8th Grade - Gateway 3
Back to 8th 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...
Usability
Gateway 3 - Partially Meets Expectations | 78% |
|---|---|
Criterion 3.1: Use & Design | 8 / 8 |
Criterion 3.2: Teacher Planning | 8 / 8 |
Criterion 3.3: Assessment | 9 / 10 |
Criterion 3.4: Differentiation | 5 / 12 |
Criterion 3.5: Technology |
Criterion 3.1: Use & Design
Use and design facilitate student learning: Materials are well designed and take into account effective lesson structure and pacing.
The instructional materials meet expectations for use and design to facilitate student learning. Materials are well designed and take into account effective lesson structure and pacing. The materials meet the criterion for use and design. The underlying design of the materials makes a distinction between problems and exercises. In essence, the difference is that in solving problems students learn new mathematics, whereas in working exercises students apply what they have already learned in order to build mastery. Each problem or exercise has a purpose. The design of assignments is not haphazard; exercises do seem to be given in intentional sequences. Furthermore, the design is not distracting or chaotic, but supports students in engaging thoughtfully with the subject. Additionally, in most cases, the manipulatives and/or models accurately and consistently represent the mathematical objectives. Overall, the materials reviewed for Grade 8 meet the expectations for this criterion.
Indicator 3a
The underlying design of the materials distinguishes between problems and exercises. In essence, the difference is that in solving problems, students learn new mathematics, whereas in working exercises, students apply what they have already learned to build mastery. Each problem or exercise has a purpose.
In the teacher edition, the section before the investigation starts is divided into the following sections:
- Launch
- Launch Video
- Connect Prior Knowledge
- Present Challenge
- Explore
- Provide for Individual Needs
- Planning for Summary
- Summary
- Orchestrate Discussion
- Reflect on Student Learning
The underlying design of the materials does distinguish between problems and exercises meeting the expectations for this indicator.
The investigations are divided into problem sets, and they typically follow a sequence. For example, Investigation 1 could be divided into the following problems set: 1.1, 1.2, and 1.3.
At the beginning of each investigation problem set, there are some explanations and definitions given. Next, there is a set of problems to be completed within the class period.
At the end of each investigation, there is a homework section. This section is divided into Application, Connection, and Extension sections.
There is also a mathematical reflection section at the end of each investigation where students reflect on the mathematics content they have learned. During this section, there is also a connection between the mathematical practices used throughout the investigation.
Indicator 3b
Design of assignments is not haphazard: exercises are given in intentional sequences.
The design of assignments is not haphazard; exercises do seem to be given in intentional sequences meeting the expectations for this indicator.
On page 12 of A Guide to Connected Mathematics, the three phases of the CMP model are explained: launching, exploring, and summarizing.
In the first phase, the teacher launches the problem with the whole class. Launches include connecting to prior knowledge as well as presenting the challenge of the problem.
For the Explore phase, the nature of the problem suggests whether students work individually, in pairs, in small groups, or occasionally as a whole class to solve the problem. As students work, they gather data, share ideas, look for patterns, make conjectures, and develop problem solving strategies.
It is during the Summarize phase that the teacher guides the students to reach the mathematical goals of the problem and to connect their new understanding to prior mathematical goals and problems in the unit. The Summarize phase begins when most students have gathered sufficient data or made sufficient progress toward solving the problem. In this phase, students present and discuss their solutions and the strategies they used to understand the problem, organize the data, and find the solution. During the discussion, the teacher helps students enhance their conceptual understanding of the mathematics in the problem and guides them in refining their strategies into more efficient, generalizable problem-solving techniques, or algorithms.
Indicator 3c
There is variety in what students are asked to produce. For example, students are asked to produce answers and solutions, but also, in a grade-appropriate way, arguments and explanations, diagrams, mathematical models, etc.
There is a variety in what students are asked to produce, meeting the expectations for this indicator.
- Throughout various investigations and within the problem sets, students are asked to produce answers and solutions as well as to describe their answers, discuss ideas, make conjectures, explain their work and reasoning, make sketches and diagrams, justify their reasoning, and use appropriate models.
- Sometimes only one aspect is specified, such as only requiring an answer, and other times a problem requires students to provide an answer, provide an explanation or steps, include a diagram and/or use a model.
Because problems require different responses, the type of response is intentional, like requiring models when a concept is introduced and then not requiring the same model when a more procedural method for solving similar problems is developed.
