5th 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 instructional materials reviewed for Grade 5 partially meet the expectations for rigor and mathematical practices. The instructional materials meet the expectations for the criterion on rigor and balance with a perfect score, but they only partially meet the expectations of the criterion on practice-content connections due to not fully attending to the meaning of each mathematical practice standard. Overall, the instructional materials are strong in regards to rigor, identifying mathematical practices, and the language of mathematics, but improvements can be made in consistently attending to the full meaning of practice standards where they are identified.
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 instructional materials reviewed for Grade 5 meet expectations for rigor and balance. The instructional materials give appropriate attention to conceptual understanding, procedural skill and fluency, and application, and the materials address these three aspects with balance, but always treating them separately and not always together. Overall, the instructional materials reflect the balances in the CCSSM, which helps students meet rigorous expectations by developing conceptual understanding, procedural skill and fluency, and application.
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 instructional materials reviewed for Grade 5 meet the expectations for giving attention to conceptual understanding. Overall, the materials develop conceptual understanding of key mathematical concepts, especially where specific content standards or cluster headings call for it.
- In each chapter and lesson of Go Math, the alignment to conceptual understanding is identified. For example, chapter 1, lesson 1, page 5A notes that conceptual understanding will be covered in the "share and show" portion of the lesson.
- Chapter 10, lesson 1, page 585A identifies the "share and show" activity as the venue where students are asked to identify conceptual understandings.
- Of the 99 lessons in the grade, 26 are primarily conceptual in nature and match the standards calling for conceptual understanding. For example, in chapter 1, lesson 1, the cluster heading for the objective is "Understand the Place Value System," and the lesson has students using base-ten blocks to build understanding.
- The beginning of each chapter has a page heading, "Teaching for Depth." For example, see chapter 8, teacher's manual, page 489C.
- Lessons have a "teaching for depth" box that specifically identifies what students should have conceptual understanding of in that particular lesson. For example, see chapter 8, lesson 5, teacher's manual, page 517A.
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 instructional materials reviewed for Grade 5 meet the expectations for giving attention to procedural skill and fluency. Overall, the materials give attention throughout the year to individual standards that set an expectation of procedural skill and fluency.
- Each lesson has a daily routine and fluency builder that provide procedural skill and fluency practice. For instance, in chapter 1, lesson 1, page 5b, the problem of the day has students solving a word problem that has one-step multiplication.
- The fluency builder of chapter 1, lesson 1 has 10 problems where students have to find the value of the underlined number ("place value in numbers up to five digits long").
- Of the 99 lessons in the grade, 58 are primarily concerned with procedural skill and fluency and match the standards calling for procedural skill and fluency. For example, in chapter 5, lesson 6, the objective is "add, subtract, multiply, and divide decimals to hundredths," and the lesson has students building procedural fluency and skill.
- Another example of a fluency builder is in chapter 7, lesson 4, on page 439B.
- Each chapter has segment called "Practice and Homework" to help with fluency. For example, see chapter 9, lesson 4, teacher's manual, pages 555-56.
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 instructional materials reviewed for Grade 5 meet the expectations for giving attention to applications. Overall, the 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.
- In each chapter and lesson of Go Math, the areas that focus on application are identified. For instance in chapter 1, lesson 1, page 5a, the application problems are identified as being found in the "think smarter and go deeper" sections of the lesson.
- Of the 99 lessons in the grade, 15 are primarily application in nature and match the standards calling for real-world application. For example, in chapter 8, lesson 5, the objective is "solve real-world problems involving division of whole numbers by unit fractions," and students are using recipes and food to solve problems.
- In chapter 2, lesson 5, questions 16 and 19 on page 166 are "think smarter and go deeper" problems that are applications.
- In chapter 10, lesson 4, the "think smarter and go deeper" questions on page 606 of the teacher's manual are application problems.
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 instructional materials reviewed for Grade 5 meet the expectations for balance. Overall, the three aspects of rigor are not always treated together nor are they always treated separately within the materials, and there is a balance of the three aspects of rigor within the grade.
- Each component of rigor is identified and covered within the lessons, and sometimes they overlap or are covered separately. For instance, in chapter 1, lesson 1, there is no overlap of the three aspects of rigor.
- Each chapter specifically outlines how rigor is addressed and balanced. For example, see chapter 11, lesson 9, page 687A of the teacher's manual.
Criterion 2.2: Math Practices
Practice-Content Connections: Materials meaningfully connect the Standards for Mathematical Content and the Standards for Mathematical Practice
The instructional materials reviewed for Grade 5 partially meet the expectations for practice-content connections. The materials meet expectations for identifying the practice standards and explicitly attending to the specialized language of mathematics as addressed in indicators 2E and 2G.iii, respectively. However, the materials only partially meet the expectations for attending to the full meaning of each practice standard and engaging students in mathematical reasoning as addressed in indicators 2F, 2G.i and 2G.ii. Overall, in order to meet the expectations for meaningfully connecting the Standards for Mathematical Content and the Standards for Mathematical Practice, the instructional materials should carefully attend to the full meaning of every practice standard, especially MP3 in regards to students critiquing the reasoning of other students.
