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  • Bryan Henning

    July 13, 2020 at 6:56 pm

    Concept: Finding the midpoint of a line segment given two endpoints (especially ones far away, like (-1,12) and (9, -8)

    Unconsciously Incompetent: Draws a picture and attempts to visualize the middle, counting the length down and over on the coordinate grid.

    Consciously Incompetent: Same as previous but is aware that there must be a better way.

    Consciously Competent: Subtracts coordinates to find x- and y-distance, cuts each distance in half, and adds to/subtracts from one endpoint – may use a diagram like a number line or right triangle

    Unconsciously Competent: Finds the average of the x-coordinates and the average of the y-coordinates. Also may use the previous strategy with mental math.

    Consciously Masterful: Can explain how both of the above strategies arrive at the same conclusion.