Indicator 3d
Manipulatives are faithful representations of the mathematical objects they represent and when appropriate are connected to written methods.
The manipulatives are almost always faithful representations of the mathematical objects they represent and, when appropriate, are connected to written models, meeting the expectations for this indicator.
On page 40 of A Guide to Connected Mathematics, an explanation is provided for the use of manipulatives in the instructional materials. Manipulatives are used only when they can help students develop understanding of the mathematical ideas.
For example, in Filling and Wrapping, students find all the different rectangular arrangements possible for a given number of cubes. They find the surface area of each arrangement by creating a net (covering) for the arrangement that require the least and the most material to wrap. This activity sets the stage for developing the ideas of surface area and volume of rectangular prisms.
Most of the manipulatives used in CMP are commonly available, and many schools may already have them. Included are rulers, protractors, angle rulers, cubes, square tiles, counters, spinners, and dice.
Two manipulatives are unique to CMP:
Polystrips are plastic strips that can be pieced together with brass fasteners to form polygons. They are used in Grade 7 to investigate the relationship among the side lengths of triangles and quadrilaterals. They also are useful in the Grade 8 Geometry unit, “Butterflies, Pinwheels, and Wallpaper.”
The CMP Shapes Set is a set of polygons used in Grade 7 to explore sides, angles, and tilings.
Indicator 3e
The visual design (whether in print or online) is not distracting or chaotic, but supports students in engaging thoughtfully with the subject.
Criterion 3.2: Teacher Planning
Teacher Planning and Learning for Success with CCSS: Materials support teacher learning and understanding of the Standards.
Teacher Planning and Learning for Success with CCSSM: Materials support teacher learning and understanding of the standards. The materials reviewed meet the criterion for teacher planning and learning. The materials support teachers in planning and providing effective learning experiences by providing quality questions to help guide students' mathematical development. Materials contain a teacher edition with ample and useful annotations and suggestions on how to present the content in the student edition. The strongest point is that each module begins with an overview section that gives teachers an understanding of the mathematical content in the lessons as well as where it fits in the scope of mathematics from Kindergarten through Grade 12. Overall, the material reviewed for the Grade 8 meets the expectations for this criterion.
Indicator 3f
Materials support teachers in planning and providing effective learning experiences by providing quality questions to help guide students' mathematical development.
Materials support teachers in planning and providing effective learning experiences through teacher questioning. This is a strength of the program with multiple questions for each lesson/problem throughout all of the Grade 8 units.
- Lesson sections that include questions are Launch, Presenting the Challenge, Explore and Summarize.
- Additionally, teachers are prompted to reflect on student learning after the lesson in order to prepare for the next daily lesson or unit.
Indicator 3g
Materials contain a teacher's edition with ample and useful annotations and suggestions on how to present the content in the student edition and in the ancillary materials. Where applicable, materials include teacher guidance for the use of embedded technology to support and enhance student learning.
The teacher’s edition has many suggestions on presenting the content to students.
- The Launch section and Connecting to Prior Knowledge are the two beginning sections of each lesson.
- The purple book contains ideas for technology implementation for student learning.
Indicator 3h
Materials contain a teacher's edition (in print or clearly distinguished/accessible as a teacher's edition in digital materials) that contains full, adult-level explanations and examples of the more advanced mathematics concepts in the lessons so that teachers can improve their own knowledge of the subject, as necessary.
The teacher’s edition is an excellent resource for mathematics teachers to understand the mathematics of the unit and for teachers to expand their understanding of the mathematical concepts.
- Mathematical background is included at the beginning of each unit. In the It’s in the System book, there are 13 pages of mathematical background for teachers to understand.
It’s in the System includes problems, explanations of problems, examples, and connections to CCSSM.
Indicator 3i
Materials contain a teacher's edition (in print or clearly distinguished/accessible as a teacher's edition in digital materials) that explains the role of the specific grade-level mathematics in the context of the overall mathematics curriculum for kindergarten through grade twelve.
The teacher’s edition clearly explains the role of specific grade-level mathematics in the context of the overall mathematics for grades 6-12.
- Standards are aligned in Grades 6-12 (curriculum is only written for these grade levels--K-5 is not an option)
- Teacher’s editions connect the learning from previous grade levels and explain how standards build on one another throughout the program.
