8th Grade - Gateway 2
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Rigor & Mathematical Practices
| Score | |
|---|---|
Gateway 2 - Meets Expectations | 100% |
Criterion 2.1: Rigor | 8 / 8 |
Criterion 2.2: Math Practices | 10 / 10 |
The materials reviewed for Grade 8 meet expectations for rigor and MPs. Each unit offers multiple opportunities for hands-on, conceptual development, skills practice for fluency, and engaging real-life situations. There is a solid balance of the three areas of rigor, with fluency being slightly weaker than the others, though the easiest to supplement if needed. MPs are identified in the materials, are used to enrich the mathematics content, and have their full meaning represented. The instructional materials support the standards emphasis on mathematical reasoning by prompting students and teachers to construct and analyze viable arguments and explicitly attending to the specialized language of mathematics. Overall, the instructional materials address all aspects of rigor and meaningfully connect the CCSSM and the MPs.
*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 for Grade 8 meet expectations for rigor and balance. Each unit offers multiple opportunities for hands-on, conceptual development, skills practice for fluency, and engaging real-life situations. In addition, teachers are provided with guidance for “how and why” questions that develop conceptual understanding. Students never have to wonder when they will use the skill because they are asked to apply what they’ve learned in each lesson. There is a solid balance of the three areas of rigor, with fluency being slightly weaker than the others, though the easiest to supplement if needed.
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 Grade 8 meet the expectations for developing conceptual understanding of key mathematical concepts.
Each unit starts with a “Looking Ahead” problem, which poses a mathematical situation that they will be learning to solve.
Looking Ahead also provides explicit scaffolding to prior knowledge.
Investigation problems frequently involve hands-on activities or models and always involve students explaining why. These problems also frequently involve error analysis. All of these help develop conceptual understanding.
Some Investigation problems can carry throughout a unit, each time adding a layer of complexity to further develop conceptual understanding.
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 for Grade 8 meet the expectations for giving attention to individual standards for developing procedural skills and fluency.
Each unit provides three or four “investigations” where students are given problems to solve that will help develop skills for the Looking Ahead problem.
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 for Grade 8 meet the expectations for students spending sufficient time working with engaging applications of the mathematics.
The instructional materials provide relevant, real-world problems. For example, problems frequently focus on school events for Grade 8.
There are opportunities for students to make their own assumptions or simplifications of situations.
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 for Grade 8 meet the expectations for a balance of the three aspects of rigor.
Almost every investigation provides instructional problems that develop conceptual understanding within an application context.
Overall for the grade, practice problems are about half procedural practice and half application. Some units lean more one way than the other, but they balance out.
Students are asked to complete a “Looking Back” problem that puts everything together. The problem asks students to explain their reasoning and to reflect to summarize learning for each unit.
The weakest area is fluency. Some students will need more skills practice for some concepts than provided in order to develop fluency.
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 8 meet the expectations for practice content connections. Mathematical practices are identified in the materials, are used to enrich the mathematics content, and have their full meaning represented. The instructional materials support the standards emphasis on mathematical reasoning by prompting students and teachers to construct and analyze viable arguments and explicitly attending to the specialized language of mathematics. Overall, the instructional materials meaningfully connect the CCSSM and the MPs.
Indicator 2e
The Standards for Mathematical Practice are identified and used to enrich mathematics content within and throughout each applicable grade.
The materials reviewed for Grade 8 meet the expectations for identifying and using MPs.
At the beginning of each unit, the practices are listed along with bullets to help students understand how use them. Teachers are provided with explicit connections of the most prevalent practices and which problems they match. The practices are not explicitly labeled for students on the problems, though they use them routinely.
Indicator 2f
Materials carefully attend to the full meaning of each practice standard
The materials reviewed for Grade 8 meet the expectations for attending to the full meaning of the MPs.
For each investigation:
Teachers are provided with a rationale of how the MPs are used in the problems.
The last thing the students reflect on is a model of a student explanation of how the MP connected to a problem and identifying what other MPs were used, then asks students to identify the MP they used in a different problem.
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.
Students are constantly prompted to explain, analyze, make connections, justify. There are frequent instances of “Do you agree with their reasoning? Why or Why not?”
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.
Teacher Planning for every investigation includes “Orchestrating the Discussion” that prompts mathematical reasoning such as “How did you know? Did you use this in your solution? Name another. Does this work for any? Etc..”
Indicator 2g.iii
Materials explicitly attend to the specialized language of mathematics.
Vocabulary is mathematical and grade-level appropriate.