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  • Jonathan Lind

    March 19, 2022 at 8:47 am

    I have a little trouble seeing the final stage from the example: isn’t distribution a whole extra topic? If the goal is multiplication, can we define the mastery stage as a different concept?

    Edit-Talked to my wife who teaches elementary, and watched the following video involving donuts, and this make a whole lot more sense to me now 🙂

    Anyway, we’re working on circle theorems in Geometry, and introducing cyclic quadrilaterals. We’ll be working towards the understanding that opposite angles must be supplementary because they open onto arcs that make up the whole circle. Students have already worked with inscribed angles and know those relationships, so I don’t expect this to be a long journey, but it’s what came to mind.

    1. I have no idea how quadrilaterals in circles relate to our prior learning. I wouldn’t be able to find the angles in an inscribed quadrilateral unless I know information that doesn’t relate to circles.

    2. I know that there must be something going on with these quads, because we studied inscribed angles and all of these angles are inscribed.

    3. I see that opposite angles open onto arcs that make up the entire circle, which is 360, and inscribed angles are half of their arcs, so the sum of opposite angles must be 180. I can find the other angle when given one.

    4. I recognize inscribed quadrilaterals and automatically apply this rule to problems involving them.

    5. I can find inscribed quadrilaterals and use them as a tool in solving more complex problems of angles and arcs in circles.

    • This reply was modified 10 months, 2 weeks ago by  Jonathan Lind.