The instructional materials reviewed for Grade 6 do not meet the expectations for focus on major clusters. The Grade 6 instructional materials do not spend the majority of class time on the major clusters of the grade.

The Common Core State Standards to Book Correlation (pages xx-xxvi) and the Book to Common Core State Standards Correlation (page xxvii) were used to identify major work, as well as the first page in each chapter which includes Common Core progression information, a chapter summary, and a pacing guide (and related online pages). The pacing guide provides the number of days to spend on each chapter opener, activity, lesson, any extensions, and review/assessment days. This guide was used to determine the number of instructional days allotted by the publisher for each standard found in the material. Lessons identified by the publisher as addressing major work were reviewed. Lessons with standards identified by the publisher as non-major work were also examined to ensure that these lessons did not contain enough material to strengthen major work.

All percentages are below 65 percent and were calculated to reflect the chapters, lessons, and instructional time spent on major work:

• The material devoted approximately 50 percent of chapters to major work of the grade (Chapters 1, 3, 5, 6 and 7). If over 50 percent of a chapter addressed major work, then the chapter was counted as major work.
• 54 percent of lessons (28 out of 52) were dedicated to major work. Lessons 4.1, 4.2 and 4.3 were not identified as major work by the material but were found to have enough examples and problems connected to major clusters 6.EE.A and 6.EE.B. Some lessons identified as major work were not counted as major work even if identified by the publisher. These lessons include 1.1, 2.1, and 2.4, as they only address work below grade-level, and 1.4 where prime factorization, a singular strategy for finding a GCF or LCM, is taught and not aligned to a particular CCSSM standard.
• Of the instructional days, 56 percent (or 87 out of 154) were spent on lessons aligned to major work.

Days were counted based on the recommendation of the pacing guide in the beginning of each chapter for all lessons reviewers found aligned to major work.

The instructional materials reviewed do not meet the expectations for having supporting content that enhances focus and coherence simultaneously by engaging students in the major work of the grade. Overall, the structure of the chapters and lessons in the Grade 6 material rarely engage students in both supporting and major work to allow natural connections.

Most connections between supporting work and major clusters are related to computation, and connections between supporting work and major clusters were either not supported by the lessons when identified or not stated for teachers or students when they did occur.

Supporting standard 6.NS.4 is isolated into several different lessons in two different chapters in this material.

• In Lesson 1-5, 6.NS.4 and 6.EE.2b are both identified by the material; however, the examples explore factors as specific parts of a product within a multiplication equation in the absence of variables (4.OA.4) and then identify the common factors to find the greatest common factor. While this partially satisfies 6.NS.4 because students are finding the GCF and LCM of two whole numbers, at no point are they having to “use the distributive property to express a sum of two whole numbers with no common factor” in either lesson 1-5 or 1-6. Since there is no occurrence of this part of the standard, these particular lessons do not fully allow students to “view one or more parts of the expression as a single entity.”
• Standard 6.NS.4 is most closely aligned with Extension 3-4, Factoring Expressions. The lesson extension does support 6.EE.3 and 6.EE.4 when students apply properties to generate equivalent expressions and identify when they are equivalent; however, the lesson does not discuss using a LCM and to generate equivalent expressions.

6.G is addressed in Chapters 4 and 8. In these chapters, students explore area, surface area, and volume in real world contexts. In order for these lessons to connect to the 6.EE domain, students should use variables to represent numbers when solving a real-world or mathematical problem and understand that a variable can represent an unknown number (6.EE.6).

• Lessons 4.1 through the lesson 4.3 extension involve applying area formulas to different geometric shapes. The majority of the questions do not explicitly ask students to write the formulas in algebraic form in the exercises. Although, the presentation of problems and some application problems (e.g., 4.1: problems 9, 17, 20; 4-2: problems 9, 20; and 4-3: problems 10, 19, 21, 22) encourage the application of standards 6.EE.2, 6.EE.5, and 6.EE.6.
• There are partial connections in lessons 8-2 (examples 1 and 2) and 8-3 (examples 1 and 2) when an equation is used to find the surface area of prisms using a given net, but the only variable used is the “S” for surface area, not the labeled parts of the equivalent expression representing the faces. In Laurie’s notes, teachers are encouraged to have students “write a verbal model and substitute the areas of the faces as they are computed,” but equations are not mentioned nor are these connections explicitly noted for teachers or students. Students are not asked to use an equation in the exercise directions.
• Lesson 8-4 does use volume formulas in worked examples, so a partial connection to 6.EE.2c is present; however, much like in Lessons 4.1-4.3 students are not encouraged to write the expressions.

