Lesson 1.1 — Day 2 of 2
Notation and the Foundational Objects
Focus: precise notation; finishing the foundational definitions; first use of the navigation instrument
Day 2 opens with any vocabulary not completed in Day 1 — keep this brief if most definitions were finished, or give it the time it needs if several remain. Then move to the card task, which is the heart of the lesson.
The card task (again taken from Mathmedic) does something no amount of explanation can: it forces students to use notation actively in order to communicate. They cannot point, they cannot gesture, they can only describe using the words and symbols available to them. Students who discover mid-task that “AB” with a line on top means something different from “AB” with an arrow on one side — because the picture on the other side of the divider is different — have learned notation in the deepest possible way.
Treat the card task as a genuine consolidation priority. The notation gap observed on the unit test — students who understood the concepts but could not write them unambiguously — is addressed here. Give it the time it needs, consolidate carefully, and make sure students leave with a complete and correct record of symbolic notation for all foundational objects.
After the card task, end the lesson by introducing the navigation instrument for this unit. Have students practice using it against the homework problems — in class, not at home. The first time students use a navigation instrument, they need a teacher nearby to help them understand what honest self-assessment looks like. If you are using Euclid’s Handbook, the foundational objects are not propositions derived from the axioms, so they do not arise naturally from the existing handbook structure. If you wish to record them there as a preamble, please do so — and note that the handbook file will need to be updated to include a definitions section.
Introducing the Navigation Instrument
Do not send the navigation instrument home as homework to be completed alone. The first time students use it, do it with them. Walk through the first two rows together. Ask: what does “basic” mean here? What does “advanced” mean? How do you know which level you’re at? The answer to that last question — you check by trying a problem, not by feeling like you understand — is one of the most important lessons of the year.
Have students work the corresponding CYU problems in class and mark the instrument as they go. This models the practice that should continue all year: the navigation instrument is a living document, updated in real time as understanding grows, not a form to fill in at the end of a unit.