3rd Grade - Gateway 2
Back to 3rd 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 3 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 MPs, 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 3 meet the expectations 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 3, fluency and procedures include "Single-digit Products and Quotients (Products from Memory by End of Grade 3)" (3.OA.C.7) and "Add/Subtract within 1,000" (3.NBT.A.2). Application problems occur in almost every lesson depending upon the focus Mathematics of the lesson. This is expected to last around 5-20 minutes for each lesson. The three aspects are balanced within the lessons and modules.
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 3 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 multiplication and division and fractions as numbers.
- In module 1, students are asked to compare multiplication strategies.
- In module 5, students are asked to explain how they know two fractions are equivalent and to explain their reasoning using a number line.
- Time is spent on using the properties of operations as a strategy for multiplying.
- In module 1, students are asked, "How does what the quotient represents affect the way a tape diagram is drawn?"
- Understanding of multiplication and division is built through contextual problems and the idea of equal groups.
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 3 for this indicator meet the expectations by attending to fluency and procedural work within the lessons. In Grade 3 this includes single-digit products and quotients, including products from memory by end of Grade 3 (3.OA.C.7) and to add and subtract within 1,000 (3.NBT.A.2).
- Within the distribution of instructional minutes, the schedule allows for 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 "How to Implement A Story of Units," "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, skip counting, sprints, dashes, problem sets 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 3 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 5-20 minutes for each lesson in Grade 3.
- If the focus standard of the lesson includes language requiring application, the application problem will become the major portion of the lesson.
- Contextual multistep word problems are used with a variety of problem types that increase in difficulty throughout the year. These problems focus on a variety of operations.
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 3 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 chart 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 3 partially meet this criteria. The MPs are often identified and often used to enrich mathematics content. There are many missed opportunities for identifying MPs, however, and some instances where they are misidentified. In module 1, only 14 out of 21 lessons identify an MP. All occur within the concept-development or the application portion of the lessons. 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. There is little explicit reference to modeling (MP4), and lessons identify this practice incorrectly. 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 3 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.
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. There are 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.
- In module 2 covers MP2 ("Reason Abstractly and Quantitatively"). Students decontextualize metric measurements and time intervals in minutes as they solve problems involving addition, subtraction, and multiplication. They round to estimate and then precisely solve, evaluating solutions with reference to units and with respect to real world contexts.
- MPs are listed in the margins of the teacher notes, mostly in the concept development portion and the student debrief of some lessons.
- In module 1, 14 of 21 lessons identify MPs. All of these occur within the concept development or the application portion of the lessons.
- In module 5, 17 of 30 lessons identify MPs. These occur within the concept development, application, and/or student debrief portions of the lessons.
- While reviewers appreciate that MPs standards are not over identified or used in contrived situations, there are many 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, in many lessons the tools are chosen for the students or the modeling expected is a simple representation.
- 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 module 1, students are making meaning of multiplication and numbers, within a multiplication story and within the context of a story problem.
- In module 6 a large part of lesson 3 address MP6 ("Attend to Precision").
- Many lessons list MPs without attending to the full meaning of the standard. For example, in module 1, students are making arrays to match equations, however in MP4 a real-world context must be present. In module 2, students are directed to use certain tools rather than selecting the appropriate tool on their own, which would meet the meaning of MP5.
- MP4 ("Model with Mathematics") 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 3 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 1, students are asked the following in an assessment question: "Would Mrs. Tran get the same result if she multiplied 5x4? Explain why or why not."
- In module 3, student materials prompt students to answer the following: "If I know 3x8=24, then I know the answer to 8x3! Explain how this is true."
- In module 5, students are asked to use personal whiteboards to help prove their answers.
- In module 5, students are asked to justify their answers in words and pictures when explaining equivalent fractions.
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 3 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, "Why is a vertical number line a good tool to use for rounding?"
- In a module 1 lesson a teacher draws a representation on the board and then asks students to "talk in partners about why you agree or disagree with my work."
Indicator 2g.iii
Materials explicitly attend to the specialized language of mathematics.
The materials reviewed for Grade 3 meet the expectations 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."
- In module 6, students are expected to use correct terminology when constructing different types of data displays.