Kreft: Math
Mathematically gifted students are able to see relationships among topics, concepts, and ideas without the intervention of formal instruction specifically geared to that particular content (Heid, 1983). Due to their intuitive understanding of mathematical function and processes, they may skip over steps and be unable to explain how they arrived at the correct answer to a problem (Greenes, 1981). -Mathematically Gifted Students: How Can We Meet Their Needs; Rotigel, J. & Fello
Differentiation for Illustrative Math
There are some Exploration Problems in each section (found at the end of the Practice Problems). Here is a link explaining how they could be used (scroll down to Exploration Problems in the Practice problems section). Practice problems are found under the Practice tab in each unit.
You could also differentiate in centers, using a higher stage for a game or activity. (found under the 'centers' tab on the IM website.)
According to our math AEA rep, there isn't a lot of opportunity for differentiation in elementary because the goal is to go deeper instead of faster for students who need more. Here is a blog post from the IM Hub that explains IM's approach to "curious students." (how they describe students who desire challenge)
Math Problem Organizer
Sample Math Rubric
Anchoring activity (defined by Carol Ann Tomlinson as, “meaningful work done individually and silently”) especially when children first begin a class or when they finish assigned work