7th Grade - Gateway 2
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Rigor & Mathematical Practices
Gateway 2 - Partially Meets Expectations | 83% |
|---|---|
Criterion 2.1: Rigor | 8 / 8 |
Criterion 2.2: Math Practices | 7 / 10 |
The Go Math 7 materials reviewed meet expectations for Rigor and Balance. The instructional materials provide students opportunity to practice in all three areas. The materials partially meet the criterion of Practice-Content Connections. There are several places in the materials that clearly identify the standards and the meanings of each. Standards were sometimes not located on identified pages or were misidentified. Students had opportunity throughout the book to explain their mathematical reasoning. There were not as many opportunities for students to discuss the work of classmates or activities that helped teachers in how to engage students in these conversations within the confines of the materials we reviewed. The materials do attend to precise language of mathematics and provide learning opportunities of vocabulary and opportunities to use the vocabulary in the context of the problems.
Overall the reviewed materials of Go Math 7 Partially Meet the Criteria for Gateway 2.
*Evidence updated 10/27/15
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 meet the criterion of rigor and balance. In the Grade 7 lessons, there is a focus on conceptual understanding, procedural skill and fluency, and real world application. The layout of the lessons provides teachers with a framework to address each component of rigor.
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.
The materials reviewed for Go Math Grade 7 meet the expectations for developing conceptual understanding of key mathematical concepts.
- The design of each lesson is set up for conceptual understanding. Each lesson has an Engage, Explore, and Explain process for teachers to follow. This provides essential question, vocabulary, questioning strategies, engagement with whiteboards or manipulatives, how to avoid common errors, focus on critical thinking, and a teaching tip.
- The standards 7.NS.1 and 7.NS.2 are addressed in Unit 1. The lessons use a variety of models and ask many questions that require students to justify their thinking. The standard 7.EE.1.B is developed in Unit 2 and Unit 5.
- Each unit has a performance task for students to solve. Most tasks require students to demonstrate conceptual understanding.
Each lesson has a page that breaks down the depth of knowledge of each question being asked. An example of this is on page 65.
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.
The materials reviewed meet the expectations for giving attention to procedural skill and fluency.
- Procedural skill and fluency with standards found in 7.NS is expected by the end of Grade 7. Modules one through three give explicit attention to these standards.
- Each lesson has a guided practice page (e.g. page 156), and most of these pages provide fluency practice.
Independent Practice, Module Quizzes, Assessment Readiness, and Study Guide Review sections are also opportunities for demonstration of procedural skill. These components are at the end of each module (e.g., 223–226).
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
The materials reviewed meet the expectations for giving attention to application without losing focus on the major work of the grade.
- All lessons contain problems that require real world application. This is demonstrated mostly in the Independent Practice pages (e.g., page 121– 22). This section also designates H.O.T. questions, which stand for higher order thinking.
- Many problems require students to solve multi-step problems.
Students are expected to apply and use concepts in real world situations in 7.NS.A.3, 7.EE.B.3 and cluster 7.RP.A. Modules one through seven provide opportunities for real world applications of these standards.
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.
The materials reviewed partially meet the expectations for showing a balance of conceptual understanding, procedural skill, and application.
- The layout of each lesson provides an opportunity for a balance of rigor. The five E’s—engage, explore, explain, elaborate, and evaluate—are the guidelines for instruction, and this structure allows for the opportunity to target conceptual understanding, procedural skill and fluency, and application.
Criterion 2.2: Math Practices
Practice-Content Connections: Materials meaningfully connect the Standards for Mathematical Content and the Standards for Mathematical Practice
The Go Math 7 materials reviewed partially meet expectations for Practice-Content Connections. There are many places that the MPs are referenced. As indicated, the identification is not always accurate. Questions could lead students to have discussions about mathematics, but there is not much guidance for how the teacher should conduct the conversations. The book does use precise vocabulary and has many places for students to use the language of mathematics.
Indicator 2e
The Standards for Mathematical Practice are identified and used to enrich mathematics content within and throughout each applicable grade.
The materials reviewed partially meet the expectations for identifying the MPs and using them to enrich the content.
- The eight MPs are defined on pages CC8–CC11 of the teacher’s edition. Along with the explanation, there are also pages referenced where the standards are implemented in the student edition. This is not a complete listing but a sample of where they can be found.
- Pages CC14–CC16 in the teacher’s edition provide more explanation of the standards and provide examples of each standard directly taken from the textbook.
- Each lesson highlights one MP. There is a box titled “Professional Development” that describes how the practice is addressed within the lesson. An example of this is on pages 117 and 118.
- The Explore and Explain sections of the teacher’s edition have the words “Mathematical Practices” in bold, but there is not a specific practice identified with the heading. An example of this is on page 117.
Although the MPs are found throughout the materials, they are often not central to the lessons/activities where they are identified. As a result, often the MPs do not enrich the mathematics content of Grade 7.
Indicator 2f
Materials carefully attend to the full meaning of each practice standard
Materials reviewed partially meet the expectations for carefully attending to the full meaning of each practice.
- Some instructional materials were not accurately aligned to MPs. For example, MP4 is listed as being addressed on page 122; however, there is not any identification of MP4 on page 122. MPs 2, 5, and 7 are cited on this page.
- MPs are listed in the index; however, they do not use precise language or numbers.
MPs are identified by the publisher. There are inconsistencies with the practice being on the page or it being accurately interpreted. For example, on page 61, MP8 is identified but MP1 and MP3 are cited on the page. Another example is on page 152, where a Critique Reasoning question is aligned to MP 8.
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 reviewed meet the expectations for prompting students to construct viable arguments and analyze the work of others.
- There are many questions in the teacher’s edition found in the Engage, Explain, and Elaborate headings that, when asked, can lead to discussion of the concepts. An example of this is on page 217 under the Explain section: “Why is adding three + 1 tiles to both sides a better strategy than adding nine -1 tiles to both sides?”
- The student independent practice sections have questions with the following headings: Critique Reasoning, Error Analysis, Justify Reasoning, and Communicate Mathematical Ideas. See examples are on page 18, problem number 33 and page 54, problem number 28.
All six of the Unit Performance Tasks include at least one question that requires students to explain or justify their answer.
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 reviewed partially meet the expectations for assisting teachers in engaging the students in constructing viable arguments.
- Teachers are provided with variety of questions designed to engage students in constructing viable arguments throughout the lesson.
The book does not assist teachers in engaging the students in analyzing the work of other students. There are a few questions that ask students for an error analysis of a worked problem but never engage them in conversation about each other’s work.
Indicator 2g.iii
Materials explicitly attend to the specialized language of mathematics.
Materials reviewed meet the expectations for attending to the language of mathematics.
- Vocabulary is in every module. Each module has two activities to assist with this practice: “Reading Start Up” and an “Unpacking the Standards.” All vocabulary words are high-lighted in yellow throughout the book.
- The “Essential Question of each lesson asks for an explanation of the current skill. Students will need to use mathematics vocabulary in their response.
- “Math Talk” is another tool for teachers in each lesson. The publisher considers this a formative assessment.
- The “Study Guide Review” includes a re-cap of the vocabulary that is in each unit.
- The “H.O.T." questions provide students an opportunity to respond and explain using precise language.
MP6 was listed and was evident in four of the six Performance Tasks, units 1, 4, 5 and 6.