Differentiation Day
Cumulative Practice and Navigation Instrument Work
After Lessons 1.1–1.3 • covers all navigation instrument rows to date
⇄ What Is a Differentiation Day?
In mathematics, to differentiate means to distinguish — to recognize what is different between two similar things. That is exactly what this day asks students to do: look across everything covered so far and distinguish between the ideas, the formulas, the notation, and the procedures. This is also, happily, what spaced retrieval practice looks like in a thinking classroom.
There is a second meaning of differentiation in education — adapting instruction to different levels of need. The navigation instrument serves that purpose here too. Students who use it honestly will find rows where they are confident and rows where they are not. The differentiation day is when they do something about the rows where they are not.
A brief note for students at the start of class: research on how memory works is consistent on one point — retrieving information is more powerful for learning than reviewing it. The struggle of trying to recall something you have partially forgotten is not a sign that you don’t know it. It is the mechanism by which you come to know it more durably. Today’s work is designed around that principle. The discomfort is intentional.
Structure
Open with 5 minutes on the navigation instrument. Students update their self-assessment based on their CYU experience since Lesson 1.1. They identify one or two rows where they want to focus today.
The bulk of class is problem sets organized by navigation instrument row — spanning all rows covered so far. Students choose where to start based on their self-assessment, but should not spend the whole period on rows they already find easy. Challenge them to work on a row where they are uncertain, check their answers against the key, and figure out where their reasoning went wrong before asking for help.
Endpoint-from-midpoint problems should appear prominently — this was identified as an area needing more practice after Lesson 1.2. Slanted-side perimeter problems should also appear, reinforcing the distance formula connection made in Lesson 1.3.
Close with 10 minutes updating the navigation instrument again and writing one sentence in response to: where am I now versus where I was at the start of class?
If you want a grade I suggest a short quiz on this material at the start of the next class. Students have just practiced; the material is fresh. Keep it low stakes and return results quickly.