4th Grade - Gateway 3

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.

Design of assignments is not haphazard: exercises are given in intentional sequences.

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.

Manipulatives are faithful representations of the mathematical objects they represent and when appropriate are connected to written methods.

The visual design (whether in print or online) is not distracting or chaotic, but supports students in engaging thoughtfully with the subject.

Materials support teachers in planning and providing effective learning experiences by providing quality questions to help guide students' mathematical development.

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.

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.

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.

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).

Materials contain strategies for informing parents or caregivers about the mathematics program and suggestions for how they can help support student progress and achievement.

Materials contain explanations of the instructional approaches of the program and identification of the research-based strategies.

Materials provide strategies for gathering information about students' prior knowledge within and across grade levels.

Materials provide strategies for teachers to identify and address common student errors and misconceptions.

Materials provide opportunities for ongoing review and practice, with feedback, for students in learning both concepts and skills.

Materials offer ongoing formative and summative assessments:

Assessments clearly denote which standards are being emphasized.

Assessments include aligned rubrics and scoring guidelines that provide sufficient guidance to teachers for interpreting student performance and suggestions for follow-up.

Materials encourage students to monitor their own progress.

Materials provide strategies to help teachers sequence or scaffold lessons so that the content is accessible to all learners.

Materials provide teachers with strategies for meeting the needs of a range of learners.

Materials embed tasks with multiple entry-points that can be solved using a variety of solution strategies or representations.

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 opportunities for advanced students to investigate mathematics content at greater depth.

Materials provide a balanced portrayal of various demographic and personal characteristics.

Materials provide opportunities for teachers to use a variety of grouping strategies.

Materials encourage teachers to draw upon home language and culture to facilitate learning.

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.

Materials include opportunities to assess student mathematical understandings and knowledge of procedural skills using technology.

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.

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.).

Materials integrate technology such as interactive tools, virtual manipulatives/objects, and/or dynamic mathematics software in ways that engage students in the Mathematical Practices.