Lesson 8.7
The Chord-Sine Connection
A shared problem, an honest self-assessment, and self-directed practice
I’m writing this one from the design rather than from a taught record, so take it as the intended shape of the day rather than a field report. Review day has three phases, and the sequencing is what makes it work.
It opens with a single shared thinking task, the satellite problem, about fifteen minutes at the boards for the whole class. It is deliberately one rich problem with more than one way in (a tangent-line route and a chord-sine route both reach the answer), which makes it a strong warm-up and gives you a fast diagnostic read on where groups actually are before they scatter into independent work. Keep the consolidation short; the job is to wake the thinking up, not to resolve every approach.
The middle phase is a few honest minutes with the navigation instrument. Students locate themselves on each row by a strict standard: “could I do a problem at this level on the assessment right now, with no notes, and get it right?” and then circle the one or two rows where they most need to improve. This phase is the one that earns its keep. The research on self-regulated learning is consistent that students who decide what to work on from honest self-evaluation, rather than from comfort, learn more.
The last phase is self-directed practice from a problem bank organized by row and level, with students choosing the boards or their desks. The predictable failure mode is the one to coach against: students drift toward what already feels good. A student who is solid at the basic level across the board but shaky one level up will reach for basic problems because they are pleasant. Your circulation is the intervention: “you are reviewing what you already know; where are you actually unsure?” and for students who are genuinely strong across all the rows, the synthesis problems and the hardest extension from 8.6 are where they belong. Don’t let the strong ones coast.