Problem
Start at the top-left corner and walk clockwise. The top edge is one segment (1), the right edge down is one segment (2). So far 2 segments along the rectangle's top and right.
Recognizing each straight side as one line segment is exactly the Grade 4 idea of identifying line segments in a figure.
4.G.A.1Draw A DiagramContinuing clockwise across the bottom: floor on the right (3), up into the notch (4), short ledge left (5), up the right side of the central tab (6), across the top of the tab (7), down the left side of the tab (8), short ledge left (9), down the left wall of the notch (10), and the floor on the left (11). That is 9 more segments.
Listing each straight stretch in walking order keeps every up/down/across step accounted for exactly once.
4.G.A.1Make A Systematic ListWalking the notched bottom of the figure from where the right floor meets it to where the left floor leaves it, it is made of exactly nine straight line segments.
A line segment here is one straight stretch between two neighboring corners, and a fresh stretch begins every time the outline turns, so the segments are simply the separate straight pieces the bottom is cut into.
Those pieces sit end to end with no gap between them and no piece lying on top of another, so together they rebuild the whole bottom and counting the pieces accounts for the whole bottom exactly.
Tracing the bottom once, in order, and tallying each stretch as you reach it lines up every stretch with one step of the walk, so no stretch is skipped and none is counted twice.
When each stretch is matched with exactly one step of the walk, the number of tallies is the same as the number of stretches — no more and no less.
Finally the left edge goes up from the bottom-left corner back to the top-left corner: that is the last segment (12), which closes the outline.
Counting the final closing side is simple addition, and the walk returning to its start confirms the loop is complete.
3.OA.D.9Draw A DiagramWalk the outline like a pencil and count every time it turns - each straight stretch between turns is one line segment!