8th Grade - Gateway 2

Materials develop conceptual understanding of key mathematical concepts, especially where called for in specific content standards or cluster headings meeting the expectations for this indicator.

• Generally, lessons develop understanding first through explicit discussion outlined in the teacher lessons.
• Closing activities often ask students to verbally review important vocabulary or apply lesson discussion to a specific problem to demonstrate understanding.
• Problems sets required students to apply lesson discussion and build from lesson to lesson.
• Module 2 focuses on the conceptual understanding of G.1, 2, 5, 6, and 7. Tasks and activities develop a solid understanding of congruence and similarity along with the Pythagorean Theorem. This development of understanding continues into Module 3 with a greater focus on similarity (G.3, 4, 5, 6, 7).
• Module 4 provides students with ample opportunity to develop understanding of EE. 5,6,8a.
• Module 7 brings back conceptual understanding for students on NS.1 and G.6, 7, 8.

Materials give attention throughout the year to individual standard that set an expectation of procedural skill and fluency meeting the expectations for this indicator.

• Procedural skill and fluency is evident in modules 1 and 7, which develop 8.EE and 8.NS.
• Besides an abundance of examples throughout the lessons, there are also computation activities designed to develop procedural skill and lead to fluency.
• Similarly, multiple lessons often cover a major cluster and offer ample practice of the required skill.
• For example, in module 4, lessons 24-30 continue to the develop 8.EE.8 using multiple methods

Materials are designed so that teachers and students spend sufficient time working with engaging applications of the mathematics, without losing focus on the major work of each grade.

• Application of the mathematical concepts is abundant throughout each module.
• Introduction of new concepts is frequently done through examples that involve applications, and lessons often reinforce those skills.
• Similarly, as students work with functions in module 6 (8.F), the work leads into bivariate data (8.SP), a natural extension.
  • Overall most lessons develop some sense of application which aligns with the publishers criteria, which suggests students increase their application as they near higher grades.
  • Specifically application is addressed in topic D of module 4 by having students use distance-time graphs to learn about linear equations, as well as create their own equations to represent real-world situations.
  • Topic E of module 4 include problems that apply the Pythagorean Theorem to real-world situations.
  • Teachers frequently introduce new concepts by posing a problem to students and then structuring discussion around that problem (or set of problems) based on questions provided in the teacher materials.
  • It is common for the problems used in classwork and problem sets to include applications that are relevant to the concepts in the standards.
  • Very often, the application problems reinforce previously learned skills as well as provide context for the mathematical concepts introduced in the lessons.

The three aspects of rigor are not always treated together and are not always treated separately meeting the expectations for this indicator. There is a balance of the three aspects of rigor within the grade.

• Conceptual understanding, procedural skill and fluency, and application are integrated into each module as needed.
• When appropriate, separate procedural skill and fluency activities are included in the series.
• At other times, skill and fluency are part of application and conceptual understanding exercises.
• Specifically, in module 4 (Linear Equations), topic A is very procedural, because students write and solve linear equations using specific steps. Topics B and C expand on the procedures presented in Topic A by relating linear equations to application problems involving constant rate.
• Also included are specific lessons focusing on the understanding of possible solutions and equations characteristics. In addition, there is a balance of the three aspects of rigor in included assessments

There is a clear articulation of connection between Standards of Mathematical Practice (MP) and content. Materials regularly and meaningfully connect MPs to the Standards for Mathematical Content within and throughout the grade

• All modules at the Grade 8 level list the focus MP in the module overview and expand on each practice's connection to the module.
• Throughout the lessons MPs are called out for the teacher
• Module 3, for example, lists MP3, MP4 and MP6 as MP focus standards. Here the practice standards are explained with examples demonstrating the connection and development of the standards to the content.
• On page 40, MP8 is easily seen by the blue line and box containing "MP8" off to the side of the discussion, clearly calling attention to where the practice standard is being developed within the lesson. Although the MPs are identified, they could be integrated more effectively within lessons.
• The MPs are identified in the margin within teacher material.

Materials frequently prompt students to construct viable arguments concerning grade-level mathematics detailed in the content standards. Occasionally materials prompt students to analyze the arguments of others.

• Throughout the discussion portion of each lesson, students are expected to explain the mathematics leading to understanding content and solving problems.
• Students are also directed to explain responses in problem-set and exit-ticket questions.
• There are very few examples of students being asked to analyze the arguments of others in the lesson material or practice exercises.
• There are opportunities for students to analyze the work of another - but it is usually in a problem set and not with another student's work within the classroom.

Materials very explicitly attend to the specialized language of mathematics.

• Correct mathematical terminology is always used, enforced, and reinforced.
• Explicit detail is always used in student-teacher discussion and explanation of process
• At the beginning of each module, terminology that is new or recent-as well as terms that should be familiar-is specifically highlighted for the teacher and defined and, in some cases, examples are provided.
• The terminology that is used in the modules is consistent with the terms in the standards.
• Relevant vocabulary is highlighted for students throughout the lessons and is reiterated at the end of each lesson (when relevant).