2nd Grade - Gateway 2
Back to 2nd Grade Overview
Note on review tool versions
See the series overview page to confirm the review tool version used to create this report.
- Our current review tool version is 2.0. Learn more
- Reports conducted using earlier review tools (v1.0 and v1.5) contain valuable insights but may not fully align with our current instructional priorities. Read our guide to using earlier reports and review tools
Loading navigation...
Rigor & Mathematical Practices
Gateway 2 - Meets Expectations | 88% |
|---|---|
Criterion 2.1: Rigor | 8 / 8 |
Criterion 2.2: Math Practices | 8 / 10 |
The materials reviewed for Grade 2 meet the expectations for Gateway 2. The materials include each aspect of rigor: conceptual understanding, fluency and application. These three aspects are balanced within the lessons. The materials partially meet the expectations for the connections between the MP and the mathematical content. There are missed opportunities for identifying MP, and some instances where they are misidentified. The materials do attend to the mathematical reasoning that is embedded in the standards.
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 2 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 2, fluency work includes single digit sums and differences (2.OA.B.2) and addition and subtraction (2.NBT.B.5). Application problems occur in almost every lesson depending upon the focus mathematics of the lesson. This is expected to last around 5-10 minutes for each lesson. The three aspects are balanced within the lessons and modules. Overall, the Grade 2 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.
The materials reviewed in Grade 2 for this indicator meet the expectations by attending to conceptual understanding within 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.
- Significant time is spent developing understanding of addition and subtraction and place value.
- In Module 2 the teacher edition provides the following guidance: "Students should be encouraged to make connections between different solution strategies and to choose what works best for a given problem or for their way of thinking."
- In Module 4, students are instructed, "Show another model to solve the problem."
- Significant time is spent writing and comparing numbers through 1,000 in the development of place-value understanding.
- Understanding of addition and subtraction and place value is built through contextual problems.
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 in Grade 2 for this indicator meet the expectations by attending to fluency and procedural work within the lessons. In Grade 2 this includes work on single digit sums and differences, including sums from memory, (2.OA.B.2) and to add and subtract within 100 (2.NBT.B.5).
- Within the distribution of instructional minutes the schedule allows 10-20 minutes per day to practice fluency. This varies according to the timeline of the school year and the focus mathematics in the module.
- As described within the "how to implement" document: "Fluency is usually first-by beginning class with animated, adrenaline-rich fluency, students are more alert when presented with the Concept Development and Application Problems."
- Attention is paid to the use of the words "fluency" and "fluent" within the standards.
- Required fluencies are listed within the section called "Curriculum Overview Sequence."
- Lessons include mental strategies, sprints, dashes and flashcard activities.
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 in Grade 2 for this indicator meet the expectations by attending to application within the lessons.
- Application problems occur in almost every lesson depending upon the focus mathematics of the lesson. This is expected to last around 5-10 minutes for each lesson in Grade 2.
- If the focus standard of the lesson includes language requiring application, the application problem will become the major portion of the lesson.
- Contextual two-step word problems are used with a variety of problem types that increase in difficulty throughout the year. These problems focus on addition and subtraction.
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 in Grade 2 for this indicator meet the expectations by providing a balance of rigor. The three aspects are not always combined together nor are they always separate.
- The distribution-of-minutes charts and the structure of the lessons show a balance of the three aspects of rigor.
- Application problems often call for fluency and procedural skills.
- Fluency work and application problems are used to develop conceptual understanding.
- Conceptual problems often involve procedures.
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 2 partially meet this criteria. MPs are often identified and often used to enrich mathematics content. There are many missed opportunities for identifying MPs and some instances where they are misidentified. The materials often attend to the full meaning of each practice; however, there are instances where the students are not using the practice as written. In describing MP4 activities, the overview of module 4 says, "Students model with mathematics when they write equations to solve two-step word problems, make math drawings when solving a vertical algorithm, or when they draw place value charts and disks to represent numbers." This description does not match the full intent of MP4. For example, in Module 4, lesson 6 (pages 4.B.5-6) students are using place-value charts showing addition with regrouping, but there is no real-world context. There are lessons in which the tools are chosen for the students or the modeling expected is a simple representation. The materials reviewed for Grade 2 attend to the standards' emphasis on mathematical reasoning. Students are prompted within problem sets and application problems to explain, describe, critique and justify. Each lesson includes a debrief section with questions for the teacher to use in facilitating classroom discussion about the mathematical content. In module 3, teachers are prompted use the following in a classroom discussion: "Turn and tell your partner how counting on the place value chart is different from that on the number line." Overall, the materials partially meet the criteria for connecting practice to content.
