3rd Grade - Gateway 2
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Rigor & Mathematical Practices
Gateway 2 - Partially Meets Expectations | 77% |
|---|---|
Criterion 2.1: Rigor | 7 / 8 |
Criterion 2.2: Math Practices | 7 / 10 |
The Grade 3 My Math instructional materials partially meet the expectations for Gateway 2's review of rigor and mathematical practices. The instructional materials partially meet the expectations for the criterion on rigor and balance due to a lack of lessons attending to multiplication and division within 100. The materials 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 identifying MP and the language of mathematics.
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 3 My Math partially meet expectations for rigor and balance. The instructional materials give appropriate attention to conceptual understanding, and application, and the materials address these three aspects with balance, not always treating them separately and not always together. However, fluency and procedural skill do not give enough treatment to multiplication and division. With multiplication and division within 100 being a required fluency for Grade 3 and the beginning of multiplication and division, six lessons are not sufficient. Overall, the instructional materials partially help 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.
Materials develop conceptual understanding of key mathematical concepts, especially where called for in specific content standards or cluster headings.
- The content in chapters 1-3 and 9 and 10 specifically and fully address standards which are explicitly outlined as conceptual standards. (3.NBT.A, 3.NF.A and 3.OA.B)
- The content in chapter 6, lesson 8, focuses on 3.NBT.A, which is a conceptual understanding standard.
- Of the 110 lessons 33 are focused specifically on the conceptual understanding standards.
- The majority of lessons in Grade 3 My Math have a section called "Investigate the Math" which targets conceptual understanding. This is contained in the online lesson presentation. For example, page 697B, teacher edition.
- All lessons in the series have a section called "Talk Math" which targets conceptual understanding. This is contained in the online lesson presentation. For example, see page 16, teacher edition and student edition.
- In the student edition, some of lessons in Grade 3 My Math have a section "Explore and Explain" to begin the lessons which targets conceptual understanding. For example, see page 779, teacher edition and student edition.
- The majority of the homework contains problems that provide students the opportunity to view and to demonstrate their conceptual understanding. For example, pages 93-94, teacher edition and student edition.
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 give limited attention throughout the year to individual standards which set an expectation of procedural skill and fluency.
- Lessons contain multiple examples of fluency practice pages.
- In the student edition fluency practice pages in chapters 2 and 3 and 6-8. For example, chapter 2, pages 119-120; chapter 3, pages 177-178; chapter 6, pages 351-352; chapter 7, pages 415-416; and chapter 8, pages 487-488.
- Homework contains multiple opportunities for students to practice fluency.
- The "Fact Dash" game is available online with the student login to practice fluency. Students can select the operation and number facts.
- Each chapter in the online teacher edition has additional fluency pages available for printing.
- "Sail through the Math" is an app game for fluency and is available for purchase ($1.99).
- The math standard 3.OA.C.7 (fluently multiply and divide within 100) has 6 lessons out of 110 which address the standard and are in chapters 5, 6 and 8. With multiplication being a required fluency for Grade 3 and the beginning of multiplication, 6 lessons are not sufficient.
- The math standard 3.NBT.A.2 (fluently add and subtract within 1000) has 14 lessons out of 110 which address the standard and are all in chapters 2 and 3.
- Procedural skills are present in the majority of the lessons. For example, see page 101, teacher/student edition, contain procedural skill.
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 Grade 3 My Math materials give attention throughout the year to individual standards which set an expectation of procedural skill and fluency. Lessons contain multiple examples of fluency practice pages.
- The teacher edition states "Math in my World"," HOT (Higher Order Thinking) Problems", and "Real-World problem solving readers" address application.
- While "Real-World Problem-Solving Readers" are available to provide additional problems, they were not reviewed by EdReports.org as they are not included in the basic package with the student and teacher editions and were therefore considered supplementary.
- Beginning in Grade 3, the majority of lessons begin with a "Math in my World" which uses real-world problems to introduce concepts. For example, see chapter 3, lesson 2, page 139.
- Some "HOT Problems" address application (for example, pages 32, 38 and 370, teacher/student edition). However, some do not (for example, pages 64 and 367, teacher/student edition).
