The design principles of the Illustrative Mathematics (IM) materials focus on developing conceptual understanding and procedural fluency. This is done by starting each unit with a pre-assessment to gauge students' prior knowledge, then introducing new concepts and representations in a way that builds on what students already know. Students have opportunities to make connections to real-world contexts throughout the materials, and activities are structured using the Five Practices for Orchestrating Productive Mathematical Discussions.
Here are the specific task purposes in the IM materials:
Provide experience with a new context.
Introduce a new concept and associated language.
Introduce a new representation.
Formalize a definition of a term for an idea previously encountered informally.
Identify and resolve common mistakes and misconceptions that people make.
Practice using mathematical language.
Work toward mastery of a concept or procedure.
Provide an opportunity to apply mathematics to a modeling or other application problem.
The IM materials also include a note about standards alignments, which indicates how each activity aligns to a specific grade-level standard. Additionally, the materials include a note about mathematical diagrams, which emphasizes that only components with mathematical meaning should be included in diagrams.
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