Mathematics Planning Essentials

Each Math Planning Essentials guide (MPE) pulls together key elements of lesson planning that are organized by a set of essential understandings—the underlying mathematical truths worth exploring for a given concept of study. 

MPEs can help make sense of these truths by providing information about how they might play out as students’ conceptual understanding develops. Each MPE provides:

  • Essential Understandings that name what students need to know for a mathematical concept.
  • Tasks to contextualize the mathematics.
  • Ways students may Use & Explain Representations in response to the tasks, paired with suggestions to further elicit student thinking.
  • Prompts and questions that
    • ask students to Make Connections among different representations shown in and across student responses and
    • require students to Explain Mathematical Reasoning about the ideas articulated in the essential understandings.
  • A generalized list of what Students Should be Able to Do and Say, if they have made sense of the essential understandings.

Here is an example of the Understanding Fractions as Number MPE guide.


A series of MPEs covers essential understandings students must learn on specific topics within a domain. Click on one of the MPE series below to learn more.

Each title within a domain is available as a pack of 10 laminated tri-folds for $150.

Learn more about the IFL's other research-backed instructional resources at ifl.pitt.edu.