Mathematically gifted students are often capable of high levels of problem solving and inductive thinking. They display high levels of logical reasoning, high self-efficacy, and intrinsic motivation for the subject (Pajares and Graham, 1999; Sriraman, 2003; Koshy et al., 2009; Leikin, 2014; Leikin et al., 2017).
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. See the "centers" tab on the Illustrative Math Website.
According to our Math AEA rep, there isn't a lot 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)
Open Middle Math: The name “Open Middle” might sound like a strange name for a website about math problems. However, it references a very specific type of problem we try to encourage here. Most of the problems on this site have:
a “closed beginning” meaning that they all start with the same initial problem.
a “closed end” meaning that they all end with the same answer.
an “open middle” meaning that there are multiple ways to approach and ultimately solve the problem.
Open middle problems generally require a higher Depth of Knowledge than most problems that assess procedural and conceptual understanding. They support the Common Core State Standards and provide students with opportunities for discussing their thinking.