 Warm-Up uses an image of a woman in stride and asks students to estimate where the woman will be in five seconds and where she was five seconds before. This activity builds off constant speed contexts in Grade 6 (6.RP.3b) and primes students for considering negative time and velocity (7.NS.3 and 7.RP.2).

The instructional materials attend to the full intent of the grade-level standards by giving all students extensive work with grade-level problems.

In the Teacher Guide under Course Information and Scope and Sequence, there is a chart which accurately reflects the mathematics in the materials. All grade-level standards are represented across the 9 units. Tasks are aligned to grade-level work and are connected to prior-grade knowledge. For example:

• Unit 2 introduces proportional relationships and is strategically divided into sections that explore conceptual understanding through comparing proportional and nonproportional relationships, tabular and graphic representations, as well as equations in the form of y = kx. Lessons 1 through 3 Warm-Ups explore ratios and patterns in tables and are connected to 6.RP.A. Lessons 4 through 6 focus on representing proportional relationships with equations with different contexts.

• In Unit 7 Angles, Triangles, and Prisms, the first five lessons focus on angle relationships. The first two lessons focus on making connections to the additive nature of angle measures found in 4.MD.6 and 4.MD.7. Lesson 1 in this unit states, “Students were introduced to angles in Grade 4, when they drew angles, measured angles, identified angles as acute, right, or obtuse, and worked with adding and subtracting angles. Earlier in Grade 7, students also touched on angles briefly in their work with scale drawings. Now they begin a more detailed study of angles. In this lesson, students gain hands-on experience composing, decomposing, and measuring angles. They refresh their memory about the relationship between right angles, straight angles (180 degrees), and ‘all the way around’ angles (360 degrees), and they fit pattern blocks around a point to find out the angles at their vertices.” The lessons then explore the properties of angles including solving for unknown angles. According to the CCSS Progressions for Grade 7, students build on earlier experiences with angle measurement to solve problems that involve supplementary angles, complementary angles, vertical angles, and adjacent angles.

A typical lesson has a Warm-Up, one or more Activities and a Cool-Down. Additionally, every lesson provides practice problems that can be used as independent or group work. Some lessons also provide an “Are you ready for more?” question. These problems are an opportunity for students to explore grade-level mathematics in more depth and often make connections between the topic in the lesson and other concepts at grade level. They are intended to be used on an opt-in basis by students if they finish the main class activity early or want to do more mathematics on their own.

Overall, the materials give students extensive work with rigorous, grade-level problems.

The instructional materials for Open Up Resources 6-8 Math, Grade 7 meet expectations that materials foster coherence through connections at a single grade, where appropriate and required by the standards.

Materials include learning objectives that are visibly shaped by CCSSM cluster headings, including:

• The Unit 2 Overview includes unit goals to understand terms and concepts related to proportionality and to recognize relationships that are proportionally aligned to 7.RP.A. Specific types of real-world situations that are used in the unit (constant speed, unit pricing, and measurement conversion) are also described. Lesson 1 begins with tasks from Grade 6 that involve analyzing differences between situations that require equivalent ratios and those that do not; in Lessons 2 and 3, students explore proportional relationships and develop formal terminology; in Lessons 7 through 9 students analyze aspects of proportional relationships as they compare to non-examples of proportional relationships; and Lessons 10 through 13 continue the work of representing and analyzing proportional relationships by comparing graphs and equations of proportional relationships.

• In Unit 2 Lesson 9, the learning targets are visibly shaped by the cluster heading and state, “I can solve all kinds of problems involving proportional relationships,” and “I can ask questions about a situation to determine whether two quantities are in a proportional relationship.”

• Learning goals for Unit 2 Lessons 18 through 21 are developed from the cluster heading 7.EE.A, including: “Use a graphic organizer for work with the distributive property.” “Understand how to rewrite subtraction as adding the opposite in order to use the commutative property.” “Apply the distributive property to expand and factor linear expressions with rational coefficients.” “Apply properties of operations to generate an equivalent expression with fewer terms.” “Identify and correct errors made when applying properties of operations.” and “Generate a variety of expressions by positioning parentheses in different places in a given expression; apply properties to write the expressions with fewer terms.”

7.EE.B Solve real-life and mathematical problems using numerical and algebraic expressions and equations.

• In Unit 6 Lesson 11, the learning target is shaped by the cluster heading, stating, “I can solve story problems by drawing and reasoning about a tape diagram or by writing and solving an equation.”

Materials consistently include problems and activities that connect two or more clusters in a domain or two or more domains in a grade, in cases where these connections are natural and important. Multiple examples of tasks connecting standards within and across clusters and domains are present. These connections build deeper understanding of grade-level concepts and the natural connections which exist in mathematics.

• Unit 1 Lesson 2 Activity 3 addresses standard 7.G.1 and builds toward 7.RP.2 when students solve problems using scale drawing of geometric figures, including computing actual lengths and areas. In Lessons 2, 3, and 5, the Activities build toward recognizing and representing proportional relationships between quantities. Lessons 8 through 10 address standard 7.G.1 and build towards 7.RP.2b as students continue to work with scale drawings.

• In Unit 3, connections are present between 7.RP.A and 7.G.B in multiple lessons. In Lesson 1, students “apply what they have learned about proportional relationships to describing geometric figures,” and in Lesson 3, “students discover that there is a proportional relationship between the diameter and circumference of a circle.”

• In Unit 5 Lesson 12 Activities 3 and 4, students apply proportional reasoning when using equations including a negative constant of proportionality (7.EE.3 and 7.RP.2) and solve real-world problems using all four operations which include rational values (7.NS.3) as they solve problems in the context of submarines. Lessons 14 through 17 include varying scenarios that involve interpreting rational values in the context of the given problem and operations with rational values.