7th Grade - Gateway 2
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Rigor & Mathematical Practices
| Score | |
|---|---|
Gateway 2 - Meets Expectations | 88% |
Criterion 2.1: Rigor | 8 / 8 |
Criterion 2.2: Math Practices | 8 / 10 |
The instructional material for the Grade 7 meets the expectation for rigor and mathematical practices. Within the concept-development sections of each lesson, the mathematical topic is developed through understanding as indicated by the standards and cluster headings. Procedural skill and fluency is most evident in modules 2, 3 and 4, with an abundance of examples and computation activities that stress fluency in conjunction with the skill. Application of the mathematical concepts is abundant throughout each module. In the instructional materials, the three aspects are balanced within lessons and modules. The instructional materials also meet the expectations for the criterion of practice-content connections. They meaningfully connect Standards for Mathematical Content and Standards for Mathematical Practice. The instructional materials are strong in rigor and in regard to emphasis on supporting the standards' emphasis on mathematical reasoning. Overall the Instructional materials meet the quality expectations for gateway 2 in rigor and mathematical practices.
Criterion 2.1: Rigor
Rigor and Balance: Each grade's instructional materials reflect the balances in the Standards and help students meet the Standards' rigorous expectations, by helping students develop conceptual understanding, procedural skill and fluency, and application.
The materials reviewed for Grade 7 meet the expectation for this criterion by providing a balance of all three aspects of rigor throughout the lessons. Within the concept-development sections of each lesson, the mathematical topic is developed through understanding as indicated by the standards and cluster headings. In Grade 7, procedural skill and fluency is most evident in module 2, which extensively covers 7.NS. Besides an abundance of examples, there are also computation activities stressing fluency in conjunction with the skill. Application of the mathematical concepts is abundant throughout each module. Overall, the introduction of new concepts is done through examples that involve applications, and lessons often follow that are application reinforcements of the skills. The three aspects are balanced within the lessons and modules. Overall, the Grade 7 materials meet the criteria for rigor and balance.
Indicator 2a
Attention to conceptual understanding: Materials develop conceptual understanding of key mathematical concepts, especially where called for in specific content standards or cluster headings.
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 require students to apply lesson discussion, and this discussion builds from lesson to lesson.
- A thorough review of the assessments in module 2 found that all of the specific content in 7.NS was assessed in various questions. (Note: Grade 7 students will likely need more time working on operations with rational numbers in order to master the content.)
- Cluster understanding was also spread over several modules at the Grade 7 level. For example, 7.EE is evident in several lessons within modules 1, 2, 3 and 4 as proportional relationships, algebraic expressions and percentages are covered.
Indicator 2b
Attention to Procedural Skill and Fluency: Materials give attention throughout the year to individual standards that set an expectation of procedural skill and fluency.
Materials give attention throughout the year to individual standards that set an expectation of procedural skill and fluency meeting the expectations for this indicator.
- Procedural skill and fluency is evident in module 2, which extensively covers 7.NS.
- In addition to an abundance of examples throughout the lessons, there are some fluency tests that provide specific problems devoted to procedural skill and lead to fluency.
- A great deal of work is done with integer cards; game-like activities lead to the understanding as well as the skill. 7.EE is present in multiple modules (1, 2, 3 and 4) and students are constantly reviewing the basics of solving equations
Indicator 2c
Attention to Applications: 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
Materials are designed so that teachers and students spend sufficient time applying the mathematics without losing focus on the major work of each grade, meeting the expectations for this indicator.
- 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.
- Module 1 uses application to develop 7.RP and represent proportional relationships.
- Module 4 continues the development of 7.RP and 7.EE with multiple applications involving percentages.
- Students are continually solving real-world problems related to the major focus of the grade level.
Indicator 2d
Balance: The three aspects of rigor are not always treated together and are not always treated separately. There is a balance of the 3 aspects of rigor within the grade.
There is a balance of the three aspects of rigor within the Grade 7 material meeting the expectations for this indicator. The three aspects of rigor are not always treated together and are not always treated separately.
- Conceptual understanding, procedural skill and fluency, and application are integrated into each module as needed.
