Problem
Pick a matching arm on the orange and green figures. In (A) the orange arm points straight up from the red pivot and the corresponding green arm points straight to the right. Turning straight-up to straight-right clockwise is a quarter turn.
Up to right, going clockwise, is exactly one corner of a square - 90 degrees.
4.MD.C.5Draw A DiagramIn (B) the orange arm and the matching green arm point in exactly opposite directions across the pivot (orange up, green straight down). Opposite directions are a half turn.
Pointing the exact opposite way is half of a full circle.
4.MD.C.5Draw A DiagramIn case (B) the green figure is the orange figure turned clockwise through exactly 180 degrees, a half turn.
A matching arm on the orange figure and its copy on the green figure point in exactly opposite directions out from the red pivot.
Two arms leaving the same point in exactly opposite directions lie along one straight line through that point.
Turning the arm clockwise until it points the exact opposite way sweeps it right along that straight line, so the turn equals the angle that fills a straight line.
In (C) the orange arm points to the right, and the green figure is tilted on a slant past straight-down (between a half turn and a three-quarter turn going clockwise). This slanted position is a larger clockwise turn than both 90 and 180 degrees - roughly 225 degrees.
The slant shows the green figure has swung past the halfway point, so its turn is the biggest.
4.MD.C.5Visualize Spatial RelationshipsCompare the three clockwise angles: (A) 90 degrees, (B) 180 degrees, (C) about 225 degrees. The largest is (C).
The figure swung furthest around the pivot was turned through the largest angle.
4.MD.C.5Eliminate PossibilitiesMatch an arm on each figure and measure the clockwise turn at the pivot - the figure that swings furthest around (C) used the biggest angle!