Indicator 3j
Materials provide a list of lessons in the teacher's edition (in print or clearly distinguished/accessible as a teacher's edition in digital materials), cross-referencing the standards covered and providing an estimated instructional time for each lesson, chapter and unit (i.e., pacing guide).
Indicator 3k
Materials contain strategies for informing parents or caregivers about the mathematics program and suggestions for how they can help support student progress and achievement.
Indicator 3l
Materials contain explanations of the instructional approaches of the program and identification of the research-based strategies.
Criterion 3.3: Assessment
Assessment: Materials offer teachers resources and tools to collect ongoing data about student progress on the Standards.
Assessment: Materials offer teachers resources and tools to collect ongoing data about student progress on the Standards.
The materials reviewed partially meet expectations for the criterion of assessment in Grade 8. The materials do not provide strategies for gathering information about students' prior knowledge within and across grade levels. Materials only sometimes provide strategies for teachers to identify and address common student errors and misconceptions. Reflections and problem sets - which could be used as formative assessment tasks - are not aligned to a specific standard or group of standards. The materials provide opportunities for ongoing review and practice. The materials offer formative and summative assessments, such as Notebook, Mathematical Reflection, Looking Back, Check Up, Partner Quiz, Unit Test, Self-Assessment, Project, and Group Work/Discussion. The materials do encourage students to monitor their own progress.
Overall, the materials reviewed for the Grade 8 partially meet the expectations for the assessment criterion.
Indicator 3m
Materials provide strategies for gathering information about students' prior knowledge within and across grade levels.
In the first phase of each lesson, the teacher launches the problem with the whole class. Launches include connecting to prior knowledge.
Indicator 3n
Materials provide strategies for teachers to identify and address common student errors and misconceptions.
Materials provide very few strategies for teachers to identify and address common student errors and misconceptions.
- In the Teacher Planning section, there were occasionally “Notes” about potential student errors.
They present situations and ask students to identify mistakes or provide rationale based on common misconceptions.
Indicator 3o
Materials provide opportunities for ongoing review and practice, with feedback, for students in learning both concepts and skills.
Materials provide opportunities for ongoing review and practice, with feedback, for students in learning both concepts and skills.
- The materials provide several opportunities for ongoing review and practice, such as Notebook, Mathematical Reflection, Looking Back, Check Up, Partner Quiz, Unit Test, Self-Assessment, Project, and Group Work/Discussion.
- Within a unit the set of practice problems includes Application, Connection, and Extension to promote both increased understanding of a concept as well as developing procedural skill/fluency.
- Beyond a lesson, future lessons/units typically expand practice and depth of previous learning.
Teacher Planning offers a multitude of prompts to orchestrate discussion.
Indicator 3p
Materials offer ongoing formative and summative assessments:
Indicator 3p.i
Assessments clearly denote which standards are being emphasized.
Assessments clearly denote which standards are being emphasized.
- Each standard is aligned to one or more lessons as noted at the beginning of each topic.
- The Check up and Unit Test appear to be developed to fully assess a particular standard and the scoring guidelines specify which item aligns to which standard.
- However, reflections and problem sets—which could be used as formative assessment tasks—are not aligned to a specific standard or group of standards.
Indicator 3p.ii
Assessments include aligned rubrics and scoring guidelines that provide sufficient guidance to teachers for interpreting student performance and suggestions for follow-up.
- Formative assessments include scoring guidelines that provide sufficient guidance to teachers for interpreting student performance but do not include suggestions for follow-up.
- Each Check up and Unit Test includes a scoring guideline as well as worked out solutions for correct responses but do not include suggestions for follow-up for below or above grade level students.
- Although the rubric and scoring guidelines are complete, there are no strategies or suggestions for follow-up provided for the teachers.
Indicator 3q
Materials encourage students to monitor their own progress.
Criterion 3.4: Differentiation
Differentiated instruction: Materials support teachers in differentiating instruction for diverse learners within and across grades.
The materials reviewed for Grade 8 do not meet expectations for the criterion for differentiated instruction. Materials sometimes provide strategies to help teachers sequence or scaffold lessons so that the content is accessible to all learners. There is no guidance to support teachers if a lesson does not work as written or if students need additional support to master the content. There is little provided that would help struggling or ELL students access the content successfully. Although there are occasionally challenge problems, there are minimal opportunities for advanced students to go beyond the mathematics provided in the classroom lessons. What is provided is not enough to guarantee that all students have content that is accessible. Overall, the materials do not meet the criterion for differentiated instruction.