- When applicable, 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, module 2 (rational numbers) tends to focus on procedural skill and fluency. However, built in to these lessons are activities designed to help the student understand the use of rational number operations. (For example, the focus of lesson is understanding subtraction of integers, not just the procedure itself.)
- Also included, when appropriate, are applications of operations involving rational number. (For example, lessons 19 and 20 apply rational numbers to percentages and investments.)
- In addition, there is a balance of the three aspects of rigor in included assessments.
Criterion 2.2: Math Practices
Practice-Content Connections: Materials meaningfully connect the Standards for Mathematical Content and the Standards for Mathematical Practice
The materials reviewed for Grade 7 partially meet the criterion of meaningfully connecting Standards for Mathematical Content and Standards for Mathematical Practice. The latter are often identified and used to enrich mathematical content. However, there are missed opportunities for identifying MPs in the student materials. Materials sometimes attend to the full meaning of each practice standard. Throughout the lessons, the materials prompt students in constructing viable arguments concerning grade-level mathematics detailed in the content standards. Students are also directed to explain responses in practice sets and exit-ticket questions. Occasionally, the materials assist teachers in engaging students in constructing viable arguments and analyzing the arguments of others. On the other hand, materials very explicitly attend to the specialized language of mathematics. Correct mathematical terminology is always used, enforced and reinforced. Overall, the materials meet the expectations for the practice-content connections criterion.
Indicator 2e
The Standards for Mathematical Practice are identified and used to enrich mathematics content within and throughout each applicable grade.
There is a clear articulation of connection between the Standards of Mathematical Practice (MPs) and content. Materials regularly and meaningfully connect MPs to the Standards for Mathematical Content within and throughout the grade.
- Throughout the lessons MPs are called out for the teacher.
- In the opening statements of all lessons and modules there is commentary connecting the appropriate mathematical practice standards to the content. For example, page 7 of Module 4 identifies MP1, MP2, MP5, MP6 and MP7 as focus standards for the module.
- They are explained with examples of how and where you can see connections and development of the practice standards within the content of the module.
- A clear and visual connection is made within the lessons by a blue line and the MP listed. For example, see MP2 on page 42 of module 4.
Indicator 2f
Materials carefully attend to the full meaning of each practice standard
Materials occasionally attend to the full meaning of each practice standard.
- Module 3 generally does a good job attending to MP2, MP7 and MP8 in the discussion of equations and explanations.
- Throughout the materials, students use properties to prove expressions equivalent and substitution to prove equivalence.
- Questions in problem sets and exit tickets sometimes ask students to construct viable arguments (MP3), but these are not identified for the students.
- Frequently when MP5 is listed the task tells the students what tools to use.
Indicator 2g
Emphasis on Mathematical Reasoning: Materials support the Standards' emphasis on mathematical reasoning by:
Indicator 2g.i
Materials prompt students to construct viable arguments and analyze the arguments of others concerning key grade-level mathematics detailed in the content standards.
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 examples of students being asked to analyze the arguments of others in the lesson material or practice exercises; however, there are missed opportunities to prompt students to critique the reasoning of others.
Indicator 2g.ii
Materials assist teachers in engaging students in constructing viable arguments and analyzing the arguments of others concerning key grade-level mathematics detailed in the content standards.
Materials are limited in assisting teachers in engaging students in constructing viable arguments and analyzing the arguments of others.
- The teacher material frequently provides quality questions the teacher can pose to students to elicit their reasoning, but it falls short in providing teachers with directions to then have students critique the reasoning of others.
- MP3 was not identified as a focus MP until modules 5 and 6.
- In module 3, MP3 was identified for teacher reference a very limited number of times (pages 20, 237 and 337). However, it was not a focus in teacher-student discussion and instruction.
Indicator 2g.iii
Materials explicitly attend to the specialized language of mathematics.
Materials very explicitly attend to the specialized language of mathematics.
- Correct mathematical terminology is always used, enforced and reinforced.
- At the beginning of each module, terminology that is new or recent is specifically highlighted and defined (examples are provided in some cases as well) for teachers, as are terms that should be familiar.
- The terminology 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).
- The highlighting and emphasis on vocabulary allows students to use their own resources in future lessons to review the relevant vocabulary and/or equations associated with such terms as "area" and "pi."