Lesson 3.4
Diagnostic Practice Day
Focus: individual work — navigation instrument rows 1–4 — self-assessment before proof begins
This lesson does not exist because students are not capable of proof. It exists because the congruence shortcuts and diagram reading are the raw materials from which every proof in this unit is built, and there is no point moving to proof structure when students do not yet have solid command of the tools. One of the clearest lessons from Year 1 was shock at how many students were still at Basic on Row 3 or Row 4 after Lessons 3.2 and 3.3. Moving on to structuring arguments when the basic facts are not yet understood guarantees mimicry rather than genuine proof writing.
This day gives both teacher and student a clear diagnostic picture before the most demanding lessons in the unit begin. Students who are solid on rows 3 and 4 at Intermediate or above are ready for the proof progression work. Students who are still at Basic on either row will need scaffolded entry points in Lessons 3.5a and 3.5c. Knowing who is who before Lesson 3.5 starts makes differentiation intentional rather than reactive.
This is not a test. It is a self-directed practice session anchored to the navigation instrument. Move students to individual seating. They work through the problem set, choose their entry level on each row, and update the navigation instrument as they go. Circulate and confer. Ask questions rather than giving answers. Students who are ready for the extension problems — the parallelogram preview that anticipates Lesson 3.5a — should be directed there.
Open the lesson with five minutes on the navigation instrument before students open the problem set. Ask them to mark honestly where they think they are on rows 1–4 before the work shows them where they actually are. The gap between self-assessment and performance is information — both for you and for the student.
Collect the navigation instruments at the end of class or scan them. Before Lesson 3.5, look for the two groups: students ready for independent proof work, and students who need additional support. The mild/medium/spicy structure of Lesson 3.5c is designed for exactly this differentiation.