Indicator 3r
Materials provide strategies to help teachers sequence or scaffold lessons so that the content is accessible to all learners.
Materials provide strategies to help teachers sequence or scaffold lessons so that the content is accessible to all learners:
- Sequencing and scaffolding are embedded into lesson development, but materials provide few strategies to help teachers sequence or scaffold lessons so that the content is accessible to all learners.
- In Teacher Planning pages, there is always a section called “Orchestrating Discussion” which offers suggestions of questions at varying levels to help students understand the content.
- There is no evidence of an explanation of how the lessons develop.
There is no guidance to support teachers if a lesson does not work as written or if students need additional support to master the content.
Indicator 3s
Materials provide teachers with strategies for meeting the needs of a range of learners.
Materials provide teachers with strategies for meeting the needs of a range of learners:
- The materials provide very general strategies to help teachers make the content accessible to a range of learners.
- There are some questioning prompts in the Teacher Planning section under “Provide for Individual Needs.” However, they do not seem geared toward a struggling learner but are simply good discussion points for all students.
- Occasionally, “Provide for Individual Needs” includes “Going Further” which offers approximately 100 challenge problems.
- The homework problems always offer “Extensions.”
- There is a concern that the suggestions provided are not enough to guarantee that all students have content that is accessible.
Indicator 3t
Materials embed tasks with multiple entry-points that can be solved using a variety of solution strategies or representations.
Materials embed tasks with multiple entry-points that can be solved using a variety of solution strategies or representations.
- A variety of solution strategies are not always encouraged.
- Students are given opportunities to create solution paths on their own.
- Most tasks do not allow students to use multiple entry points; they start at the same place.
- Students do have the opportunity to solve problems using a variety of strategies, paths and/or models, though the materials sometimes undermine this concept by using tasks that explicitly state how to solve the problem or which representation to use.
Indicator 3u
Materials suggest support, accommodations, and modifications for English Language Learners and other special populations that will support their regular and active participation in learning mathematics (e.g., modifying vocabulary words within word problems).
Materials provide little support, accommodations, or modifications for English language learners and other special populations that will support their regular and active participation in learning mathematics (e.g., modifying vocabulary words within word problems).
- This series is clearly designed with best practices for all students in mind; however, there is nothing explicitly differentiated or modified for struggling or ELL students, other than translating assessments into Spanish.
- What is provided is not enough to guarantee that all students have content that is accessible.
Indicator 3v
Materials provide opportunities for advanced students to investigate mathematics content at greater depth.
Materials provide limited opportunities for advanced students to investigate mathematics content at greater depth.
- Occasionally there are challenge problems.
- There were minimal opportunities for advanced students to go beyond the mathematics provided in the classroom lessons.
Indicator 3w
Materials provide a balanced portrayal of various demographic and personal characteristics.
Materials provide a balanced portrayal of various demographic and personal characteristics.
Indicator 3x
Materials provide opportunities for teachers to use a variety of grouping strategies.
Indicator 3y
Materials encourage teachers to draw upon home language and culture to facilitate learning.
Criterion 3.5: Technology
Effective technology use: Materials support effective use of technology to enhance student learning. Digital materials are accessible and available in multiple platforms.
Effective technology use: Materials support effective use of technology to enhance student learning. Digital materials are accessible and available in multiple platforms.
Indicator 3aa
Digital materials (either included as supplementary to a textbook or as part of a digital curriculum) are web-based and compatible with multiple internet browsers (e.g., Internet Explorer, Firefox, Google Chrome, etc.). In addition, materials are "platform neutral" (i.e., are compatible with multiple operating systems such as Windows and Apple and are not proprietary to any single platform) and allow the use of tablets and mobile devices.
Indicator 3ab
Materials include opportunities to assess student mathematical understandings and knowledge of procedural skills using technology.
Indicator 3ac
Materials can be easily customized for individual learners. i. Digital materials include opportunities for teachers to personalize learning for all students, using adaptive or other technological innovations. ii. Materials can be easily customized for local use. For example, materials may provide a range of lessons to draw from on a topic.
Indicator 3ad
Materials include or reference technology that provides opportunities for teachers and/or students to collaborate with each other (e.g. websites, discussion groups, webinars, etc.).
Indicator 3z
Materials integrate technology such as interactive tools, virtual manipulatives/objects, and/or dynamic mathematics software in ways that engage students in the Mathematical Practices.