Even though there are some natural connections, the material does not explicitly express these connections. Lessons are often treated as disconnected topics, and there are few visible connections.

The instructional materials reviewed for Grade 6 do not meet the expectation for having materials that are consistent with the progressions in the Standards. Materials are not intentionally written to follow the progressions of the grade level as few lessons are identified as work from prior grade levels, and there are no lessons identified to connect grade 6 work to the work of future grades. General explanations for how lessons are related to prior knowledge are present. Materials do not give all students extensive work with grade-level problems.

The materials do not develop according to the grade-by-grade progressions in the standards. Content from prior or future grades is not clearly identified and related to grade-level work.

• Explanations of Common Core Progressions are given at the beginning of each chapter connecting both Grade 4 and Grade 5 level work to the Grade 6 work students will encounter in each of the chapters. These connections to below grade-level work are presented as bulleted lists of skills and are not aligned to specific standards.
• Math Background Notes include vocabulary review as well as a general explanation of the most important skills and understandings from the prior grade level(s). For example, in Chapter 6, the notes mention that students should convert one of the numbers so both numbers are in the same form. It does not explain for the teacher the representations of rational numbers, such as tape diagrams or double number lines, used in Grade 4 and Grade 5.
• The first page of each chapter is “What You Learned Before.” The teacher page adjacent to this page identifies the CCSSM addressed, which is usually from a previous grade level, but no explanation of what connects this previous material to current concepts is included.
• Once into the chapter, teachers can see previous skills being reviewed, but they are not identified. Examples of this include:
  • In Section 1.1, addition and subtraction of whole numbers is reviewed. This is stated as a Grade 4 standard in the Common Core progression chart. It also reviews multiplying whole numbers, which is stated as a Grade 5 standard in the progressions chart but not in the section. Although the material does address dividing fluently, Section 1.1 is identified as aligned to standard 6.NS.2 without reference to the lower grade content present in the section,.
  • In Section 1.3, Activity 3 Reviewing Fractions and Decimals, the Teacher Edition states this is an opportunity for students to review prior work. It does not identify from which grade-level the prior work is most closely aligned.
  • Section 2.1 is identified as preparing for 6.NS.1, but the entire chapter is about multiplying fractions and not identified as 5.NF.B.
  • Section 2.4 Activity 4, Using a Place Value Chart, is an unidentified Grade 4 skill.
• Content of progressions beyond the current grade-level is neither visible nor identified in the material.

Extensive grade-level problems are provided for all students if they are given the opportunity to access all of them. There is an assignment guide in each lesson that levels students into basic, average, or advanced. These charts exclude the “basic” learner from the reasoning and critical thinking problems. These problems are critical for all students in order for them to reach the depth of the standard in many of the lessons. Specific examples follow:

• In lesson 1-6, the critical thinking problems 29-31 support students in making generalizations about the LCM and GCF of two values.
• Many lessons contain explanations in “Laurie’s Notes” of a specific homework problem and how “Taking Math Deeper” can apply to that problem. Usually, it is a item that can get to the depth of a standard; however, it is in part of the Basic Assignment in 6 out of 52 lessons in the material. If students are only assigned Basic or Average Level Assignments, they will often not engage with the problems reaching the full meaning of the standard.
• Occasionally, “Laurie’s Notes” contains a basic idea for differentiating instruction for low-level or average students.
• Each lesson also contains “Reteaching and Enrichment Strategies” that can be found within the chapter or online resources.

The materials do not relate grade-level concepts explicitly to prior knowledge from earlier grades.

• Each chapter begins with a What You Learned Before page just before the first lesson. These pages contain problems for students from prior grade-levels and/or chapters found earlier in the material. Connections to specific grade levels or standards are not identified.
• Laurie’s Notes are found in each lesson. In the margin of these notes for instruction, specific Grade 6 standards that will be addressed are identified. Most of them contain a Previous Learning section that describes prior knowledge students should possess before engaging in the lesson, but again, they are not explicit about the particular grade level or standard tied to the skills or understanding needed. For example, in section 7.1 the Previous Learning states, “Students should be familiar with the vocabulary specific to the four operations.” Neither the specific CCSSM standards nor the grade level is stated.

Overall, explicit connections to prior knowledge are made at a general level through the chapter and lesson features in this series. Connections are not clearly articulated for teachers and are merely lists of skills without indication of standards, clusters, or domains. There is not a clearly defined progression for teachers to demonstrate how prior knowledge is being extended or developed.