Indicator 2e
The Standards for Mathematical Practice are identified and used to enrich mathematics content within and throughout each applicable grade.
The Standards for Mathematical Practice (MPs) are often identified and often used to enrich mathematics content. This instructional material, however, only partially meets expectations. There are many missed opportunities for identifying MPs and some instances where they are misidentified.
- MPs are listed at the beginning of each module with a description of the explicit connection to the mathematics of the module.
- Module 4 describes MP1: "Students solve two-step word problems, and are challenged to make sense of more complex relationships within situations. They flexibly solve problems with a variety of strategies at their disposal, sometimes finding many ways to solve the same problem."
- MPs are listed in the margins of the teacher notes, mostly in the "Concept Development" and the "Student Debrief" portions of some lessons.
- While reviewers appreciate that the MPsare not over identified or used in contrived situations, there are missed opportunities for identifying MP in order to enrich the content in these lessons.
- The debrief section of the lessons offers an opportunity to highlight, for both teachers and students, how they might reason abstractly and quantitatively (MP2) and construct arguments and critique the reasoning of others (MP3).
- There is little explicit reference to modeling (MP4), and some lessons identify this practice incorrectly.
Indicator 2f
Materials carefully attend to the full meaning of each practice standard
The materials often attend to the full meaning of each practice; however, there are instances where the students are not using the practice as written. For example, there are many lessons in which the tools are chosen for the students or the modeling expected is a simple representation. As a result, this instructional material only partially meets expectations.
- Students are using MPs when engaging with the content as designed, fully meeting Publisher's Criteria #9.
- Throughout the lessons the debrief section includes opportunities to construct viable arguments and critique the reasoning of others (MP3).
- In describing MP4 ("Model with Mathematics"), the overview of module 4 says, "Students model with mathematics when they write equations to solve two-step word problems, make math drawings when solving a vertical algorithm, or when they draw place value charts and disks to represent numbers." This description does not match the intent of MP 4. Example: Module 4, lesson 6 (pages 4.B.5-6) students are using place-value charts showing addition with regrouping, but there is no real-world context.
- Many lessons list MPs without attending to their full meaning.
- In module 4, students are offered problems to solve and specifically told how to solve each problem, not taking advantage of learning with MP1.
- In module 4, students are answering questions the teacher asks, when they could be constructing arguments and critiquing arguments of others (MP3).
- MP4 is irregularly applied. There is ambiguity over whether "model" means to draw a picture representing the problem or whether it means to create a mathematical representation in a real-world context.
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 materials reviewed for Grade 2 meet the expectations of this indicator by attending to the standards' emphasis on mathematical reasoning.
- Students are prompted within problem sets and application problems to explain, describe, critique and justify.
- In module 4, students are asked on an exit ticket, "Explain how problem 1(a) can help you solve problem 1(b)."
- In module 4, students are asked on an exit ticket, "Explain how Kevin's work and your work are similar."
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 materials reviewed for Grade 2 meet the expectations of this indicator by attending to the standards' emphasis on mathematical reasoning.
- Each lesson includes a debrief section with questions for the teacher to use in facilitating classroom discussion about the mathematical content. For example, "What did we do today to make our counting strategy more efficient?"
- In module 3, teachers are prompted use the following in a classroom discussion: "Turn and tell your partner how counting on the place-value chart is different from that on the number line."
- In module 4, the teacher is prompted to ask, "Explain how and why you changed each number. Be sure to use place value language."
- In module 7, teachers are prompted to ask, "Can you think of other math skills we have learned where the same value can be represented in different ways?"
Indicator 2g.iii
Materials explicitly attend to the specialized language of mathematics.
The materials reviewed for Grade 2 meet the requirement of this indicator by attending to the standards' emphasis on mathematical reasoning.
- Each module lists terminology for the module including "new or recently introduced terms" and "familiar terms and symbols."