” Is it THAT much easier to reason through the proof when you know what you are supposed to conclude?”

I believe the answer to this is a resounding YES.

I think that the confidence that comes with knowing the conclusion/solution makes the act of reasoning easier.

This is one of the places SBAR helps a lot for me. The standard for me is understanding of angles and intersections, including parallel and perpendicular lines. (Pretty broad but this is a class that covers all of HS math!) I can give hard problems, or open ended problems, because their grade isn’t based on solving the problem, it’s based on showing understanding. I like that, because real math is like that. You don’t immediately solve the best problems.

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Definitely using this one!

]]>What about a miniproject where learners each draw a segment, then rotate it to a new group member, they have to rotate it +/- 90 deg, etc? The visual might help them confirm, then there’d be so much data on points and slopes.

]]>I would have Power Rule/Chain Rule questions of 3-4 levels of difficulty including your √ question without providing the answer. I don’t recommend the “Show that the derivative is…” type IF you’re testing skill. Of course there will always be an issue of the FORM of their answer.

Giving the derivative is ideal for concept/graph questions:

Given f(x)=√(25-x²), f'(x)= -x/√(25-x²)

(a) Find f'(4) .

(b) Explain relationship between answer to (a) and the graph of f(x).

Note: This is difficult for non-AP students but I’m sure you would only ask it if they experienced many of these.

Students will always opt for “EASIER”!

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