- Real-world problems are found in the majority of lessons and homework assignments.
- "Count-down to Common Core" provides performance tasks requiring application of the 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.
Grade 3 My Math materials are designed so teachers and students spend sufficient time working with engaging applications of the mathematics, without losing focus on the major work.
- At the beginning of each lesson a "rigor" section exists identifying levels of complexity by problem or exercise number. For example, chapter 1, lesson 5 has two problems for conceptual learning (understand concepts), 16 problems for fluency/procedural skill (apply concepts), and five problems for application (extend concepts).
Criterion 2.2: Math Practices
Practice-Content Connections: Materials meaningfully connect the Standards for Mathematical Content and the Standards for Mathematical Practice
The Grade 3 My Math instructional materials 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. Attending to mathematical vocabulary is a strength of the materials. However, the materials only partially meet the expectations for attending to the full meaning of each practice standard and engaging students in mathematical reasoning. Overall, in order to meet the expectations for meaningfully connecting the CCSSM and the MPs, the instructional materials should carefully attend to the full meaning of every practice standard, especially practice 3 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.
In the Grade 3 My Math, Standards for Mathematical Practice (MPs) are identified and used to enrich mathematics content within and throughout Grade 3. Overall, the instructional materials do not over-identify or under-identify the MPs, and the MPs are used within and throughout the grade.
- The teacher edition, pages T22-T24 state the MP and the corresponding pages.
- The practices are identified throughout all 110 lessons. Each lesson has three to four practices, which are the focus.
- The student edition does indicate which MPs the student is working in the lesson and in the homework.
Indicator 2f
Materials carefully attend to the full meaning of each practice standard
The Grade 3 My Math instructional materials 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. Some practice standards do not fully address the intent/context of the MPs. Some examples include:
- MP1, make sense of problems and persevere in solving problems, chapter 2, lesson 5 page 90, teacher/student edition.
- MP2, reason abstractly and quantitatively, pages 579-580, 581B and 583-584. Overall, practices labeled as reason quantitatively addressed the full intent of the practice, however those labeled as reason abstractly do not.
- MP4, model with mathematics, pages 30 and 163 teacher/student edition.
- Some practice standards fully address the intent/context of the MP. Overall, standards for MPs 5, 6, 7 and 8 are well developed.
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 3 My Math 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 students to analyze other students' arguments.
- Materials sometimes provide opportunities for students to construct viable arguments independent of the teacher.
- Some "HOT problems" have students constructing viable arguments. For example, pages 82, 214, 392 and 604 in teacher/student edition.
- More time is given to constructing arguments than analyzing the arguments 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.
The instructional materials reviewed for Grade 3 My Math 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 do not consistently assist teachers in having students construct viable arguments or analyze other students' arguments.
- Teacher materials do not consistently provide true opportunities for students to construct arguments or analyze the arguments of others.
- The content in pages 36, 403-404 and 429B, provide opportunities for students to construct arguments.
- The content in pages 45, 339A and 457-458 provides an opportunity for students to construct an argument and analyze the arguments of others.
- The content in pages 265A, 309, 401-402 and 613 do not provide opportunities for students to construct arguments or analyze the arguments of others as stated in the teacher edition.
Indicator 2g.iii
Materials explicitly attend to the specialized language of mathematics.
The Grade 3 My Math instructional materials explicitly attend 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 are consistently present throughout the materials.
- The special language of mathematics is a strength of the series.
- Individual vocabulary cards are found at the beginning of each chapter in the student edition.
- Vocabulary checks are included in some homework assignments. For example, chapter 1, lesson 1, page 14.
- Vocabulary assessments can be created online.
- Virtual word walls are available online.
- "Match the Pairs" is an interactive vocabulary component.
- "Check my Progress" assesses vocabulary.
- Each chapter begins with a foldable which supports vocabulary development.
- At the beginning of some chapters there is "My Math Words" like in chapter 4, page 186.
- The teacher, student and online editions contain extensive glossaries in English and Spanish.
- Lessons contain mathematical terminology.