Indicator 2e
The Standards for Mathematical Practice are identified and used to enrich mathematics content within and throughout each applicable grade.
The instructional materials reviewed for Grade 5 meet the expectations for identifying the Standards for Mathematical Practice (MPs) and using them to enrich the mathematical content. Overall, the instructional materials do not over-identify or under-identify the MPs, and they are used within and throughout the grade.
- Each lesson has MPs identified, and they are mostly used to enrich the content of the work.
- The identified MPs are found on the "lesson at a glance" page. For an example, see chapter 3, lesson 1, page 151A.
- Chapter 11, lesson 3, page 649A of the teacher's manual has a "lesson at a glance" page.
- In the Grade 5 teacher planning guide on page 23, there are a list of questions that teachers can use to prompt students that are aligned to the practices.
- The practices are related to grade-level work in the "teaching for depth" section, located in the teacher's manual of each chapter. For example, see chapter 11, teacher's manual, page 635E.
Indicator 2f
Materials carefully attend to the full meaning of each practice standard
The instructional materials reviewed for Grade 5 partially meet the expectations for carefully attending to the full meaning of each practice standard. Overall, the instructional materials carefully attend to the full meaning of some of the practice standards but not for all of them.
- Chapter 8, lesson 3, page 504 of the teacher edition lists MP2 and asks students to reason abstractly about a different way to make four equal shares.
- Chapter 8, lesson 5, page 517 of the teacher edition lists MP2 and provides teachers with questions to help student reason about the problems.
- The full meaning of MP5 is for students to consider all available tools to solve a mathematics problem. In some instances, Grade 5 materials give students the tool to use for solving the problem, which means students do not get to choose strategically. For examples, see chapter 6, lesson 1; chapter 8, lesson 1; and chapter 7, lesson 3. In chapter 8, lesson 1, page 491 of the teacher's manual directs students to use a number line or fraction strips to solve problems.
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.
The instructional materials reviewed for Grade 5 partially meet the expectations for prompting students to construct viable arguments and analyze the arguments of others concerning key grade-level mathematics detailed in the content standards. Overall, the materials consistently allow students to construct viable arguments, but they do not consistently prompt them to analyze other students' arguments.
- There are several places where MP3 is identified on the student materials, but the full intent of the practice is not met.
- In chapter 11, lesson 6, page 669 of the student edition identifies MP3 as a practice the students will engage in, but the lesson has directions for students to create an argument or engage with other students.
- In chapter 11, lesson 11, page 699 of the student edition identifies MP3, but the students are not engaging with one another.
- In chapter 4, lessons 1 and 4, there are two examples of students getting to engage in the full intent of MP3: problem 10 of lesson 1 and page 252 in lesson 4.
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.
The instructional materials reviewed for Grade 5 partially meet the expectations for assisting teachers in engaging students in constructing viable arguments and analyzing the arguments of others concerning key grade-level mathematics detailed in the content standards. Overall, the materials consistently assist teachers in having students construct viable arguments but not in having students analyze other students' arguments.
- The materials do not assist teachers in engaging students in constructing viable arguments and analyzing the arguments of others.
- In chapter 7, lesson 5, page 445 of the teacher edition lists MP3, but instead of having students construct an argument and critique the reasoning of others, they are asked to give a right or wrong question.
- In chapter 4, lesson 4, page 252 of the teacher edition has students walk through an example.
- There are some opportunities within lessons where the materials prompt students to create dialogue, share their thinking on how they got their answer and explain their rationale. For example, see page 30 of lesson 5 in chapter 1.
Indicator 2g.iii
Materials explicitly attend to the specialized language of mathematics.
The instructional materials reviewed for Grade 5 meet the expectations for explicitly attending to the specialized language of mathematics. Overall, the materials for both students and teachers have multiple ways for students to engage with the vocabulary of mathematics that is present throughout the materials.
- Each chapter begins with vocabulary builders and vocabulary games. An example can be found in chapter 6 on pages 350-350D.
- The lessons pay attention to using correct vocabulary. For example, the questions for teachers to ask use correct vocabulary, as seen in chapter 6, lesson 1, page 352 of the teacher edition where the questions for teachers to ask students use correct vocabulary such as "denominator," "fraction," and "equivalent."
- Vocabulary is developed in the vocabulary builder, mathematics talk, the literacy connection, the writing prompts, and the mathematics journal.
- In chapter 4, page 231H, the chapter vocabulary is identified as well as a vocabulary activity for ELL students and vocabulary strategies for using a graphic organizer.
- Within the introduction of each chapter is a vocabulary builder exercise for students to complete. For example, see pages 232-232B that show a vocabulary builder which gives teachers prompts to help students visualize the vocabulary along with games they can play, writing prompts, and ways to incorporate a vocabulary journal.
- The beginning of each chapter includes a "developing math language" page. For example, see chapter 9, page 531H of the teacher's manual.
- A vocabulary game is included in each chapter. For example, see chapter 9, pages 532B-532C of the teacher's manual.